Update Dim. 12 octobre 2025
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DevWebStatique/Rapport - séance 5 - Mar. 07 octobre 2025.pages
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DevWebStatique/Rapport - séance 5 - Mar. 07 octobre 2025.pdf
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English/30ieltsspeakingpracticecards 1.pdf
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@ -15,6 +15,7 @@ Dream car: Ford Mustang (from the 60s)
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# IELTS
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Session: 24-25 April
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## Writing Task 1 - Visual Information
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This bar chart shows the percentage of the population living in urban areas, worldwide and on specific continents, from 1950 to 2030.
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@ -55,3 +56,38 @@ However, I would argue that applying a restriction to international travel would
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Overall, I would say that denying the impact of transportation would be disingenuous. I do however wholeheartedly believe that restricting international travel would not yield the results people might expect.
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# Speaking
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## **Internet**
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How often do you go online?
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What do you use the internet for?
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How do you get online?
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Do you have your own computer?
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## **Hobbies**
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Do you have a hobby?
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What equipment do you need for it?
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Do you think hobbies should be shared with other people?
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Did you have a hobby as a child?
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## **Music**
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Do you like music?
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What’s your favourite type of music?
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If you could learn a musical instrument, what would it be?
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Do you think music is important?
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Notes
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![[Pasted image 20251007151529.png]]
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English/attachments/Pasted image 20251007151529.png
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EnjeuxSocioEco/2025-10 ESTIA TD Energie Climat ING1 A.pdf
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EnjeuxSocioEco/TD1.md
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EnjeuxSocioEco/TD2.md
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@ -0,0 +1,83 @@
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![[2025-10 ESTIA TD Energie Climat ING1 A.pdf#page=2]]
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### 1) Les deux leviers pour baisser les émissions de l’UE
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- **Réduire les émissions**
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- **Augmenter les puis de carbone**
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---
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### 2) L’UE est-elle sur la bonne trajectoire ?
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Données du sujet : 1990 = **3,87 GtCO₂e** ; 2018 = **3,05 GtCO₂e**. Objectif 2030 : **–55 %** vs 1990, soit un niveau cible de **1,74 GtCO₂e**. Entre 1990 et 2018, la baisse observée est de **0,82 Gt** (≈ –21 %), bien en-deçà des –55 % requis pour 2030 ; il faut donc **accélérer fortement** la baisse. Conclusion : **non, la trajectoire 1990-2018 n’est pas suffisante pour atteindre –55 % en 2030.**
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---
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### 3) À rythme inchangé, quand atteindrait-on –55 % ?
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Baisse moyenne 1990→2018 : $((3{,}87-3{,}05),\text{Gt}/28\ \text{ans} \approx 0{,}0293,\text{Gt/an})$.
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À partir de 2018, années nécessaires pour passer de 3,05 à 1,74 Gt : $((3{,}05-1{,}7415)/0{,}0293 \approx 44{,}7\ \text{ans})$.
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**Échéance ≈ 2018 + 45 ≃ 2063.**
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---
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### 4) Effet de serre : texte complété
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L’effet de serre est un mécanisme **naturel** qui se produit en plusieurs étapes. Le soleil envoie de **l’énergie** sous forme de **rayonnements** à la Terre. Une fois réchauffée, la Terre rejette la chaleur vers **l’espace**. La chaleur est retenue par des gaz présents dans l’atmosphère, les **gaz à effet de serre**. On les appelle ainsi, car comme dans une serre de jardin, ils **emprisonnent** l’énergie et la renvoient vers la Terre. Sans cela, la température sur Terre serait de **–18 °C** au lieu de **15 °C**.
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---
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### 5) Conséquence de l’augmentation des GES
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**Renforcement de l’effet de serre** → **réchauffement climatique** global, avec effets associés : hausse du niveau de la mer, événements extrêmes plus fréquents/intenses, perturbations des écosystèmes et de l’agriculture, etc. ([IPCC](https://www.ipcc.ch/report/ar6/syr/downloads/report/IPCC_AR6_SYR_FullVolume.pdf?utm_source=chatgpt.com "CLIMATE CHANGE 2023"))
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---
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### 6) Pourquoi cibler surtout le CO₂ ? Quels autres leviers ?
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- Le **CO₂** est **le principal** contributeur anthropique au forçage, issu surtout de la combustion d’énergies fossiles ; il a une **longue durée de vie** et s’accumule (enjeu cumulatif). D’où la priorité à sa réduction. ([IPCC](https://www.ipcc.ch/report/ar6/wg3/chapter/chapter-2/?utm_source=chatgpt.com "Chapter 2: Emissions trends and drivers"))
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- **Autres leviers** complémentaires : réduire **CH₄** (fuites de gaz, déchets, élevage), **N₂O** (engrais), **gaz fluorés**, **protéger/augmenter les puits** (forêts, sols), **CCS/CCUS**, et **sobriété/efficacité** transversales. ([IPCC](https://www.ipcc.ch/srccl/?utm_source=chatgpt.com "Special Report on Climate Change and Land"))
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---
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### 7) D’après le document GIEC « Émissions de CO₂ et activités humaines depuis 1850 »
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**a.** Les émissions liées aux activités humaines **ont fortement augmenté** depuis 1850, passant de niveaux très faibles au XIXᵉ siècle à des niveaux records au XXIᵉ siècle (pics autour de ~2017-2019). ([Our World in Data](https://ourworldindata.org/co2-emissions?utm_source=chatgpt.com "CO₂ emissions"))
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**b.** En **2017**, la part des **énergies fossiles + ciment** dans les émissions de CO₂ était d’environ **~89 %**, le reste provenant des changements d’usage des terres (~11 %). ([Carbon Brief](https://www.carbonbrief.org/analysis-global-co2-emissions-set-to-rise-2-percent-in-2017-following-three-year-plateau/?utm_source=chatgpt.com "Analysis: Global CO2 emissions set to rise 2% in 2017 after ..."))
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**c.** L’usage des énergies fossiles **émet du CO₂** lors de leur combustion ; plus on consomme de charbon/pétrole/gaz, plus les émissions augmentent. **Stratégies** :
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- **Décarboner l’offre** (sortie des fossiles, renouvelables, nucléaire, CCUS) ;
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- **Électrifier** les usages finaux et **améliorer l’efficacité** ;
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- **Réduire la demande** (sobriété) ;
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- **Limiter les émissions liées aux terres** (lutte contre la déforestation, gestion durable des sols). ([IPCC](https://www.ipcc.ch/report/ar6/wg3/chapter/chapter-6/?utm_source=chatgpt.com "Chapter 6: Energy systems"))
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---
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## Sources
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- ESTIA / 2025-2026 / JB Jarin – **TD « Climat et GES » (énoncé et données)**. 2025.
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- **IPCC AR6, WGIII – Chapter 2: Emissions trends and drivers** (version web). ([IPCC](https://www.ipcc.ch/report/ar6/wg3/chapter/chapter-2/?utm_source=chatgpt.com "Chapter 2: Emissions trends and drivers"))
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- **IPCC AR6, WGIII – Chapter 2 (PDF)**. ([IPCC](https://www.ipcc.ch/report/ar6/wg3/downloads/report/IPCC_AR6_WGIII_Chapter02.pdf?utm_source=chatgpt.com "Emissions Trends and Drivers"))
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- **IPCC AR6, WGIII – Chapter 6: Energy systems**. ([IPCC](https://www.ipcc.ch/report/ar6/wg3/chapter/chapter-6/?utm_source=chatgpt.com "Chapter 6: Energy systems"))
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- **IPCC AR6 Synthesis Report (2023), Full Volume (PDF)**. ([IPCC](https://www.ipcc.ch/report/ar6/syr/downloads/report/IPCC_AR6_SYR_FullVolume.pdf?utm_source=chatgpt.com "CLIMATE CHANGE 2023"))
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- **Our World in Data – CO₂ emissions** (séries longues, niveau global). ([Our World in Data](https://ourworldindata.org/co2-emissions?utm_source=chatgpt.com "CO₂ emissions"))
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- **CarbonBrief (2017)** – _Global CO₂ emissions 2017: land-use changes ≈ 11 %_ (donc fossiles+ciment ≈ 89 %). ([Carbon Brief](https://www.carbonbrief.org/analysis-global-co2-emissions-set-to-rise-2-percent-in-2017-following-three-year-plateau/?utm_source=chatgpt.com "Analysis: Global CO2 emissions set to rise 2% in 2017 after ..."))
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- **US EPA – Climate Change Indicators / GHG overview** (rappels sur sources et GES). ([Environmental Protection Agency](https://www.epa.gov/ghgemissions/global-greenhouse-gas-overview?utm_source=chatgpt.com "Global Greenhouse Gas Overview | US EPA"))
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---
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Si tu veux, je peux te fournir la feuille de calcul détaillant les calculs des questions 2 et 3.
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86
EnjeuxSocioEco/TD3.md
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@ -0,0 +1,86 @@
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![[2025-10 ESTIA TD Energie Climat ING1 A.pdf#page=4]]
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### 1) Puissance totale – Fruges vs. Gravelines
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- **Parc(s) éolien(s) de Fruges** : 70 éoliennes. La fiche technique de l’éolienne du parc indique **2,3 MW** nominaux →
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$(P_\text{Fruges} = 70 \times 2{,}3 = \mathbf{161\ MW})$.
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- **CNPE de Gravelines** : 6 réacteurs de **900 MW** chacun →
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$(P_\text{Gravelines} = 6 \times 900 = \mathbf{5,400\ MW})$.
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---
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### 2) Nombre d’éoliennes pour égaler la puissance de Gravelines
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- Avec des machines **2 MW** : $(5,400 / 2 = \mathbf{2,700})$ éoliennes.
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- Avec des machines **15 MW** : $(5,400 / 15 = \mathbf{360})$ éoliennes.
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---
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### 3) Nombre d’éoliennes pour égaler la **production annuelle** (CF 85 % vs 45 %)
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Hypothèses demandées : **nucléaire CF = 85 %**, **éolien offshore CF = 45 %**.
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On égalise l’énergie annuelle :
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$N = \frac{P_\text{nuke}\times CF_\text{nuke}}{P_\text{turbine}\times CF_\text{wind}}$
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- **Turbine 2 MW** : $(N = \frac{5,400 \times 0{,}85}{2 \times 0{,}45} \approx \mathbf{5,100})$ éoliennes.
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- **Turbine 15 MW** : $(N = \frac{5,400 \times 0{,}85}{15 \times 0{,}45} \approx \mathbf{680})$ éoliennes.
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> Vérif énergie annuelle de Gravelines (ordre de grandeur) : (5{,}4\ \text{GW} \times 8,760\ \text{h} \times 0{,}85 \approx \mathbf{40,2\ TWh/an}). (cohérent avec les historiques publics) ([Wikipedia](https://en.wikipedia.org/wiki/Gravelines_Nuclear_Power_Station?utm_source=chatgpt.com "Gravelines Nuclear Power Station"))
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---
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### 4) Limites et proposition pour un remplacement 100 % éolien
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- **Limites** de l’équivalence par facteur de charge :
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- Le **CF éolien est subi** (dépend du vent, variable, corrélé régionalement), donc la **puissance garantie** et l’**adéquation instantanée** ne sont pas assurées.
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- Besoin de **réserves**, **stockage**, **flexibilité de la demande**, **renforcement réseau** et **pilotage** pour passer les creux de production.
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- Le **CF nucléaire est choisi** au sens où l’outil est **pilotable** : on peut décider quand produire (modulation/arrêts planifiés), indépendamment de la météo.
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- **Feuille de route 100 % éolien** (idée de mix et d’infrastructures) :
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- **Surdimensionnement** de la capacité éolienne (overbuild) par rapport à la moyenne nécessaire.
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- **Stockages** multi-échelles : batteries (intra-jour), **STEP** et **hydrogène**/PtX (inter-journalier à saisonnier).
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- **Flexibilité** (effacement industriel, pilotage conso, tarification dynamique), **réseaux** (renforcement, interconnexions), et **backup** pilotable bas-carbone transitoire si nécessaire.
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- **Diversification géographique** et **technologique** (onshore + offshore, couplage avec solaire) pour lisser la variabilité.
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||||
---
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### 5) Comparaison d’empreinte CO₂ annuelle (à **100 % de CF** pour simplifier)
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À puissance installée identique (**5,4 GW**), l’énergie annuelle serait (5{,}4 \times 8,760 = \mathbf{47{,}3\ TWh}). Les émissions annuelles dépendent alors des **facteurs ACV** (gCO₂e/kWh) :
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- **Nucléaire (France/Europe, ACV)** : ~**5,5–6 gCO₂e/kWh** (médiane UNECE ≈ 5,5 ; base ADEME ≈ 6). → **≈ 0,26–0,28 MtCO₂e/an**.
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- **Éolien onshore** : ~**11–16 gCO₂e/kWh** (IPCC/UNECE ; ADEME ~14,1). → **≈ 0,52–0,67 MtCO₂e/an**.
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- **Éolien offshore** : ~**12–23 gCO₂e/kWh** (UNECE ; ADEME ~15,6). → **≈ 0,57–1,09 MtCO₂e/an**.
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**Conclusion** : sur une base ACV, **nucléaire et éolien sont tous deux très bas-carbone**, l’ordre de grandeur annuel reste **< 1,1 MtCO₂e** pour 5,4 GW. **Le nucléaire ressort généralement un peu plus bas** que l’éolien (surtout offshore haut de fourchette), mais **les fourchettes se recoupent** selon hypothèses (mix amont, logistique, durée de vie, facteurs régionaux). Le différentiel CO₂ n’est **pas l’argument principal** pour trancher entre ces deux options ; la décision se joue plutôt sur **pilotabilité, coûts système, réseaux, acceptabilité, calendrier et risques**.
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|
||||
---
|
||||
|
||||
## Sources
|
||||
|
||||
- ESTIA / 2025-2026 / JB Jarin — **TD 3 : Mix énergétique, pilotable & intermittent (nucléaire / éolien)** — Énoncé et données.
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- **UNECE (2021)** — _Life Cycle Assessment of Electricity Generation Options_ (PDF) — valeurs ACV : nucléaire ≈ 5,5 gCO₂e/kWh ; éolien onshore < 16 ; offshore < 23.
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- **ADEME (Base Carbone / Bilans-GES)** — facteurs ACV pour électricité nucléaire en France ≈ **6 gCO₂e/kWh**. ([sfen.org](https://www.sfen.org/rgn/les-emissions-carbone-du-nucleaire-francais-37g-de-co2-le-kwh/?utm_source=chatgpt.com "Les émissions carbone du nucléaire français : 4g de CO2 ..."))
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- **Les Énergies Renouvelables (2025)** — synthèse ADEME : éolien **onshore ≈ 14,1** gCO₂e/kWh ; **offshore ≈ 15,6** gCO₂e/kWh. ([ECOinfos](https://www.les-energies-renouvelables.eu/conseils/bilan-carbone/bilan-carbone-emission-co2-source-energie-renouvelable/?utm_source=chatgpt.com "Emission de CO2 par source d'énergie renouvelable"))
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- **Wikipedia / EDF / presse** — données de cadrage public sur **Gravelines** (6×900 MW ; puissance ~5,46 GW ; prod. annuelle typique). ([Wikipedia](https://en.wikipedia.org/wiki/Gravelines_Nuclear_Power_Station?utm_source=chatgpt.com "Gravelines Nuclear Power Station"))
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EnjeuxSocioEco/podcast.pages
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110
Español/Index.md
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@ -1,3 +1,4 @@
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# Martes
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![[Pasted image 20250923163517.png]]
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1. debajo de la meza
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2. sobre la meza (o encima de la meza)
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@ -58,7 +59,7 @@ significado:
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|||
4. Boca de metro
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||||
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||||
---
|
||||
Martes, 30 de Septiembre 2025.
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||||
# Martes, 30 de Septiembre 2025.
|
||||
|
||||
Llamar la attencion:
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||||
- Oye
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||||
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@ -108,3 +109,110 @@ Conjuga el verbo ir:
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|||
11. ¿Vamonos nosotros al restaurante?
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||||
12. Mis hijos van a cordoba
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||||
13. Carlos va de vacaciones
|
||||
|
||||
---
|
||||
# Martes, 7 de octubre 2025
|
||||
|
||||
Correction du mail de Juanjo:
|
||||
```
|
||||
Hola Inés,
|
||||
|
||||
Para llegar a Ponme otra, coges la linea 4 del metro hasta la parada "parlamento". Despues, vas todo recto al norte y coges la segunda a la derecha. Sigues la callercalle hasta la Plaza San Isabel y el bar se situa a la en la izquierda.
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||||
|
||||
¡Hasta luego!
|
||||
```
|
||||
|
||||
Quand il y a 2 verbes dans une phrase, un à l'infinitif et un conjugué, on met le pronom avant ou après
|
||||
```mermaid
|
||||
flowchart TD
|
||||
1["Voy a te ayudar"]
|
||||
2["Te voy a ayudar"]
|
||||
3["Voy a ayudarte"]
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||||
1 --> 2 & 3
|
||||
```
|
||||
|
||||
Toujours mettre **de** après después et antes.
|
||||
Después/Antes **DE** la salida
|
||||
|
||||
Le mot **para** s'utilise pour parler d'une destination (destinatario) ou d'un but (finalidad)
|
||||
|
||||
Le mot **por** s'utilise pour parler d'une cause (causa).
|
||||
|
||||
![[Pasted image 20251007161106.png]]
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||||
|
||||
Este verano vamos ***a*** ir ***de*** vacaciones ***a*** las islas Canarias.
|
||||
Queremos ir ***en*** avión y después hacer excursiones ***en*** coche.
|
||||
Nos vamos a quedar ***en*** un pequeño hotel ***en*** el este de la isla.
|
||||
El hotel está cerca de una playa, y hay muchas otras playas ***a*** pocos kilómetros de distancia.
|
||||
|
||||
![[Pasted image 20251007162909.png]]
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||||
|
||||
Carlos va a jugar al golf.
|
||||
El niño va a ver la tele.
|
||||
Carmen y Maria van a cenar al restaurante.
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||||
Los padres van a pintar la casa.
|
||||
La abuela va a acostarse / La abuela se va a acostar.
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||||
Miguel va a prepararse para salir / Miguel se va a preparar para salir.
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||||
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||||
|
||||
Verbos irregulares
|
||||
|
||||
| | Preferir | Querer |
|
||||
| -------- | ---------- | -------- |
|
||||
| Yo | prefiero | quiero |
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||||
| Tu | prefieres | quieres |
|
||||
| El | prefiere | quiere |
|
||||
| Nosotros | preferimos | queremos |
|
||||
| Vosotros | preferis | quereis |
|
||||
| Ellos | prefieren | quieren |
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||||
|
||||
Ejercicio
|
||||
|
||||
1. Las tiendas (cerrar) **cierran** a las 8.
|
||||
|
||||
2. El partido de tenis (empezar) **empieza** a las 1:15
|
||||
|
||||
3. ¿(encender, tú) **enciendes** la luz, por favor?
|
||||
|
||||
4. (yo, preferir) **Prefiero** una cerveza.
|
||||
|
||||
5. ¿En qué (pensar, tú) **piensas** ?
|
||||
|
||||
6. ¿(querer, tú) **Quieres** un café?
|
||||
|
||||
7. Carlos siempre (perder) **pierde** el autobús.
|
||||
|
||||
8. ¿(tú, entender) **Entiendes** lo que dice el profesor?
|
||||
|
||||
9. El director (querer) **quiere** este informe para finales de mes.
|
||||
|
||||
10. Juan (despertar) **despierta** siempre a los niños.
|
||||
|
||||
11. La clase (comenzar) **comienza** a las 10:30.
|
||||
|
||||
12. (yo, sentir) **Siento** no poder ir a la fiesta.
|
||||
|
||||
13. Ellos (sentarse) **se sientan** siempre ahí.
|
||||
|
||||
14. (nosotros, querer) **Queremos** vender nuestro piso.
|
||||
|
||||
15. Hoy (yo, sentirse) **me siento** muy bien.
|
||||
|
||||
16. ¿Cuándo (empezar, tú) **empiezas** con las clases de inglés?
|
||||
|
||||
|
||||
Audio
|
||||
|
||||
Escucha a dos personas y marca la información que se refiere a Marta, a Antonio o a los dos.
|
||||
|
||||
| | Antonio | Marta |
|
||||
| ----------------------------------------------- | ------- | ----- |
|
||||
| 1. Tiene poco dinero. | | x |
|
||||
| 2. Quiere ir a una ciudad. | x | |
|
||||
| 3. Busca relax.<br> | | x |
|
||||
| 4. Quiere viajar en barco.<br> | x | x |
|
||||
| 5. Quiere un viaje cultural.<br> | x | |
|
||||
| 6. Tiene muchos días de vacaciones.<br> | | x |
|
||||
| 7. Quiere conocer una cultura diferente.<br> | x | x |
|
||||
| 8. Busca naturaleza.<br> | x | x |
|
||||
| 9. Tiene pocos días de vacaciones. | x | |
|
||||
|
|
|
|||
BIN
Español/attachments/Pasted image 20251007161106.png
Normal file
|
After Width: | Height: | Size: 2.6 MiB |
BIN
Español/attachments/Pasted image 20251007162909.png
Normal file
|
After Width: | Height: | Size: 525 KiB |
BIN
Español/attachments/Pasted image 20251007164417.png
Normal file
|
After Width: | Height: | Size: 297 KiB |
BIN
Español/attachments/Viaja.pdf
Normal file
BIN
Español/visite.key
Normal file
48
GénieÉlectrique/Exam2022/Exam2022.md
Normal file
|
|
@ -0,0 +1,48 @@
|
|||
![[Exam2022.pdf]]
|
||||
# Exercice 1: Générateur équivalent Norton Thevenin
|
||||
|
||||
a)
|
||||
![[Drawing 2025-10-09 15.10.26.excalidraw|1000]]
|
||||
|
||||
Convertir les deux Thevenin de gauche en Norton:
|
||||
![[Drawing 2025-10-09 15.10.26.excalidraw 1|1000]]
|
||||
$i_1=\frac{E_{Th_1}}{R_{Th_1}}=\frac{10V}{2K\Omega}=0.005A=5mA$
|
||||
$i_2=\frac{E_{Th_2}}{R_{Th_2}}=\frac{6V}{3K\Omega}=0.002A=2mA$
|
||||
|
||||
J'ai deux Norton en parallèles. Je vais simplifier.
|
||||
![[Drawing 2025-10-09 15.10.26.excalidraw 1 1]|1000]
|
||||
$\frac{1}{R_{eq}}=\frac{1}{2K\Omega}+\frac{1}{3K\Omega}=\frac{5}{6000\Omega}\implies R_{eq}=\frac{6000}{5}\Omega=1.2K\Omega$
|
||||
|
||||
Maintenant j'ai deux générateurs de Norton en série, je vais les convertir en thévenin.
|
||||
![[Drawing 2025-10-09 15.10.26.excalidraw 1 1 1|1000]]
|
||||
|
||||
Puis faire l'équivalent.
|
||||
![[Drawing 2025-10-09 15.10.26.excalidraw 1 1 1 1|1000]]
|
||||
|
||||
b)
|
||||
$i_{target}=\frac{E_{eq}}{R_{eq}}=\frac{9}{2000}=0.0045A=4.5mA$
|
||||
|
||||
# Exercice 2:
|
||||
![[Pasted image 20251009162100.png]]
|
||||
a)
|
||||
![[Drawing 2025-10-09 16.35.15.excalidraw]]
|
||||
Loi des mailles
|
||||
$E=U_R+U_L=R_i+L\frac{di}{dt}$; $\frac{E}{R}=i+\frac{L}{R}\frac{di}{dt}$ donc $\tau=\frac{L}{R}$
|
||||
|
||||
b)
|
||||
$i=\frac{E}{R}$
|
||||
|
||||
c)
|
||||
|
||||
# Exercice 3:
|
||||
![[IMG_7441.jpeg]]
|
||||
|
||||
|
||||
# Exercice 4:
|
||||
|
||||
![[Pasted image 20251009171649.png]]
|
||||
$H=\frac{V_0}{V_S}$
|
||||
$V_0=\frac{Z_L}{Z_L+Z_R}V_S$
|
||||
|
||||
b)
|
||||
j
|
||||
|
|
@ -0,0 +1,96 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
200 Ohms ^LPhWKBMv
|
||||
|
||||
A ^jNY6AaqW
|
||||
|
||||
B ^8kJhcOlg
|
||||
|
||||
1800 Ohms ^Vg8ka0Jn
|
||||
|
||||
9V ^OP48Ok2s
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
4/Tm301Ee5yJEWKXCSIoGhguYNseiU6H0Aah2QpAFoEhmonIhWJpAdiReKvFw8+mM4uwPWgQCLBmABoKXHAFPHnipcgkm8dSEWCEBGAr0IcfUTQDJZ6BXodIMpISTOYhATIAwJmLQKjtRBu9XaiyC5G6TMJuXezngm0QIxlJqk9SfYgxF/46ArycIASLnrgQgAA=
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,128 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
200 Ohms ^LPhWKBMv
|
||||
|
||||
A ^jNY6AaqW
|
||||
|
||||
B ^8kJhcOlg
|
||||
|
||||
600 Ohms ^Vg8ka0Jn
|
||||
|
||||
1.2 KOhms ^lIZhsuC0
|
||||
|
||||
0.6V ^n9fPoOFh
|
||||
|
||||
8.4V ^OP48Ok2s
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
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|
||||
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|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,138 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
200 Ohms ^LPhWKBMv
|
||||
|
||||
A ^jNY6AaqW
|
||||
|
||||
B ^8kJhcOlg
|
||||
|
||||
600 Ohms ^Vg8ka0Jn
|
||||
|
||||
1mA ^b1zNOGHD
|
||||
|
||||
ieq ^TTulWADF
|
||||
|
||||
Req ^lIZhsuC0
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
yyachAAqC9DM2Rnoz1mvdeXxlmXC2cEZo+a5pPlPDPNGskmPer83pkAt98ioFGffXK5R+3657bFuiwz9wAm8DFHADgBGhlo3AaCNAHkiZAzMbBW4AwAFkUBKgDkyGcm0GDDmRzawCANgBECtwEwG4fQEaHO6UbZ945yc3ZGnMZB+zfK2jUrsKBLnvEK5mc3UBzlGntzE53c9kFXOznzx82nc1OZnNznXQepnzcubPMzmRgfS9jdeb3MZA7od4vah
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
IHtcx2gjtECMZa6tfWv2III4APXK5PCAtnwIIAcCEAA=
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,148 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
200 Ohms ^LPhWKBMv
|
||||
|
||||
A ^jNY6AaqW
|
||||
|
||||
B ^8kJhcOlg
|
||||
|
||||
600 Ohms ^Vg8ka0Jn
|
||||
|
||||
3 KOhms ^SKn2gV3d
|
||||
|
||||
2 KOhms ^r1BkRYAm
|
||||
|
||||
1mA ^b1zNOGHD
|
||||
|
||||
i1 ^V7UxoibQ
|
||||
|
||||
i2 ^TTulWADF
|
||||
|
||||
R1 ^sQbpZJvu
|
||||
|
||||
R2 ^lf1Zf0m6
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
0sxuAFYADgT+gGZ9gBYj+KSeeOr+o/5SmG5nbaPtAHYXi6Pqzb7+gcT+26QCgkdRbF7aTabC48T48Y77F6bQFSBCEZTSbjxbb7BKJd79F77RL7HjbeI8JGFSDWFbiVDVZHMKCkNgAawQAGE2Pg2KQKgBieIIIVCtaQTS4bCs5QsoSNLk8vkSZnWZhwXCBbJiiCDQj4fAAZVgqwkgg82qZLPZAHUQZJuHwqRBLWyEEaYCb0GbysjZeiOOFcmh4si2
|
||||
|
||||
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|
||||
|
||||
lGqD9No+zVNsT79L02wvNsbGJI60wQMCxCgmg/QMXOIkvL0vxvMcNF8ZIqLonhaAUsiNKegyjbMq6Cq8gKIrCkge6StKVbEDpSroCqHBqhqWR4ZmeqGsa2Hei2jJaTadoOu5Vpus5FSuZWwj+oGmKhuGkaYjGTpxleSbnhmTpZrgOb3qg9b/k6xbEKWEi4PEQVysQNZ1n+jIIMBqALokmxHLVAyjkw46DqgZyNf2E5TnSPDVExiTbBSZLLmuwR3l
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,128 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
200 Ohms ^LPhWKBMv
|
||||
|
||||
A ^jNY6AaqW
|
||||
|
||||
B ^8kJhcOlg
|
||||
|
||||
600 Ohms ^Vg8ka0Jn
|
||||
|
||||
3 KOhms ^SKn2gV3d
|
||||
|
||||
2 KOhms ^r1BkRYAm
|
||||
|
||||
10V ^RumA6HTq
|
||||
|
||||
6V ^owVBcwYX
|
||||
|
||||
1mA ^b1zNOGHD
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
L2RjJ7U96e4hBBHAAM0S54QBzSLPAhAA
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,84 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
UL ^dcNekxvT
|
||||
|
||||
UR ^rRoNBtHQ
|
||||
|
||||
E ^bumf53e2
|
||||
|
||||
i ^bENrNZkM
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
AhM5TJJnRsadCKLYKEa4I+LyI2f4Vdf9fCTFZcE4Akcw0YubA9UsqY67DkJYys0qXbRGBY+9By6Aes5qR/NOc7F/I4v/e7Dsoy3gb/Py1sgKyAAAwcj7UA64iAxsKAh4mAp4kikHOcpA3AWoJc7gCea6DksjVcmnZcJbKyabYEggg5PctjNAUqwcM5OTbiU+C82g5iiABg2+W85ckHB89jOnaTckMiN874wkz8sBLnLTMQnTa5SQ55E3NBPGEyox
|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
B9Q2+4B7fHe2+Z+3eEJ5hCBGA0s5eqsQ7YIqewhgg9/c0CK3qlS4epLkXPOXGrzUMDB9R0hL+sjc7QnGQI09+D+j/H47EcAEWm1C6hwgOVVCG2CAA===
|
||||
```
|
||||
%%
|
||||
BIN
GénieÉlectrique/Exam2022/attachments/Exam2022.pdf
Normal file
BIN
GénieÉlectrique/Exam2022/attachments/IMG_7441.jpeg
Normal file
|
After Width: | Height: | Size: 1.1 MiB |
|
After Width: | Height: | Size: 359 KiB |
|
After Width: | Height: | Size: 268 KiB |
BIN
GénieÉlectrique/Fondements du GE_2025_Ch2.pdf
Normal file
BIN
GénieÉlectrique/Fondements du GE_2025_Ch3.pdf
Normal file
|
|
@ -60,7 +60,7 @@ a((" ")) --> R1 --> b((" "))
|
|||
a((" ")) --> R2 --> b((" "))
|
||||
b --> bb((" "))
|
||||
```
|
||||
En parallèle, c'est la somme des inverses ($R_{parallèle}=\sum{\frac{1}{R_i}}$)
|
||||
En parallèle, c'est la somme des inverses ($\frac{1}{R_{parallèle}}=\sum{\frac{1}{R_i}}$)
|
||||
|
||||
2 Resistances identiques en parallèle ont pour somme la moitié.
|
||||
Ex:
|
||||
|
|
@ -107,5 +107,22 @@ N'importe quel circuit peut être résumé en un générateur de courant avec un
|
|||
|
||||
$R_{Th}=R_{N}$
|
||||
|
||||
Théorème de Millman
|
||||
-> Le théorème bulldozer
|
||||
Théorème de Millman $\rightarrow$ $\frac{\sum_{i\in{[0,n]}}\frac{V_i}{R_i}}{\sum_{i\in{[0,n]}}\frac{1}{R_i}}$
|
||||
|
||||
-> Le théorème bulldozer
|
||||
|
||||
|
||||
# Chapitre 2. Analyse temporelle.
|
||||
![[Pasted image 20251006090339.png]]
|
||||
|
||||
# Chapitre 3. Analyse fréquentielle.
|
||||
|
||||
![[Pasted image 20251006093323.png]]![[Pasted image 20251006093350.png]]
|
||||
|
||||
![[Pasted image 20251006093856.png]]
|
||||
![[Pasted image 20251006093952.png]]
|
||||
![[Pasted image 20251006094004.png]]
|
||||
|
||||
Diagramme de Bode -> Représente le signal sous forme phase et amplitude.
|
||||
|
||||
![[Pasted image 20251009085622.png]]
|
||||
|
|
|
|||
BIN
GénieÉlectrique/TD2/02a58d4198.pdf
Normal file
|
|
@ -1 +1,63 @@
|
|||
![[TD_FGE_2025.pdf]]
|
||||
![[TD_FGE_2025.pdf#page=7]]
|
||||
# Exercise 1. Equivalent Generator
|
||||
## a. ![[1.A.]]
|
||||
- On éteint les générateurs: ![[1.A.Eteint]]
|
||||
$R_{th}=R_{eq}=\frac{R_1R_2}{R_1+R_2}$
|
||||
|
||||
- On fait un circuit ouvert après AB: ![[1.A.Ouvert]]
|
||||
$U_{AB}=\frac{E\times R_1}{R_1+R_2}=E_{th}$
|
||||
|
||||
## b. ![[1.B.]]
|
||||
- On éteint les générateurs ![[1.B.Eteint]]
|
||||
$R_n=R_{eq}=R_1+R_2$
|
||||
|
||||
- On fait un court-circuit en AB: ![[1.B.Ouvert]]
|
||||
$I_n=\frac{R_1}{R_1+R_2}I$
|
||||
|
||||
## c. ![[1.C.]]
|
||||
- On éteint les générateurs: ![[1.C.Eteint]]
|
||||
$R_{eq}=R_{th}=\frac{5r}{2}$
|
||||
- On fait un circuit ouvert après AB: ![[1.C.Ouvert]]
|
||||
$U_{AB}=E_{th}=$
|
||||
D'après la loi des mailles:
|
||||
$U_{AB}=U_{eq}-e$
|
||||
Que vaut $U_{eq}$ ? ![[1.C.Ouvert.Ueq]]
|
||||
Loi des mailles:
|
||||
$ri-ri+e-2e=0$
|
||||
|
||||
Superposition:
|
||||
En éteignant le générateur de $2e$, on obtient $U_1=\frac{e}{2}$
|
||||
En éteignant le générateur de $e$, on obtient $U_2=2e-\frac{2e}{2}=e$
|
||||
$U_{eq}=U_1+U_2=e+\frac{e}{2}=\frac{3e}{2}$
|
||||
|
||||
## g. ![[1.G.]]
|
||||
Générateur dépendant -> Problème
|
||||
Calcul de $I_n$: Courant lorsque court-circuit:
|
||||
![[1.G.CourtCircuit]]
|
||||
$I_n+I_1=I$
|
||||
$I_1=\frac{V}{R_1}$
|
||||
$I_n=I-\frac{V}{R_1}$
|
||||
|
||||
$0=V+\lambda V-R_2I_n$
|
||||
$R_2I_n=V(1+\lambda)$
|
||||
$V=\frac{I_nR_2}{1+\lambda}\implies I_n=I-\frac{I_nR_2}{R_1(1+\lambda)}$
|
||||
$\implies \boxed{I_n=I\times\frac{R_1(1+\lambda)}{R_2+R_1(1+\lambda)}}$
|
||||
|
||||
![[02a58d4198.pdf]]
|
||||
|
||||
# Exercise 2: Power analysis
|
||||
![[Pasted image 20251003135122.png]]
|
||||
![[Drawing 2025-10-03 13.51.44.excalidraw]]
|
||||
|
||||
# Exercise 3: Millman Theorem
|
||||
![[Pasted image 20251003135519.png]]
|
||||
![[Drawing 2025-10-03 13.56.01.excalidraw]]
|
||||
Pour trouver $R_{th}$, on éteint les générateurs et on calcule $R_{eq}=R_{th}$.
|
||||
$R_{th}=\frac{5R}{4}$.
|
||||
|
||||
Pour trouver $E_{th}$, on met un circuit ouvert entre A et B:
|
||||
D'après Millmann, $U_{AB}=\frac{\sum{\frac{E_i}{R_i}}}{\sum{\frac{1}{R_i}}}=\frac{\frac{E_1}{R}+\frac{E_2}{R}+\frac{E_3}{R}+\frac{0}{R}}{\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}}=\frac{E_1+E_2+E_3}{4}=E_{th}$
|
||||
|
||||
![[Drawing 2025-10-03 14.07.09.excalidraw]]
|
||||
Diviseur de tension: $U_{ch}=\frac{R_{ch}}{R_{ch}+R_{th}}\times E_{th}=\frac{R}{R+\frac{5R}{4}}\times \frac{E_1+E_2+E_3}{4}=\frac{E_1+E_2+E_3}{9}$
|
||||
|
||||
|
|
|
|||
BIN
GénieÉlectrique/TD2/attachments/Pasted image 20251003135122.png
Normal file
|
After Width: | Height: | Size: 115 KiB |
BIN
GénieÉlectrique/TD2/attachments/Pasted image 20251003135519.png
Normal file
|
After Width: | Height: | Size: 101 KiB |
72
GénieÉlectrique/TD2/draws/1.A..md
Normal file
|
|
@ -0,0 +1,72 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
Eth ^jO5b802B
|
||||
|
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Rth ^2uyUdtY9
|
||||
|
||||
A ^OyoHlbN9
|
||||
|
||||
B ^86RjNZ1A
|
||||
|
||||
%%
|
||||
## Drawing
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|
||||
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||||
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||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
68
GénieÉlectrique/TD2/draws/1.A.Eteint.md
Normal file
|
|
@ -0,0 +1,68 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
R2 ^U1vjJCPz
|
||||
|
||||
R1 ^u32HhQwQ
|
||||
|
||||
A ^RnM7aduJ
|
||||
|
||||
B ^XnsbGU9B
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
N/TeJpEc5mGBxr2vOcLtnToJrQAKkc5Jp6uYemvNtnT80fT82zktP0gtDOAupdSr24UTLyfBOGczPPlDgGwSsI8i3zSKPMMo6s3fzSU2UF3rvPujlA79ykB0AQ1zKHESkoGFw/DhCCPRw2yhe7AD7+YgFjL7GBmGgHoewCg/B1ZKHnkFye4ZF7iLoQoB8n0GcmQA4uj2/1Bbr2uooBjBGpWZQUW2w5GIK35U7fO/lA5M3sipAuQUDsvigfkBu8j7
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
6nJW1D0SQXUd5MqhUEgIdTLH67W4gC0BAd5PLLW1BYgKYNgUadG3ATQYIGS/W829VFGMYfkNGUgZQGUAACk+DBF4AUmoH9r9uA0SAAEoDRCFlAyxdRlhPbcAfaqRA7gY2ReBE7WRjhw6FaQb9qEAHrgFOB2Kd0jRKbu8mBuzUAUYchbb7buAr0qsiATbL1esXCD1CroVm6ow8FDz26+t3R9BdQeRSBVwPVa6O6+6B6mAba7bVoYUFa7BsYEBVhmA
|
||||
|
||||
zQD1oSraEAp6a7dKNcVZVhCBGAwT+RpbFkiaPRMg969o10hAOQDBCbeEkbpkrdt7DDi6DAzRz7863i9Ll5y8KJgED7Jb8BJlUqRt+AMLggWxuwQBuwgA
|
||||
```
|
||||
%%
|
||||
78
GénieÉlectrique/TD2/draws/1.A.Ouvert.md
Normal file
|
|
@ -0,0 +1,78 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^CPJvQkOH
|
||||
|
||||
B ^t1QOg47A
|
||||
|
||||
R2 ^6gJLpm6D
|
||||
|
||||
R1 ^hdwbIKzo
|
||||
|
||||
E ^n3CrLVL2
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
yExuZxSABgB2bV2AFm2ADkS2trOUxKSANjWIGE34lJTtRNvDw5Tdk9vbnjxbZtQ4PCgkdTceKA7SfbYAxIPSQIQjKaRQ17abY8XYpb67RHFSDWZTBbjbB7MKCkNgAawQAGE2Pg2KQqgBieIILlc9JlSCaXDYWnKGlCDjEJkstkSanWZhwXCBXJ88oAM0I+HwjVgZIkgg8qoE1LpCAA6hDJNw+ESIFSafSdTA9egDZUHmK0Rxwvk0PEHmxFdg1E8/
|
||||
|
||||
dsKbbRcI4ABJYi+1AFAC6DzV5Gyce4HCEWoehAlWCquG2RogYol3uYCdK/Og8HEvCJAF9KQgEMQoTwUl3EolDoTa4wWOwuGhLg8h6xOAA5Thia3h863FIXFJ55gAEUyUHb3DVBDCD00wglfWC2VyCaK/JKRPKlQkRiG8V2zgAstE340xmrsJgOgAjhufRQF0G5GnM9ZFqQNJUHeTZEimtpCHAxC4DuHZ+gSbTdkciR/LcbQPEQHC0lmOb4MRbDCr
|
||||
|
||||
uaD7vgYTFC2xQ1pAD7oD0ACCJzMMQtSEAA0mq2ycZoABanFmrSUDOGwtR9KW8wNmWCDYFEHCkqstobGgzhAvEsLbIcJzQgCPB7NsKT+raoaoM4XYGbs8QnLihxHNCQIgmClpQrc2zaH85zbIkuy3C+zkEkiKJolA3C9gcII8IkRknCcPAmUlDwki6Ea1vappSqyHI8tyWm1oKwpRuKkrMkVsrkBwCpKjksWppq2q6spbodpSJr0haxCQmgNp5X1C
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
PIRoPdOAG1u1vdWd51uONSQgRgKZNgZkSVsoluTIPdjJFdIkx5fQAl0hS88upS7/SANMAwRoc9wtnGwYhFV4ziPdg9o9/AELJicADmEfTUcIJ6BCJsIAA===
|
||||
```
|
||||
%%
|
||||
74
GénieÉlectrique/TD2/draws/1.B..md
Normal file
|
|
@ -0,0 +1,74 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
Rn ^i75oHoQp
|
||||
|
||||
In ^68I92ijO
|
||||
|
||||
A ^gEFFliQi
|
||||
|
||||
B ^spKJtRCJ
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
6Ye5tvBe/PYinPyA72tlbXKPe4BM0CpFn+6VQHSyHcVF/eD9EUPAMw9d9ZUDvApxtwYjj9H/qRKv9uZjsDxCvgEOg+UTDN5JjFnDkb5M6YjU/MjERanESSSUSWjWRM3SiJnYAz5VnVjKzMoRTbneTLA/nAyUFcEAmUTJvSRJSe4MFYTGXIzOXaRUzKmJXYgeVRmZFLVAgmvYg7qUglvCg9vDVQWMoeZdWMWILK3W/OWQLS3EjYQzWZ3Z1aLJ3U2e
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
3rqlPrTsm6WHhHtYFHxGI4/qwa585HtHchFGJGOkijigjHRHxHJGLQZLDGtHrGsgw55LN9NH5GTHxHo1cpB7QyrGdGsgI5f7vi5zyhHGAn9AgnP6sG3iwmPGoBTGxbdbgGHT/HPGshKHbc5D2rWi0mEnxGRhOq4sMwEL3HjH8msgPV/Zs0IA95BHwn0nImYEXGbRydtRsAyRFQdFuBMQHg3g0ReCqCWHmAOmaR8BkI163h0roQsR3g4CJ0WGjA2A
|
||||
|
||||
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|
||||
|
||||
cGkfK2bsA9gQBTmYCVEtrgCeZectpVc+a7xTkIEYH9mWfwFWfsWMuTOCDNbtiRKEBJAMGqeMqQI7JNcdLJAkcyEdY935ppPJgQjNYtatZVmIeZP4F+uCALHLBAHLCAA=
|
||||
```
|
||||
%%
|
||||
70
GénieÉlectrique/TD2/draws/1.B.Eteint.md
Normal file
|
|
@ -0,0 +1,70 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
R2 ^1yKgfeMI
|
||||
|
||||
R1 ^r8UB5GCU
|
||||
|
||||
A ^NaoPTYNK
|
||||
|
||||
B ^Gfyr39D4
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
NpdrZ1ggLgsWIgnAXQjkEQyQ9wBlaFUQJg+lcLaUXFWrbCmY8GNggylYyLQ6PoGqKyKQHeZY6Yw4/WE45rUwIQ8QwXHCiA3YKrggMsMwN0HFXAHgwQ3Ff46Q5SMsIQIwLvL/fgP/dcuvWEMEIk6Jp8kIAyAYGvZVW0ejZ0epeUJmAYN0JkDk4ieU/+gyBhIk8k6k/PIhOAONNqLqOEErVLS2EAA=
|
||||
```
|
||||
%%
|
||||
96
GénieÉlectrique/TD2/draws/1.B.Ouvert.md
Normal file
|
|
@ -0,0 +1,96 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
R1 ^Xc7xtiqs
|
||||
|
||||
In ^vr9UufFb
|
||||
|
||||
A ^88cXLVoX
|
||||
|
||||
B ^igiyhZIj
|
||||
|
||||
R2 ^XMD8P6QJ
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBGAFZtAGYaOiCEfQQOKGZuAG1wMFAwMogSbggAaQBRWrhqgEE2ADEOAAUABi6AFQAzAE0AeUHlDk0ufnLYRCqgojkkachM
|
||||
|
||||
bmcUgA4ANm0u7YAWA/iDgE4Adk2unnOUg5WIGHWL7UTt8/OulJ4Dz8+U+IPCgkdTceLxU7aU7xHjxLqnFLnRIPSQIQjKaRgpKpRJJbY8ZHFSDWZTBbhdB7MKCkNgAawQAGE2Pg2KQqgBieIILlc9JlSCaXDYWnKGlCDjEJkstkSanWZhwXCBXJ88r9Qj4fAAZVgZIkgg8qoE1LpCAA6iDJNw+ESIFSafSdTA9egDZUHmKMRxwvk0IDbWxFdg1E8/
|
||||
|
||||
T0HqLhHAAJLEX2oAoAXQe/XI2Vj3A4Qk1D0IEqwVVwXSNEDFEu9zHjpX50Hg4l4RIAvpSEAhiNaeJtNkkdoSa4wWOwuH7EQ8B6xOAA5ThiMGIxLQ3Hbf01wjMAAimSgbe4/QIYQemmEEtqwWyuXjSYeQjgxFw2/bfqRCM7PQJm3ODyIHFpmez+C/NhhR3NA93wMJimbYpq0gSoJCZGAeB4ABHAAZZChEkVDUO2U4EFOOAKEkJomhLWZ6wgb9lltN
|
||||
|
||||
Y0A2U4um0fF4m2bYF0SA5Ek2U5NnuW1Q1QDZNgSbiDm2TYtkRbj9iBS0wR+bQeEOTskKUt4CRRNEMSgckElYro8Q020SRdClbXtU0pVZDkeW5aia0FYVI3FSVmWs2VyA4BUlRyHSUw1bVdQot120pE16QtYhQTQG0awsx0gqqEKS09SQK3jFdykDIUQzBcNbWcmM40KZNbVTXB00fVAsxzW082IAsJFweIUuPYh0u4GDIHI60mxbEDUGXbiuK6Y4
|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
fBRu4tD0BaHAwFqEyAETUWuRBlGLFQnoTMJ+AQWJBHADc4ukGocIJ1BOGNggAA==
|
||||
```
|
||||
%%
|
||||
106
GénieÉlectrique/TD2/draws/1.C..md
Normal file
|
|
@ -0,0 +1,106 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^NwSZUS7g
|
||||
|
||||
B ^8ef5hHpu
|
||||
|
||||
e ^D4CTYvHY
|
||||
|
||||
r ^NqrzqP4Y
|
||||
|
||||
r ^GQAYKmof
|
||||
|
||||
2r ^cIRrfnec
|
||||
|
||||
2e ^9KXLA8iV
|
||||
|
||||
e ^FbQ7QgwY
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
100
GénieÉlectrique/TD2/draws/1.C.Eteint.md
Normal file
|
|
@ -0,0 +1,100 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^OAnSGuXk
|
||||
|
||||
B ^IieGrM5I
|
||||
|
||||
r ^qHWQwtHs
|
||||
|
||||
r ^v4qE4AYM
|
||||
|
||||
2r ^DwLCKoG1
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
LKjDekfSvpgSGCOAA5Jf5ggZfaCCAGghAA==
|
||||
```
|
||||
%%
|
||||
95
GénieÉlectrique/TD2/draws/1.C.Ouvert.Ueq.md
Normal file
|
|
@ -0,0 +1,95 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
r ^R47jNlSN
|
||||
|
||||
r ^rZO2ofvP
|
||||
|
||||
e ^7OipIK7s
|
||||
|
||||
2e ^LYeY1VjP
|
||||
|
||||
i ^HWEOcV7s
|
||||
|
||||
ri ^xAb2jGkU
|
||||
|
||||
## Embedded Files
|
||||
994ab975e81811be8219a079dc2b2096ec009408: $$U_{eq}$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
HBSONEpKRh77VHkdE6U9LyXWMfGRe91hqrx4NrTW65fqfQJeUfeWKoLj3jCfM+VVH6ELvmAB+V9IHX0fkQwEpwVxfC+H0vsUlqF8ucPQkEckwQcxwY9NE+C2WSqaQkckasrgAnIagohlw4jCpRSiN6aIvhyR4Mqq+7LxZjW1RKq+eq+niw1rTEEtdRnsMWJw7hzI+ECJkG2YRZ9CiP2lbazp4i3jOsGW6kZ5kVEmNIOozRmwaWQD0QYxwqbAWqKT
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
tscRjU5Vje2V3rjeod2f3qOXWUTU8VZfjeTe8ZTcFdTd8bTeFfTZFeUO9ivuqSuZWH0JzVuSTLCYsPCcCkNKiiiL2L+TDmRg9ulZAGfiLagMZDXKiBZAVVLffjLU+djuSXjqkZVSrZtGcH/tSuqQ1TrayeUCBRyeBbfNyZai/Hyv3ZLKQkPTQuuuSJcKiMSHvnGRatygmnvHhfwvKcQEGqIlzSRcmoYtqW+ZRYI9RW+fw2WqaRRcaY4gxVXVQOxZ
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
kPgCJj4ZuwHESYk0grL0w++RgNgAYFb4kYCAiWOEIUTIEn8sgv/bqP9hdBJNSAGffpiQA469U2+MoawbuABaNI++9g4gFjDYCtRKBqzYIPbysGPsTY1uVCNyACSkBlAEoAABTvxqAvAFeNEKiEMhTgAASh1AxZlAxYTUKsDCG4BIhz0OIbkN4D5D6EiQZIfoIIEv8EAIA+zJwAVq31OBeiJgGqVQDW4cg3goaAdS9rB5uA7Q+MKUU74G4K+McSLB
|
||||
|
||||
kn6Fqd4whjHvkwBnBvIuhAw50OMI5CkAvBmgHwTMMSz6C7AqMc5nkENClE4A7gzwaUWWH4dxk6wQgIwAGAaD8AWgv3hOzCDBBThM0Oap8yiz6BmB+Beqj70fK1CDAhoTIA8Isy+9PuzIWoKcPOGXCd4sEcAOAWuLBBISMEEADBCAA===
|
||||
```
|
||||
%%
|
||||
115
GénieÉlectrique/TD2/draws/1.C.Ouvert.md
Normal file
|
|
@ -0,0 +1,115 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^uKv7Ylmu
|
||||
|
||||
B ^4RpUiNTT
|
||||
|
||||
r ^tWbLRAeW
|
||||
|
||||
r ^sTYHFhDY
|
||||
|
||||
2r ^moGgLdTM
|
||||
|
||||
2e ^Am7NHbbn
|
||||
|
||||
e ^Ms9SzNpt
|
||||
|
||||
i=0 ^wCeZlrVv
|
||||
|
||||
## Embedded Files
|
||||
e1349fb6e62250567f75c748e6408aa92e51b67d: $$U_{AB}=E_{th}=?$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
g3Z+HA9askzjPte4ehS+Pu6QnnBrD96Cv2T/uykX5F2AsQ5RdD5HRtnKm2Hgjih1/8XIbRymyAoUXYYcI9FOPeP73Ut/0dCJ2xx/3KDJ2ZQoypzZRpw5XpzoxTBi15WkUz1YzZ1LEOC5zIyN3tBlQjHOCvXOEkgk21TKQYDMU1WWksS+CuG2EJCE0NX2mNWcTN1IVUwuktQQM028TtV10dUCTtE/ENxY1i1M2YMBjAGBmG2OQkGXDHHGEOCW1Ikk
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
|
||||
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|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
105
GénieÉlectrique/TD2/draws/1.G..md
Normal file
|
|
@ -0,0 +1,105 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^x6oPPXYd
|
||||
|
||||
B ^msYCM7Iq
|
||||
|
||||
V ^KVYrrAlP
|
||||
|
||||
R2 ^Pnbocb34
|
||||
|
||||
R1 ^qyyPBV5x
|
||||
|
||||
I ^NzRi4UuW
|
||||
|
||||
## Embedded Files
|
||||
62e203f7c1ef225e71380d45a803cdc8a165e5d3: $$\lambda V$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
mq19/Xeg9aat0XrgM+pXp1N19HA1Nj/lm2DkAlmgM+eNeMMaoEzXjYtcdByNqoJQokDNWarYpTzSdT4hCaLnF8qWx5UIzKvMnO8xhlE6VEN+nxioLaAVtpJrlCGAiwXnN7ZC5Gg7W7nC3IihRSmJ2qM4kCp2FMHzU15svMo/MnwwLAMzMoexhwypsj8FhgTUQ5LKM4RDBxyJInOD8dDviUgM3uFF3moG3iY1jDdDEMGitgHSxkg48SbgYwuJKlOA
|
||||
|
||||
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|
||||
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||||
|
||||
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|
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||||
|
||||
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||||
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||||
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||||
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|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
115
GénieÉlectrique/TD2/draws/1.G.CourtCircuit.md
Normal file
|
|
@ -0,0 +1,115 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^EoZSlIXb
|
||||
|
||||
B ^y0LFRZMc
|
||||
|
||||
V ^1JzfkbiQ
|
||||
|
||||
R2 ^ojz6EWpY
|
||||
|
||||
R1 ^2Mw6Q6np
|
||||
|
||||
I ^kyS8URiZ
|
||||
|
||||
In ^HQTUxM35
|
||||
|
||||
## Embedded Files
|
||||
62e203f7c1ef225e71380d45a803cdc8a165e5d3: $$\lambda V$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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||||
|
||||
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||||
|
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||||
|
||||
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||||
|
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
61rOGgONgZf99p3szMAYF1CZBLlyZH0Q5n5iSRLlByo5S6zRTgB0U/GbUOEGbnoQWwQAA===
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,99 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
8a649409eaf2056eb2e976f7d24d6382a0f878a7: $$I_1$$
|
||||
|
||||
e2c089acc2a2571c0bae769e70c2453afa2b9a1e: $$I_2$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,136 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
A ^7qwiESYk
|
||||
|
||||
B ^uecM9vk5
|
||||
|
||||
R ^leCUteIX
|
||||
|
||||
R ^TSV77M2j
|
||||
|
||||
R ^9xYWNiMm
|
||||
|
||||
R ^eCLif9Ks
|
||||
|
||||
R ^HguGo8CV
|
||||
|
||||
Rch ^SVDgTuPm
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
zxAdOnV60DAuoTIB+cNbu1oYO5aoHeYfMPT8AV8JCOAHRi19ggNYZsCAGbBAA===
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,74 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
Rch ^KcK3m4pV
|
||||
|
||||
Rth ^99lES8HE
|
||||
|
||||
Eth ^m1umCxq0
|
||||
|
||||
Uth ^bzrXMcOI
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
DBQmEElKR7RMD80zOR8HZXQXZcGkb4lkv5hXRXxXd4f7WD+AjQTRwhXrOwQBOwgA
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,54 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
tAnMDhwj7LsVW9oMTq0sj84E3zUC/LjuC4RgVHbrxBa7RtkLvbQuSoouF7oEWaIKhHShKKtF9qDhiusqcvG4sztVAl21zGWNJXWNqHVTXUpcTXRI9diAzuZdA6ObLvIcoDCuBiSzfgpH5VtI65j4miqngtahb4jZ60usvS1R516qvydeQpH1946rKX9RIa5/oPJNeXOpkBob31ukq4EcA2CFh3tYiaRQ5hlDzthiamqyiYaw4WhE+y9hlqw2ABoe
|
||||
|
||||
HST4YgPgUIUAWT6H0GoZ8AAFFDqpoNmstlEUgUBah9ULMoDd9ocjEEE5KYTonvJ8agAAQVIPSCgGJcCUpvnWcTinlOqfUzBiAyH8AwGUAKqCTSwCdxfqjBo4wACy9ALRURgDAJk8nahxhgH0ZwRgGgzion0JkoaqjhoWagOE2hbgkesoZD8dluEQBknEF4DFknKUhFcAcfw82UOI8Wsjply1PKrXWmtvDzaIsbYCltIU22SMEdIhUXbVQ9tSgnHR
|
||||
|
||||
k7eNDuRYitF/aOuQGnTi2V5RjE50XUS2MhcAPlDXRSmT5RnG0uOLu/dPjD1Ng7kEzlSlvwZpvTE+9IqOATyfcsq4kxpWvA/Qqr9yrBS/pev+jVe8vqHxA1+cDiRIOX3m7Bi1CHv11mQ6hm8GGJqUYeLhrD+GwCEbmLl0jpaCsUao9Dmj/4GNMZYzIDsHHUO/YdMqATQnOIE/E5JxwpPuNZSJ9ptgKmQh6Z45ALTSn6e6YJ4Z4zpnsnmcs60qokwS
|
||||
|
||||
LNCMMoTAVM2DtAJk9SQkhUKbgGBaXA4wgsSBC8CVmzgJIc0uALf4lw+hHWG48Z40roSKWlWdxEHCLjZajv4thykjZ2TuCgi7zDnn7Ay85VaSPJZVPcmVqkFX6sAubRGyA4jQVu2ihCmRTXfarthW19FIdZNdfzbwHr46SoeL8NigxAY8UmJkjcJdxKpvPbJeu6nvUq4lm6Ctpla36YbeaSe+adkzjdCOgvYVe0tqj0iQPk74rpVgbsqia96TP0A7
|
||||
|
||||
u5Hh728V1aqA294+U+3xpONT92v5qYZz6Q5xtDyYwco8h5RvDkO4dlE+PsC9zvpUnGsn3rDzgve/B98iFc/ueDUbmLR+jWkLHVjXHI/AnWkInCnaTXfcocnEnETGA2OWnNnBnNTMnSUOnVApnQ/IzEzLaVea1JGAXCQM8aYAmPoWoEiHUQgamCmHgDgRIZwOMGcJkTQOMVXdAdXHiLYXsCLPuJcY2O4PWaVafaSZ4ZZBSJyAhb/S4WeeLChe3DSZ
|
||||
|
||||
IRIE4I4PuFIHYS7B5CtFhRZfYSLDNIGXBDhD8IEQPZmatQdARd2MPB2CPCAKPdtUPOPRrBKZrP2XtFPPrNPTrJ0Yde3UdAqXrCdHwgbLFGdY3CAUbBdMvCbe8SvZMWjWbexKlOvGlEseTJvQvVAA9VvX/TbdlQ+XsT8Q4Y4LBYfYeNAQ3G9UfLsS4ahb8NLa7TJeaOkSiXJc8P9Y/VIwDV7UpY+C4I3FcapK+Ho+pffMzRDe0YHJ7E/LDa/CHcHV
|
||||
|
||||
Hf/K/cHJIN4QQlQmLI2Iw8/UWI6OEX4JQyMTmc4S/U/LDJQ7QFQ3lFEZcTQkSGOMobYOIM6BEZyfsI6b8bsP/MoAAzHAwbHdjMA9DS46NG4tQ+4mLK4SHF4tNd4jhAeb43sdHTRSA+A9AiTDExAwnfjTAjnHE1nHTRnTnVkbnfAvncAd6GuOAOAPUA+bgWsaADEbIYLStAUBgQgBACgWoWrCKSrdUQUoUjk7AEQH2OMXcfQPUAqSrcPEUsUxKCUr
|
||||
|
||||
IXksKJwmwlwr2NwxPSAUUpTRUyU9oZPQOXPYoCAXU8UyU6Uvw7rU080/UrIK0xkYIk08oO03IJU/QCmcIobdYM0hU90yUnCedUvOqW0/0qAD09oTgKAdodqLUGSMhP0vUgMrIKM3IagowQ6C2JMi0rIQZTABTIgZQLaOjBAdUbUnM+0qUuTfEkkmAyslM/QM8DAlAgk1xFA+U5MiMyUzA1CVvViR6Ts3M/QdoEuL0t0MY00bAekbUAmbgFEPoBIU
|
||||
|
||||
4DSfmSEXWYGKcmc/APCaaC7BIf4M4G4GEBoxMowNgAwRk9aAgSiLsVIKWK4QgnU8Mj0r0xlbIgciKDksUEgDMrM30784gPUBAENTWf80gEgWzNgfqZs3ATQYIW7MCkgcFZGWoVkVGUgZQIUAACmuAul4CXGoHwrwrwUSAAEoTQKYEBlA8xlQYFMLcAcLHJCLfhqQ2ZWKSLyLHyGyoBHSEAgyoBRwkxJzZtKKixwKqccixMOBYL4LuA2j58zSVg5L
|
||||
|
||||
SB2j7RpLWS0B5KgwhAoAQtNKVKFK+lSBGRSAZxyVlLVK6wjKTKYK4LWiDKuK7BmgEB2JmAdRpK4BILoLpK7KELTThQBLGBUJzz8BLy6x1tTRMh2JolgRRTaQDA+y/Exi/sJjecpjV16QpSoqBKecckoYGN5NoqgqQrTU4JwBEYIAFFwhGTmwQBmwgA==
|
||||
```
|
||||
%%
|
||||
52
GénieÉlectrique/TD3/Index.md
Normal file
|
|
@ -0,0 +1,52 @@
|
|||
|
||||
|
||||
![[TD_FGE_2025.pdf#page=10]]
|
||||
![[b5364d1697.pdf#page=5]]
|
||||
# Exercise 1.
|
||||
|
||||
Loi des mailles $\rightarrow E=U_R+UC$
|
||||
$E=R_i+U_C$
|
||||
$E=RC\frac{dU_C}{dt}+U_C$
|
||||
|
||||
La solution est une courbe de la forme $U_C(t)=A_e^{-t/RC}+B$
|
||||
|
||||
Conditions aux limites:
|
||||
À $t=0$, $U_C(t)=0$ par lecture du circuit.
|
||||
$U_C(t)=A_e^{-0/RC}+B=A+B$
|
||||
$\implies 0=A+B\implies A=-B$
|
||||
|
||||
À $t\rightarrow ∞$, $U_C(t)=E_0$ par lecture du circuit.
|
||||
$U_C(∞)=B$ par la forme de la solution.
|
||||
Finalement, $U_C(t)=-E_0e^{-t/RC}+E_0=E_0(1-e^{-t/RC})$
|
||||
|
||||
$V=E-U_C(t)$
|
||||
$V(t)=E_0e^{-t/RC}$
|
||||
|
||||
# Exercise 2.
|
||||
![[Pasted image 20251003152305.png]]
|
||||
|
||||
|
||||
$\tau=RC=10E^3\times100E^{-6}=1s$
|
||||
![[IMG_7370.jpeg]]
|
||||
|
||||
# Exercise 3: Second order DC circuits
|
||||
![[Pasted image 20251003160147.png]]
|
||||
|
||||
$\implies I=CL\frac{d^2i_1}{dt^2}+i_1$
|
||||
|
||||
Puisque $0=LC\frac{d^2U}{dt^2}+U+°\times\frac{dU}{dt}$
|
||||
$\implies$ Solution: $U(t)=A\cos{(\omega_0t)}+B\sin{(\omega_0t)}$
|
||||
À $t=0$, $U(t)=0$ donc $A=0$.
|
||||
|
||||
Donc $U(t)=B\sin{(\omega_0t)}$
|
||||
d'où: $\frac{du}{dt}=B\omega_0\cos{(\omega_0t)}$
|
||||
Or, $\frac{dU}{dt}=\frac{i_C}{C}$ et $i=i_C+i_L$
|
||||
Donc $\frac{dU}{dt}=\frac{i-i_L}{C}$
|
||||
|
||||
À $t=0$:
|
||||
$\frac{dU}{dt}=B\omega_0=\frac{I}{C}$
|
||||
Parceque $I_L$ est continu:
|
||||
$I_L(0^+)=I_L(0^-)=0$
|
||||
$\implies B=\frac{I}{i\omega_0}=\frac{I}{\frac{C}{\sqrt{LC}}}=\frac{I\sqrt{LC}}{C}$
|
||||
|
||||
Finalement, $U(t)=\frac{I\sqrt{LC}}{C}\sin{(\frac{1}{\sqrt{LC}}t)}$
|
||||
BIN
GénieÉlectrique/TD3/attachments/IMG_7370.jpeg
Normal file
|
After Width: | Height: | Size: 1.3 MiB |
BIN
GénieÉlectrique/TD3/attachments/Pasted image 20251003152305.png
Normal file
|
After Width: | Height: | Size: 116 KiB |
BIN
GénieÉlectrique/TD3/attachments/Pasted image 20251003160147.png
Normal file
|
After Width: | Height: | Size: 126 KiB |
BIN
GénieÉlectrique/TD3/attachments/b5364d1697.pdf
Normal file
200
GénieÉlectrique/TD4/Index.md
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
![[TD_FGE_2025.pdf#page=15]]
|
||||
|
||||
# Exercise 1. Fresnel vector
|
||||
![[Pasted image 20251006094239.png]]
|
||||
a) polar form (modulus and argument)
|
||||
$\overrightarrow{v_1}=(15A,\frac{7\pi}{6})=15e^{j(\phi)}=15e^{j210}$
|
||||
|
||||
b) rectangular form (a+jb)
|
||||
$\overrightarrow{v_1}=(\begin{matrix}15A\cos{(\frac{7\pi}{6})} \\ 15A\sin{(\frac{7\pi}{6})}\end{matrix})=(\begin{matrix}-12.99A \\ -7.5A\end{matrix})$
|
||||
$\overrightarrow{v_1}=a+jb$ avec $a=15\cos{210}$ et $b=15\sin{210}$
|
||||
$\overrightarrow{v_1}=-12.99 - 7.5j$
|
||||
|
||||
|
||||
# Exercise 2:
|
||||
![[Pasted image 20251006100509.png]]
|
||||
a)
|
||||
$\overrightarrow{V_1}=63+j16=\sqrt{63^2+16^2}e^{j\arctan{(\frac{16}{63})}}=65e^{j0.249}$
|
||||
$\overrightarrow{V_2}=-5-j12=\sqrt{(-5)^2+(-12)^2}e^{j\arctan{(\frac{-12}{-5})}}=13e^{j(1.176+\pi)}$
|
||||
|
||||
$\overrightarrow{V_1}\wedge\overrightarrow{V_2}=65\times13\times e^{j(0.249+\pi+1.176)}$
|
||||
|
||||
b)
|
||||
$\overrightarrow{V_1}/\overrightarrow{V_2}=\frac{65}{13}e^{j(0.249-\pi-1.176)}$
|
||||
|
||||
# Exercise 3:
|
||||
![[Pasted image 20251006101747.png]]
|
||||
## Figure 2: ![[Drawing 2025-10-06 10.49.08.excalidraw]]
|
||||
a)
|
||||
$U=\underline{z}_1i_1\implies i_1=\frac{\underline{U}}{\underline{z_1}}=\frac{\underline{U}}{R}$
|
||||
$U=\underline{z}_2i_2\implies i_2=\frac{\underline{U}}{\underline{z_2}}=\frac{\underline{U}}{jL\omega}$
|
||||
|
||||
$||\underline{i_1}||=||\frac{\underline{U}}{R}||=\frac{||\underline{U}||}{||R||}=5A$
|
||||
$||\underline{i_2}||=||\frac{\underline{U}}{\underline{Z_2}}||=\frac{||\underline{U}||}{||\underline{Z_2}||}=2A$
|
||||
|
||||
b)
|
||||
$\underline{i}=\underline{i_1}+\underline{i_2}$
|
||||
$i_2=\frac{\underline{U}}{jL\omega}=\frac{-j\underline{U}}{L\omega}$
|
||||
![[Drawing 2025-10-06 10.55.18.excalidraw]]
|
||||
|
||||
$||\underline{i}||=\sqrt{||\underline{i_1}||^2+||\underline{i_2}||^2}=\sqrt{29}\approx5.3851648071A$
|
||||
$\phi=\arctan{(\frac{||\underline{i_2}||}{||\underline{i_1}||})}=\arctan{(\frac{-2}{5})}\approx-0.3805063771 rad$
|
||||
|
||||
c)
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{Z_R}+\frac{1}{Z_L}\implies Z_{eq}=\frac{\underline{Z_L}\underline{Z_R}}{\underline{Z_L}+\underline{Z_R}}$
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{R}+\frac{1}{jL\omega}=\frac{1}{R}-j\frac{1}{L\omega}$
|
||||
ou
|
||||
$Z_{eq}=\frac{jRL\omega}{R+jL\omega}=\frac{(R-jL\omega)(jRL\omega)}{(R+jL\omega)(R-jL\omega)}=\frac{RL^2\omega^2+jR^2L\omega^2}{R^2+L^2\omega^2}=\frac{RL^2\omega^2}{R^2+L^2\omega^2}+j\frac{R^2L\omega}{R^2+L^2\omega^2}$
|
||||
$||Z_{eq}||=\frac{||R||||Z_L||}{||R+Z_L||}=\frac{1000}{\sqrt{20^2+50^2}}\approx\frac{1000}{53.8516480713}=18.5695338177\Omega$
|
||||
|
||||
d)
|
||||
$\underline{U}=\underline{Z_{eq}}\underline{I}$
|
||||
$||\underline{U}||=||\underline{Z_{eq}}||||\underline{I}||\approx18.5695338177\times5.3851648071=99.9999999993V$
|
||||
|
||||
## Figure 3: ![[Drawing 2025-10-06 11.17.18.excalidraw|1000]]
|
||||
a)
|
||||
$U=\underline{z}_1i_1\implies i_1=\frac{\underline{U}}{\underline{z_1}}=\frac{\underline{U}}{R}$
|
||||
$U=\underline{z_2}i_2\implies i_2=\frac{\underline{U}}{\underline{z_2}}=\frac{\underline{U}}{\frac{1}{jC\omega}}$
|
||||
|
||||
$||\underline{i_1}||=||\frac{\underline{U}}{R}||=\frac{||\underline{U}||}{||R||}=\frac{120}{20}=6A$
|
||||
$||\underline{i_2}||=||\frac{\underline{U}}{\underline{Z_2}}||=\frac{||\underline{U}||}{||\underline{Z_2}||}=\frac{120}{30}=4A$
|
||||
|
||||
b)
|
||||
$\underline{i}=\underline{i_1}+\underline{i_2}$
|
||||
$i_2=\frac{\underline{U}}{\frac{1}{jC\omega}}=\underline{U}jC\omega$
|
||||
|
||||
![[Drawing 2025-10-06 11.25.11.excalidraw]]
|
||||
$||\underline{i}||=\sqrt{||\underline{i_1}||^2+||\underline{i_2}||^2}=\sqrt{52}\approx7.2111025509A$
|
||||
$\phi=\arctan{(\frac{||\underline{i_2}||}{||\underline{i_1}||})}=\arctan{(\frac{4}{6})}\approx0.5880026035 rad$
|
||||
|
||||
c)
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{Z_R}+\frac{1}{Z_C}\implies Z_{eq}=\frac{\underline{Z_C}\underline{Z_R}}{\underline{Z_C}+\underline{Z_R}}$
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{R}+\frac{1}{\frac{1}{jC\omega}}=\frac{1}{R}+jC\omega$
|
||||
ou
|
||||
$||Z_{eq}||=\frac{||R||||Z_C||}{||R+Z_C||}=\frac{20\times30}{\sqrt{20^2+30^2}}\approx\frac{600}{36.0555127546}=16.6410058868\Omega$
|
||||
|
||||
d)
|
||||
$\underline{U}=\underline{Z_{eq}}\underline{I}$
|
||||
$||\underline{U}||=||\underline{Z_{eq}}||||\underline{I}||\approx16.6410058868\times7.2111025509=119.9999999998V$
|
||||
|
||||
## Figure 4: ![[Drawing 2025-10-06 11.38.13.excalidraw|1000]]
|
||||
a)
|
||||
$U=\underline{z}_1i_1\implies i_1=\frac{\underline{U}}{\underline{z_1}}=\frac{\underline{U}}{\frac{1}{jC\omega}}$
|
||||
$U=\underline{z}_2i_2\implies i_2=\frac{\underline{U}}{\underline{z_2}}=\frac{\underline{U}}{jL\omega}$
|
||||
|
||||
$||\underline{i_1}||=||\frac{\underline{U}}{\underline{Z_1}}||=\frac{||\underline{U}||}{||\underline{Z_1}||}=\frac{100}{20}=5A$
|
||||
$||\underline{i_2}||=||\frac{\underline{U}}{\underline{Z_2}}||=\frac{||\underline{U}||}{||\underline{Z_2}||}=\frac{100}{30}=3\frac{1}{3}A$
|
||||
|
||||
b)
|
||||
$\underline{i}=\underline{i_1}+\underline{i_2}$
|
||||
$i_1=\frac{\underline{U}}{\frac{1}{jC\omega}}=\underline{U}jC\omega$
|
||||
$i_2=\frac{\underline{U}}{jL\omega}=\frac{-j\underline{U}}{L\omega}$
|
||||
|
||||
![[Drawing 2025-10-06 11.43.56.excalidraw]]
|
||||
$||\underline{i}||=||\underline{i_1}||-||\underline{i_2}||=5-3\frac{1}{3}=1\frac{2}{3}A$
|
||||
$\phi=180°$ ou $\pi rad$
|
||||
|
||||
c)
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{Z_L}+\frac{1}{Z_C}\implies Z_{eq}=\frac{\underline{Z_C}\underline{Z_L}}{\underline{Z_C}+\underline{Z_L}}$
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{jL\omega}+\frac{1}{\frac{1}{jC\omega}}=-j\frac{1}{L\omega}+jC\omega$
|
||||
ou
|
||||
$||Z_{eq}||=\frac{||Z_L||||Z_C||}{||Z_L+Z_C||}=\frac{20\times30}{||20-30||}\approx\frac{600}{10}=60\Omega$
|
||||
|
||||
d)
|
||||
$\underline{U}=\underline{Z_{eq}}\underline{I}$
|
||||
$||\underline{U}||=||\underline{Z_{eq}}||||\underline{I}||\approx60\times1\frac{2}{3}=100V$
|
||||
|
||||
## Figure 5:![[Drawing 2025-10-06 12.02.59.excalidraw|1000]]
|
||||
a)
|
||||
$U=\underline{z}_1i_1\implies i_1=\frac{\underline{U}}{\underline{z_1}}=\frac{\underline{U}}{\frac{1}{jC\omega}}$
|
||||
$U=\underline{z}_2i_2\implies i_2=\frac{\underline{U}}{\underline{z_2}}=\frac{\underline{U}}{jL\omega}$
|
||||
$U=\underline{z_3}i_3\implies i_3=\frac{\underline{U}}{\underline{z_3}}=\frac{\underline{U}}{R}$
|
||||
|
||||
$||\underline{i_1}||=||\frac{\underline{U}}{\underline{Z_1}}||=\frac{||\underline{U}||}{||\underline{Z_1}||}=\frac{100}{30}=3\frac{1}{3}A$
|
||||
$||\underline{i_2}||=||\frac{\underline{U}}{\underline{Z_2}}||=\frac{||\underline{U}||}{||\underline{Z_2}||}=\frac{100}{60}=1\frac{2}{3}A$
|
||||
$||\underline{i_3}||=||\frac{\underline{U}}{R}||=\frac{||\underline{U}||}{||R||}=\frac{100}{20}=5A$
|
||||
|
||||
b)
|
||||
$\underline{i}=\underline{i_1}+\underline{i_2}+i_3$
|
||||
$i_1=\frac{\underline{U}}{\frac{1}{jC\omega}}=\underline{U}jC\omega$
|
||||
$i_2=\frac{\underline{U}}{jL\omega}=\frac{-j\underline{U}}{L\omega}$
|
||||
|
||||
![[Drawing 2025-10-06 12.09.17.excalidraw]]
|
||||
|
||||
$||\underline{i}||=\sqrt{(||\underline{i_1}+\underline{i_2}||)^2+||i_3||^2}=\sqrt{(3\frac{1}{3}-1\frac{2}{3})^2+5^2}=\sqrt{27.7777777778}\approx5.2704627669A$
|
||||
$\phi=\arctan{(\frac{||\underline{i_{1+2}}||}{||\underline{i_3}||})}=\arctan{(\frac{1\frac{2}{3}}{5})}\approx0.3217505544 rad$
|
||||
|
||||
c)
|
||||
$\frac{1}{Z_{eq}}=\frac{1}{Z_L}+\frac{1}{Z_C}+\frac{1}{Z_R}=\frac{Z_RZ_C+Z_CZ_L+Z_RZ_L}{Z_RZ_LZ_C}$
|
||||
$Z_{eq}=\frac{Z_RZ_LZ_C}{Z_RZ_C+Z_CZ_L+Z_RZ_L}$
|
||||
ou
|
||||
$||Z_{eq}||=\frac{||Z_R||||Z_L||||Z_C||}{||Z_RZ_C||+||Z_CZ_L||+||Z_RZ_L||}$
|
||||
|
||||
# Exercise 4: Application
|
||||
![[Pasted image 20251006122351.png]]
|
||||
|
||||
a)
|
||||
![[Drawing 2025-10-06 12.24.01.excalidraw]]
|
||||
$Z_{eq}=30+\frac{80}{j}=30-j80$
|
||||
$Z_C=\frac{1}{jC\omega}=\frac{80}{j}$
|
||||
|
||||
b) ![[Drawing 2025-10-06 12.28.41.excalidraw]]
|
||||
$Z_{eq}=(r,\theta)=(\sqrt{30^2+80^2}, \arctan{(\frac{-80}{30})})=(85.4400374532, -1.2120256565 rad)$
|
||||
$V=85.44e^{-1.21j}$
|
||||
|
||||
# Exercise 5: Application, Study of a real inductor
|
||||
The series model of a real inductor is defined by its series resistance $R_S$ and its series inductance $L_S$. It is possible to define a parallel model equivalent to the series model as shown in Figure 6.
|
||||
![[Pasted image 20251008135058.png]]
|
||||
|
||||
a)
|
||||
Modèle en série $\implies Z_{eq_1}=L_S+R_S=R_S+jL_S\omega$
|
||||
Modèle parallèle $\implies \frac{1}{Z_{eq_2}}=\frac{1}{L_P}+\frac{1}{R_P}$ $\implies Z_{eq_2}=\frac{R_PjL_P\omega}{R_P+jL_P\omega}$
|
||||
|
||||
Multiplication par le conjugué
|
||||
$\frac{jR_PL_P\omega(R_P-jL_P\omega)}{(R_P+jL_P\omega)(R_P-jL_P\omega)}=\frac{R_PL_P^2\omega^2+jR_P^2L_P\omega}{R_P^2+L_P^2\omega^2}$
|
||||
|
||||
Or, $Z_{eq_1}=Z_{eq_2}\implies\begin{cases}R_S=\frac{R_PL_P^2\omega^2}{R_P^2+L_P^2\omega^2} \\ L_S\omega=\frac{R_P^2L_P\omega}{R_P^2+L_P^2\omega^2}\end{cases}$
|
||||
|
||||
$R_S+jL_S\omega=\frac{R_P^2L_P\omega}{R_P^2+L_P^2\omega^2}+j\frac{R_PL_P^2\omega^2}{R_P^2+L_P^2\omega^2}$
|
||||
|
||||
b)
|
||||
$U(t)=U_2\cos{(\omega t)}$
|
||||
$\underline{U}=U_2e^{j\omega t}$
|
||||
$\underline{I}=\frac{\underline{U}}{\underline{Z_{eq}}}=\frac{U_2e^{j\omega t}}{\underline{Z_{eq}}}$
|
||||
|
||||
c)
|
||||
![[Drawing 2025-10-08 14.39.38.excalidraw|1000]]
|
||||
|
||||
$V_{total}^2=V_{L_S}^2+(V_0+V_{R_S})^2$
|
||||
$V_{total}^2=V_{L_S}^2+V_0^2+2V_0V_{R_S}+V_{R_S}^2$
|
||||
|
||||
$V_{bobine}^2=V_{L_S}^2+V_{R_S}^2$
|
||||
|
||||
D'après Pythagore:
|
||||
$$
|
||||
\begin{cases}
|
||||
V_{bobine}^2=V_{L_S}^2+V_{R_S}^2 \\
|
||||
V_{total}^2=V_{L_S}^2+(V_0+V_{R_S})^2 \\
|
||||
V_0=R_0I
|
||||
\end{cases}
|
||||
\implies
|
||||
\begin{cases}
|
||||
V_{bobine}^2=L_S^2\omega^2I^2+R_S^2I^2 \\
|
||||
V_{total}^2=L_S^2\omega^2I^2+(R_S+R_0)^2I^2 \\
|
||||
V_0=R_0I
|
||||
\end{cases}
|
||||
$$
|
||||
![[IMG_7432.jpeg|400]]
|
||||
|
||||
$$
|
||||
\begin{cases}
|
||||
L_S^2=(V_{bobine}^2-\frac{R_S^2V_0^2}{R_0^2})\times\frac{R_0^2}{V_0^2\omega^2} \\
|
||||
R_S=\frac{V_{tot}^2-V_{bobine}^2-V_0^2}{2V_0}\times R_0
|
||||
\end{cases}
|
||||
$$
|
||||
|
||||
d)
|
||||
Application Numérique: $\begin{matrix}R_S=4.93\Omega \\ L_S=32mH\end{matrix}$
|
||||
|
||||
e)
|
||||
Au lieu de mettre $R_0$ en série pour mesurer les tensions, on peut le mettre en parallèle pour mesurer les courants.
|
||||
|
|
@ -0,0 +1,118 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
100V ^pPEP3b1T
|
||||
|
||||
i1 ^CbAUVXp9
|
||||
|
||||
i2 ^QsfRLFiD
|
||||
|
||||
20Ohm ^PHabeeQo
|
||||
|
||||
50Ohm ^0Csw0Dfq
|
||||
|
||||
U ^D11CR5il
|
||||
|
||||
z1 ^yd2nFaKW
|
||||
|
||||
z2 ^EwOpiDmF
|
||||
|
||||
i ^tMfMOEtf
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
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||||
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|
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|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
faGk0cU4psWmLJFQM0GShWsUSKsgPQfVrKQY7gydFziuhd4RaDOZhZwUFRZ4rMWZxNFboV4maGwD0gdQWEFuD8DFj95IR7pdWDgsmAZL8ARmbgKYOsjzRUqn8dHsGTQVGA2ABgVBW3AIACJQQWFfxfIo0VDQP8sSqUBQvFAkB3ZOPHBYMuIi7hM6F/V5iQFIhsAeoQSh3sEE4kxhQOxC1AOTD0Rsg/opAZQMKAAAUiqagOgJUjHKjlcSRIAAEpTQ
|
||||
|
||||
3CZQHmBVD0RdluAA5ckiOXMpqQvAF5Smx5RXKOluil+A0mPEIJOAU/HBZg24RFhQOEpcmDkEWWzR45OipYFZM3H2hwOmC43sipB4cJLE6KzqvoBVBMhSAbQe/EitxX4qmACyzQEspJUdK7AOiBAIxGYC6hwOcAWZfMvA6UqURkAEUAgkYAtBGl+AZpe9BiVhBggjEdaNggI6cJE8zmNqvbLOnfx6Q9CzIGKpyaWDBWICMVbyv5XvIYI4AUmN/G1D
|
||||
|
||||
hACGUMJsEAA=
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
U ^Kn15tU1P
|
||||
|
||||
i1 ^ffSESVe2
|
||||
|
||||
i2 ^cDjedbwX
|
||||
|
||||
i1+i2=i ^ia5sDJST
|
||||
|
||||
## Embedded Files
|
||||
42ee155d1d029d6bce99644c5e742c89bee942b2: $$\phi$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
U6iqOqOigQDYAiAwoJj7j6DGg2jBFHSHWiNaOLCai6NZAKND6QK7Wj4naK6aPaMWN6O+p6lXUkVOPmO5CWP6Oz14a/n3ZeM6N6MGNL7YXT64XBMuNZA1pkUpgbzRM+N6NtBb5UVbRJNQC+O+pOWS5BrSNmMhNZA5O5D2UnGmPOPJNZB7F+WRqeWOOFMxN+P8Grk6aZO+NokZYe2u3NXe3lCNNVP6BNI9x1ZPUywaMDNZOuPoxxOeig7kNLAGgaFo
|
||||
|
||||
D9hjSnB7wXDC2/pBPxSLP4BTpCZXwPq7B6IKKq3SNGBsAGAiMswEDNoPCyHtN6NxNsoEpjNEwaPSgkBlPCXSNfPEDGgIBcN/l/NG7EAdBsBn5om4CaDBBpmQD/Mbb1xyRciuSkDKDigAAUA4RivAPFeLuLS1AAlJaHWsoAWAsFUOi1i14YyLwIiNQPS3S8SxAI85M2E+yKk/GpwETaI79XWiWEbhOfXDkDC3C9wDCYFUQMC5K/WCbhI3bslbjcSl
|
||||
|
||||
Wm2hK0qxiLHaQOyKQHOLSuqylUOFqzq9C7C75Pbo83YCodgHkIaCbnABC1Cybma/C25Da4QIwD3Fc41SItuqM2EMEO62OFrmHtWr3HVgAzTdpdZmdksPo5kEGxGqMTxHxCZO656966pDw1lXQOA7WC2CAC2EAA==
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,118 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
z1 ^EowiJ97o
|
||||
|
||||
120V ^4cH6Vc2o
|
||||
|
||||
i1 ^f4UjqGOJ
|
||||
|
||||
i2 ^ZuhZPq89
|
||||
|
||||
20Ohm ^Ty07DFA4
|
||||
|
||||
30Ohm ^TLXDc5jm
|
||||
|
||||
U ^otL86C55
|
||||
|
||||
z2 ^60xhEJfu
|
||||
|
||||
i ^rJpW4k64
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBGAFZtAGYaOiCEfQQOKGZuAG1wMFAwMogSbgh8AFkAfTqADQAVAAkALQB5AEkABQBBAAZMAGVmHl6ARyNNdLLIWEQqoKI5
|
||||
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||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,83 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
U ^rE2xVULQ
|
||||
|
||||
i1 ^R0buD7IG
|
||||
|
||||
i2 ^VpTNriPF
|
||||
|
||||
i1+i2=i ^uPh71FIl
|
||||
|
||||
## Embedded Files
|
||||
42ee155d1d029d6bce99644c5e742c89bee942b2: $$\phi$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,126 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
100V ^bx8y19kl
|
||||
|
||||
i1 ^ts395ueC
|
||||
|
||||
i2 ^6bkWwky2
|
||||
|
||||
20Ohm ^OmupJgvl
|
||||
|
||||
U ^7EpTWyO7
|
||||
|
||||
z2 ^seZWaoSi
|
||||
|
||||
i ^L6idugZg
|
||||
|
||||
z1 ^LqTadgge
|
||||
|
||||
30Ohm ^MhxsJawN
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
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gPqGxZwBVt627Fkzp21ihNCjAEiJ1qLwHbsJ2UTIJ/MYTvUhADIAwMlpyK+S7F/HWkQYH1Ay6odAZJ9ZxRdiy7Rd4uu2DBHAB1ZjeuocILhtMVtggAA=
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
U ^WfMsGdeJ
|
||||
|
||||
i1 ^xqG4OZ8H
|
||||
|
||||
i2 ^o1TS0Wht
|
||||
|
||||
i1+i2=i ^VxBLTjnh
|
||||
|
||||
## Embedded Files
|
||||
42ee155d1d029d6bce99644c5e742c89bee942b2: $$\phi$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,144 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
100V ^p1eRjU8M
|
||||
|
||||
i1 ^YXbvr1C1
|
||||
|
||||
i2 ^wKdzvhnJ
|
||||
|
||||
30Ohm ^4PzJD6Sf
|
||||
|
||||
U ^7hNtRzAx
|
||||
|
||||
z2 ^QVPbMOT1
|
||||
|
||||
i ^T3rxvThY
|
||||
|
||||
z1 ^LR5RpCOg
|
||||
|
||||
60Ohm ^fCro86jg
|
||||
|
||||
z3 ^qwnpSfwX
|
||||
|
||||
20Ohm ^csUo0fdU
|
||||
|
||||
i3 ^8FtfpeP0
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,85 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
U ^OmHpSpZT
|
||||
|
||||
i1 ^2y3lUdg4
|
||||
|
||||
i2 ^kdicXDhQ
|
||||
|
||||
i1+i2+i3=i ^r7j9c9O7
|
||||
|
||||
i3 ^wtUlGdR0
|
||||
|
||||
## Embedded Files
|
||||
42ee155d1d029d6bce99644c5e742c89bee942b2: $$\phi$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
vFQtXt6b7t84Va0gRkUgGcHfTb1b6sHbvbmLuLvyK3RzuwbKBAdoZgHUfXOASL6L/XC7hLkUMNRgJKKz/AGz8YZasIYIdoITVXf2mNfQUTudFcly+563VMAwHUTIEHxROH5JMyEH7737tSIdrq/gAb5WysBsEABsIAA=
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,57 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
9673c2680c9c0e69946c77027116ca5b82a54c31: $$30\Omega$$
|
||||
|
||||
a827b999a096f2876c3babb0da8f13e2fbff4f01: $$80\Omega$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
85cuxXhpLieew6l6sUAfKJecF96Hzoufcg+Fr14gWawai76P7MXEOxSDXFFCQOEpoQysoWyGFUOcKZ4k5nLNCUsrBzb8GdssoEWylDxBRE02I6KrDfMcPyy5gR7DRH3sYdUWR2jT2PvEBo7KujEAGOmKVWAZdaqTb0CZgaZQVNry0WCWxQg+hojycgO1Nh8QBIlJ/KekNz8pLLjOPjpI00DN8XiPJVcxnkodZaCZe4icN2QgMyluzyaiRyXkm9Xo
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
BUcOAQEIF8tvtSc8foK8ScvMhINyR8VKCQEiSiS8IaTbMQEaAgJvmgNCUacQNhGwNPnSbgJoMEJoYXtoRaarkbEzJyCbKQMoGKAABTXBTi8AoLUARnhk3BUoACUWoUwCAyg+Y6oSwQZuAoZb0UZL+9IvA2ZdI8ZEAGpQJUAJxbIvxUAY4t0u8g6eWSZxYNsOGRsOQrp7p3ATIapa+RANpqAnZnpkAHAeWHZpAXZc8QgUA3saA/ZlImOpAbIpAc4w
|
||||
|
||||
505o5A5EAc5C5Lpbpo0/ZGpdg7QCAKwzABoQ5cAjpzpQ525HpHx4oVZjAZEip+AypDqnsHomQKwLya+i+UABgHJtILuGKf6cEN65QmYBgBo75VZkOIFkAxM4sH595j5+R0O4AKqOoeo4QFRLYIALYQAA
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,59 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
-80 ^LwU2aGJA
|
||||
|
||||
30 ^5VbKPYJT
|
||||
|
||||
## Embedded Files
|
||||
feb9fea6595245059dfddd6901e8d08536b7323c: $$\theta$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
Nip+csxuZxS4nn6UgHZE/oA2eMPEpMTNyBhuS5TtABZEo/6Xs9OADiOf4bnO4QCgkdTcfrAyQIQjKaTcHg/OIpM4pFLxeJHM4nf7xYHWZTBCHA5hQNYAawQTTY+DYpCqAGJ4ghmcy5uVNLhsOTlGshBxmjS6VUydZmHAVjkoOzIDVCPh8O1YESJIIPDKIKSKQgAOpgyQIklktiUpUwFXoNWVYF8uEccL5NB44qQNgS7BqB5O/qQl0QXnCOAASWIj
|
||||
|
||||
tQBQAusCauRsiHuBwhArgYQBVhlv0NXyBfbmGHSvNoPBxLwXQBfEkIBDEbjDE79HiJJFHYGMFjsLhoH4/VtMVicABynDEtfiZx+8R48XRKeYABFMlBq9wagQwsDNMIBYNgtlcmHE8m/UI4MRcEua06TnWvokzsNp7c/UQOOSE0n8MDadzl2hV/h1z9OA2FTPJChdMAinmMpfWgsB+ggqMIKg6DYOg5xEWRVF0UxbF3gnRCXSQwt8FCKBqX0fQ1Av
|
||||
|
||||
AAFEDcnfI9C1JFYoBaVNHA4ZRGM/P0cmIdiBVTbi0EPXjmKiUgoDqVZ1mhXBL1QMTgX4mS1goeTFIgFZ1I1IJNwoX9UH/MJigrYoC0gSoJGwAdRAAfQAaXiDgjmUAAVJofkmAAtUgACkfOIGBsA1RYS202SNj9bY0GcMcfleI40ReRFhkSU5/mBL1UGcM5+m0fpcX6G9J0uYYXmBUFiHBNAeCOOIzh4e9EnRRsoRhOFpTQNDIAJC1es1Y1KWpWl6
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
bn/QUVVolQIG0/RygVJdXaN19r+2GrqfUhooHajAVUPaMM/APQdI8YEr0PSwA+oNb6IYVb/VlLGBA8YpZMXKODFu2keAoJzOgtAiMixLDqqjf2VZFJtX+GiYYeNSaPC7nwjs5NKaoEnCVfoPxJHYlnAuYI/M/yJ1Zgtdme4wLkPEuUXm54jKYhHkLb4TVAQ9mfKmSWHsKHi1lpSeWSigL0XUeGZCEF4Ka3gtrZxcFl6rwquvHgm9t5uKSEcI+J9T
|
||||
|
||||
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|
||||
|
||||
oA6Um1QE7SQRAjUD9KRHUXgPCSCCMWqixTaYQdoGFiMwe6d63o8F8h+oQ6MJCyEWM0VZNM1DcBpDJQteGjCILMJLDwNhzEOGPHeB3P4KQSpCIJk6JIcqybDhLJcS+XdsQtnpnIhACjjJ2MLJuFRu5OZ/R5qeHRik9E3kMYkRslyJZlPidYhpgFCxK33OBaCutepa3NjrFxo8xxnHHB8DERwolPLKDK9uKR14pG7NiSNHjvUuPinEP4Lw9g/AuNm/
|
||||
|
||||
5biPlfPyjm35uJGwxLKHEhJ5EDC21oqktA6s8qvFnpPHNeb2oQReC8VIqUvhIguBGq+lsoEZKEvk7JfFcmZInWy52gcSkKSdRU4OS7qlLNqfHWxjTk4WTBlpYgPBCA1H6KMFosxgThSqIQfQ0QkDNwRKPbs2yhY9xSH3LV+ydjdteFPDV8RS0Tk7YWBeJ1UBoleACYtWIvjryzbvLqCIzhHwfKG/o4aolfHxECu+IKqRgsZD6IjmZ35zS/vC5aYo
|
||||
|
||||
AFSg1CA7a5oIqSC5BoQI2LoF4rA5cnFF1iWWlJXdclaC8wYL9Fg2lYjPoCb5ZS0GYrdHocnkq7gJwlUiNVZjAEk5xwAu0Xq61BiMr1WuLIxm263XlHwb9RtcSjXbhNZ66zX4zFOu/DYlcBqAYstDpYiAIDSFaRqAgTQwxAu4G+OlfxpwR7EBqMQOL950MIB+MQSRrUziaGSjwFIoUSTuBLOrMWYB4gjsLFQ5YLw2PniEGGCAiBx3cWBNgNYcAeK7
|
||||
|
||||
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|
||||
|
||||
iB1znuflFc66lmQ2sBvIgM4KRWZKDuWl1UOXJHgGcCgO0QgRhhWDRqBrouQN5Q5QBaN6SRBlCdnQMEGo43CxtigOYAgdQLdW+gG6DUehci4FTEwVlsnyh0lhKmAgSuxsq/l/iIQUA2CdHCNrksZIhCS5Ir73onUzvxBXokNrJQOsSESAANU0I5GiABNfy7k5kRTN8s7gXxQkJsBJjGeFVso7EnkfXZ3b8rdsibw+eu3GyvA7hPIdzUGfdlO284DN
|
||||
|
||||
8cNXcB6Cpad2oWPdhd/BFf9kU0bRfRq6yC/tD7w8D66oPCz3X5VS0TNKYcSfpYGBHjmkdA38yjzlywzgY8vwHnHujgnoZFgH3t0p3lV4DnmAPxmVQplVURGuCzQfE/UoQZnkQl2UTsw5gcznWPAtT0352+H+CzXALFxFywJIhdTMxT3KFrwkBlQVwoDDxl1oOjA1y1x1wRD1wNyN3wBN0vWlxd1hDdxtztwpykid3wH4MtxFA90aw1x93tFIH92x
|
||||
|
||||
wgCD38FD2VxoLV0LFwGj1j3jzYLQCT0oPFjTwzzeSz3LWaXAGIm0jgDgCVB0QRmKGgGhGyCqAt3hE2AYEIAQAoBaBhXI1uwhRqGCJCPZAgGwBEBRSDCXH0CVG1BewhVfgeycIiNWClGiKyD8LI2e0CMRSo3WmEPCMiPSJiKLi2hPwPxSOKNyAyNiPYyPyqLSJqJiLiKB141P1unKFSKiJiM6EE0vyJiKKaKgFqNLhvxykuDQiGJ6KyCLk4Kom4O4
|
||||
|
||||
GvmmJKNmJYIT3YM8O6NWP0AYIkMEIQFtzCO2OaKyHsIXUqVKVFxWNOP0EGAFCDg0iuIWSbkaJmP0EePcgbnQC/mOOqJGNKJIT6ItAD01CaxpHwAAA0yd6pCoRYokJ4kQgNPDmBwSFQy968fQko7VTh/Ez4XggQnCM4DBHD7cCBk9Hhc8biASsg+jpMIcfjYYwjeQSBWDddPCWTiAlQEAWs0BljOTug2BiAEB7jcBNBggKCOTSASAEjU4WgaQtJSB
|
||||
|
||||
lBOQAAKKcFsXgTEagTUjUgqRIAASg1Dj2UCTBWCqCVNVLp21KtN4BlW1L1MNKpJOM12gTGMd04C5goV8yBP4iYCyVQFThyDFIlO4EMMayIF5NQDDL9A4Bf1DNIGT0wWjxfETwTKMIgFvVIEpFIAHDjIMLTOBEzOzNFPFKMkMKpLsAACsEBsA8h2hYy4BBThSSyQzFFGlPCuRHdGB3I2AaRSSqDvjNRMhazSdGtqsY9djvif9nU5Z3N2ykcDB2hhz
|
||||
|
||||
3SrdWcSIyIGguyEAey+yNEzJwAWlfN5RwgEYywQAywgA
|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,183 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
R0 ^8Fs0OQLO
|
||||
|
||||
RS ^QnSgsORY
|
||||
|
||||
LS ^0KpOtU2S
|
||||
|
||||
## Embedded Files
|
||||
8c89c325f01932b1ea6b5ab190bb4a36212df99a: $$\color{#9C36B5}V_{L_S}$$
|
||||
|
||||
def7c29d8031f630dd7913235d2b34a448557e4d: $$\color{#1971C2}V_0$$
|
||||
|
||||
55be3bc14ff58d958e0f93b4eecf51e1c8983580: $$\color{#F08C02}i$$
|
||||
|
||||
0eec7588357b84a6e134895882b123d8e6e5d2bb: $$\color{#2F9E44}V_{R_S}$$
|
||||
|
||||
8dd0451c5433788bb390deb0dde0ec8097b27edb: $$\color{#343a40}V_{bobine}$$
|
||||
|
||||
0eabec84a6e0457fd947222bde0bab265c32161d: $$\color{#e03131}V_{total}$$
|
||||
|
||||
57e2ddc4017248083fb3142a71ae60d36cd18a0a: $$\color{#e03131}V_{total}$$
|
||||
|
||||
ee2202e4bbc6d1e3a4c88ed96592596aad3f5646: $$\color{#343a40}V_{bobine}$$
|
||||
|
||||
04825015f524ba0d3a5e67e9b1256cbbd8c8f3fb: $$\color{#1971C2}V_0$$
|
||||
|
||||
58b2bf57d8f215dcd06bccdf6d9fec94638cd0b9: $$\color{#F08C02}i$$
|
||||
|
||||
354c0f551db2bba8f82c773ee794b8dfdb7bf06e: $$\color{#e03131}V_{total}$$
|
||||
|
||||
46ab13516241fab23c86b96295c8541d8738770f: $$\color{#9C36B5}V_{L_S}$$
|
||||
|
||||
98e0632e71aa6be16fdeaca9e3071665868bf70d: $$\color{#343a40}V_{bobine}$$
|
||||
|
||||
4ed5148bc3056edbd335824c2c65e2ea4e78be79: $$\color{#2F9E44}V_{R_S}$$
|
||||
|
||||
a0a5873f27c023f5acfbfd112bf261257e856e17: $$\color{#1971C2}V_0$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBGADYEmjoghH0EDihmbgBtcDBQMBKIEm4ITHxEgH1NAHU7fDhnNgBmACtlCgBrAFkoAEUAeVSSyFhECsDsKI5lYLHSzG5n
|
||||
|
||||
HkTkgAZNngBWAHYADn223dP43cT+UphVngAWXe02xPi2nkP4vevIChJ1bjxQ6bbQ8fYATnBm32PHWl2+hUgkgQhGU0kB220iR2PE2bRe4Pi902iT4iIg1gW4lQmx+EGYUFIbB6CAAwmx8GxSBUAMTxBD8/lLSCaXDYHrKJlCDjEdmc7kSRnWZhwXCBbLCiAAM0I+HwAGVYIsJIIPJqGUyWfV/pJuGTxvTGcyEIaYMb0KbynSpWiOOFcmh4nS2Krs
|
||||
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|
||||
```
|
||||
%%
|
||||
BIN
GénieÉlectrique/TD4/attachments/IMG_7432.heic
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BIN
GénieÉlectrique/TD4/attachments/IMG_7432.jpeg
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After Width: | Height: | Size: 1.3 MiB |
BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251006094239.png
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BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251006100509.png
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|
After Width: | Height: | Size: 55 KiB |
BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251006101747.png
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|
After Width: | Height: | Size: 246 KiB |
BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251006111706.png
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|
After Width: | Height: | Size: 45 KiB |
BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251006122351.png
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|
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BIN
GénieÉlectrique/TD4/attachments/Pasted image 20251008135058.png
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|
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67
GénieÉlectrique/TD5/Index.md
Normal file
|
|
@ -0,0 +1,67 @@
|
|||
![[TD_FGE_2025.pdf#page=20]]
|
||||
|
||||
# Exercise 1. Composed Transfer Function
|
||||
![[Pasted image 20251009091732.png]]![[Pasted image 20251009091748.png]]
|
||||
|
||||
1.
|
||||
Étude asymptotique de $\underline{G}=1+j\tau_i\omega$:
|
||||
$G_{dB}=||20log(\underline{G})||=20log(\sqrt{1^2+\tau^2\omega^2})$
|
||||
$\phi=arg(\underline{G})=\arctan(\frac{\tau\omega}{1})$
|
||||
|
||||
Étude en basses fréquences:
|
||||
Pour $\omega\rightarrow∞$:
|
||||
$G_{dB}\approx20log(1)=0$
|
||||
$\phi\approx\arctan{(0)}=0$
|
||||
|
||||
Étude en hautes fréquences:
|
||||
Pour $\omega>>1$
|
||||
$G_{dB}\approx20log(\tau\omega)=20log(\tau)+20log(\omega)$
|
||||
$\phi\approx\arctan{(∞)}=\frac{\pi}{2}$
|
||||
|
||||
On cherche le croisement des deux asymptotes.
|
||||
On cherche donc $20log(\tau\omega)=0$, ce qui implique que $\tau\omega=1$ et par conséquent que $\omega=\frac{1}{\tau}$.
|
||||
Alors, $G_{dB}(\frac{1}{\tau})20log(\sqrt{2})\approx3$
|
||||
$\phi(\frac{1}{\tau})=\arctan{(1)}=\frac{\pi}{4}$
|
||||
|
||||
![[Drawing 2025-10-09 09.27.54.excalidraw]]
|
||||
|
||||
2.
|
||||
$G_2=\frac{1}{G}$, donc
|
||||
$G_{dB_2}=20log(1)-20log(|\underline{G}|)=-G_{dB}$
|
||||
|
||||
$\phi_2=-\phi$
|
||||
|
||||
![[Drawing 2025-10-09 09.53.13.excalidraw]]
|
||||
|
||||
3.
|
||||
$G_{tot}=\frac{(1+j\tau_1\omega)(1+j\tau_2\omega)}{(1+j\tau_3\omega)(1+j\tau_4\omega)}=\frac{G_1G_2}{G_3G_4}$
|
||||
|
||||
# Exercise 2: .Bandpass filter 2nd order
|
||||
|
||||
![[Pasted image 20251009105118.png]]
|
||||
|
||||
1.
|
||||
![[Pasted image 20251009105236.png]]
|
||||
|
||||
On cherche $\underline{V_S}$.
|
||||
|
||||
$Z_{eq}$ correspond à $L$ et $C$, donc $\frac{1}{Z_{eq}}=\frac{1}{Z_L}+\frac{1}{Z_C}=jC\omega-j\frac{1}{L\omega}$
|
||||
Par le pont diviseur, $\underline{V_S}=\frac{Z_{eq}}{R+Z_{eq}}V_e=\frac{1}{\frac{R}{Z_{eq}+1}}V_e$
|
||||
$\implies H=\frac{V_S}{V_e}=\frac{1}{1+jR(C\omega-\frac{1}{L\omega})}$
|
||||
Je cherche $\alpha$ et $\beta$ tel que $C\omega-\frac{1}{L\omega}=\alpha(\frac{\omega}{\beta}-\frac{\beta}{\omega})$
|
||||
$\frac{\alpha}{\beta}=C$ et $\alpha\beta=\frac{1}{L}\implies\begin{cases} \alpha=\beta C\implies\alpha=C\sqrt{\frac{1}{LC}}=\sqrt{\frac{C}{L}} \\ \beta^2C=\frac{1}{L}\implies\beta=\sqrt{\frac{1}{LC}} \end{cases}$
|
||||
|
||||
|
||||
Donc $H(j\omega)=\frac{1}{1+jR\sqrt{\frac{C}{L}}(\frac{\omega}{\sqrt{\frac{1}{LC}}}-\frac{\sqrt{\frac{1}{LC}}}{\omega})}$
|
||||
|
||||
# Exercise 3:
|
||||
![[Pasted image 20251009115819.png]]
|
||||
## Part I: Impedance analyses
|
||||
1.
|
||||
$Z_{eq}=\frac{RjL\omega}{R+jL\omega}+\frac{\frac{R}{jC\omega}}{R+\frac{1}{jC\omega}}=$
|
||||
![[IMG_7440.jpeg]]
|
||||
|
||||
2.
|
||||
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
383d65aa2a52a07a31727ced72b99a4a026f9067: $$G_{dB}$$
|
||||
|
||||
acd1800c42346192175acf7183643ef2a6dff614: $$\phi$$
|
||||
|
||||
359c7b9d494f03fc07d1931f1ca8e042626674dd: $$\color{red}\frac{1}{\tau}$$
|
||||
|
||||
4f89de5548103229895bfdabab304099d2883258: $$\color{red}\frac{1}{\tau}$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
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|
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
```
|
||||
%%
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
383d65aa2a52a07a31727ced72b99a4a026f9067: $$G_{dB}$$
|
||||
|
||||
acd1800c42346192175acf7183643ef2a6dff614: $$\phi$$
|
||||
|
||||
359c7b9d494f03fc07d1931f1ca8e042626674dd: $$\color{red}\frac{1}{\tau}$$
|
||||
|
||||
4f89de5548103229895bfdabab304099d2883258: $$\color{red}\frac{1}{\tau}$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
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||||
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||||
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||||
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|
||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
BIN
GénieÉlectrique/TD5/attachments/IMG_7440.heic
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BIN
GénieÉlectrique/TD5/attachments/IMG_7440.jpeg
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|
After Width: | Height: | Size: 783 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009091732.png
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|
After Width: | Height: | Size: 130 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009091748.png
Normal file
|
After Width: | Height: | Size: 25 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009105118.png
Normal file
|
After Width: | Height: | Size: 461 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009105236.png
Normal file
|
After Width: | Height: | Size: 41 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009115819.png
Normal file
|
After Width: | Height: | Size: 680 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009122017.png
Normal file
|
After Width: | Height: | Size: 680 KiB |
BIN
GénieÉlectrique/TD5/attachments/Pasted image 20251009122026.png
Normal file
|
After Width: | Height: | Size: 680 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006090339.png
Normal file
|
After Width: | Height: | Size: 363 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006093323.png
Normal file
|
After Width: | Height: | Size: 334 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006093350.png
Normal file
|
After Width: | Height: | Size: 634 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006093856.png
Normal file
|
After Width: | Height: | Size: 345 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006093952.png
Normal file
|
After Width: | Height: | Size: 406 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251006094004.png
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|
After Width: | Height: | Size: 575 KiB |
BIN
GénieÉlectrique/attachments/Pasted image 20251009085622.png
Normal file
|
After Width: | Height: | Size: 242 KiB |
141
ModélisationEnMeca/Drawing 2025-10-01 14.27.18.excalidraw.md
Normal file
|
|
@ -0,0 +1,141 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
6a262ccbae353e8cc05b0faf6160875fddb93275: $$\overrightarrow{e_y}$$
|
||||
|
||||
7fdb0c24b187f7d76522a9c4d485a7425759d17e: $$I$$
|
||||
|
||||
1e089744421e86f53df500b70e37ec1831d9c1f5: $$\overrightarrow{e_x}$$
|
||||
|
||||
6aa0cfeefb27ef8536ae8116afe5b050994abc34: $$\overrightarrow{e_r}$$
|
||||
|
||||
685c1767b0522fdc5f185927bd8de5104266e352: $$\color{red}i$$
|
||||
|
||||
521dc4d5162a4746ca7ba548126ef74c6fa207ff: $$\color{red}e$$
|
||||
|
||||
bcb7b78cd00504331b57a5710f16ed64fb98eaf7: $$J$$
|
||||
|
||||
ca3832c943862ce2128ea4860529dcd5a1553467: $$\color{blue}A$$
|
||||
|
||||
d52cb46dd0d13af67043b52511647cec78d2c75f: $$bi$$
|
||||
|
||||
bab93bdeb4c8624eeda96c4eab791df06a61e16c: $$\color{red}bi$$
|
||||
|
||||
49585cb74ff6727096eea73a3eb3afdeb50fb3fc: $$C$$
|
||||
|
||||
a953b785a61514b2de4dcb91ff99f6691405e474: $$\overrightarrow{e_\theta}$$
|
||||
|
||||
58cd790aed46987ebcfd2457d056c93d1bac0343: $$O$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
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|
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|
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|
||||
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|
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|
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
133
ModélisationEnMeca/Drawing 2025-10-02 09.54.32.excalidraw.md
Normal file
|
|
@ -0,0 +1,133 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
09a164dcad95a326d155dcba78f412fcdf60a9ef: $$\color{red}\overrightarrow{j}$$
|
||||
|
||||
092dd01314566fc0cf41be707360e9bb8b56e0cf: $$\color{red}\overrightarrow{i}$$
|
||||
|
||||
95747095a5e08af685fdf95159a25b3e4e62cc18: $$\color{red}\overrightarrow{F_{N1}}$$
|
||||
|
||||
06ceb09334ec479a6d0575deb1653daa2af1ba52: $$\color{red}\overrightarrow{F_{N2}}$$
|
||||
|
||||
96545cdb9e24cc91564b055942f45c57256f412e: $$\color{orange}\overrightarrow{F_{T1}}$$
|
||||
|
||||
a842e24e0aa6b190dc49313dd3bca13d31c14df7: $$\color{orange}\overrightarrow{F_{T2}}$$
|
||||
|
||||
4ea08391950e45a3369e4b21af22ce969cda61a7: $$\color{purple}\overrightarrow{p}$$
|
||||
|
||||
5a009ab579b55495433ed0aedaab35936dc45921: $$\alpha$$
|
||||
|
||||
efc680781f725614cb59983ceb8a2e9010330d10: $$\color{blue}I$$
|
||||
|
||||
b28f47b6021dea66e6ac89e80c3a163ce3df26a1: $$\color{blue}J$$
|
||||
|
||||
fcd48c9f21ed956313606096cc8d14d4bdb2aa45: $$\color{blue}H$$
|
||||
|
||||
88be5f7d962298e8d6f162f82b78765a4063ce1b: $$\color{blue}G$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
2o6ad82qUH9sYCBUat+AOreTBQlhBgg68ZlAK25ZQADAYWp1Lot1WSi1xBgI0JkAl1w5Vxa+AyBLv52C6Il4ALJLQvCCkwom7YIAA===
|
||||
```
|
||||
%%
|
||||
89
ModélisationEnMeca/Drawing 2025-10-02 10.15.02.excalidraw.md
Normal file
|
|
@ -0,0 +1,89 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
b060c72e4479d8d99037b3bfe7a59fc8ac66af63: $$\color{red}\theta$$
|
||||
|
||||
434e92c3fc83d47bfbc23cc011f37feb3dfd4c49: $$\pi$$
|
||||
|
||||
3c821b85ce03f5a1e4e80af9b7b226532ea9f70f: $$\alpha$$
|
||||
|
||||
3466c5e409ca3caa2f68e17dcd0fc445fb0090c0: $$\alpha$$
|
||||
|
||||
26f6a29fa97ffac5b09861594a652d8744b4c619: $$\frac{\pi}{2}-\alpha$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
|
||||
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||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
57
ModélisationEnMeca/Drawing 2025-10-02 11.54.47.excalidraw.md
Normal file
|
|
@ -0,0 +1,57 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
## Embedded Files
|
||||
edcc6bc64370a2abcfa36ee0836eeea684899aa8: $$\overrightarrow{F_T}$$
|
||||
|
||||
09b32b2f343cfc9984dcaa57a763e8edd191131b: $$\overrightarrow{F_N}$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
```
|
||||
%%
|
||||
119
ModélisationEnMeca/Drawing 2025-10-02 12.14.37.excalidraw.md
Normal file
|
|
@ -0,0 +1,119 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
|
||||
|
||||
|
||||
# Excalidraw Data
|
||||
|
||||
## Text Elements
|
||||
G ^a64nsYrJ
|
||||
|
||||
## Embedded Files
|
||||
b98018b905b5ee15ac7c32c42a3719f3f745b3c5: $$\overrightarrow{x_0}$$
|
||||
|
||||
a0a29d6e61781ef232c4f2cb1e7bec347ab88142: $$\overrightarrow{y_0}$$
|
||||
|
||||
a42d190bde77f8aadf045842fdf4730a99db50c8: $$\overrightarrow{x_1}$$
|
||||
|
||||
c88aa21145c5cc413113eaeabfaa71659633ac55: $$\overrightarrow{y_1}$$
|
||||
|
||||
a0080036c4c28a770da1e2e61015dcfb12e8a681: $$O_0$$
|
||||
|
||||
b25418d5c33c03057113385a6b94b00113e21229: $$\theta(+)$$
|
||||
|
||||
d1b127a8fe03cea322af5e9441038a3e1e79b147: $$\color{red}\overrightarrow{p}$$
|
||||
|
||||
c671c06e0c71806be6ad8bce161837c754d4f40b: $$\color{#9C36B5}\overrightarrow{R_y}$$
|
||||
|
||||
5f2fbdbc02c52a70a2975d035f9941fe71855286: $$\color{#9C36B5}\overrightarrow{R_x}$$
|
||||
|
||||
%%
|
||||
## Drawing
|
||||
```compressed-json
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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|
||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
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||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
SkSBJW+T+RQCBTBShThSRTRSAbFhql5U9Y3RIwvDnCaLdGfDM56rgzkU3QaK7ADknYHLXXPDWuoH/RjhPUlGGp/0uv76Ei7DsNtMa7M0HzNijM35xLiVDEQAMh7D6H4veFRvTOwfL1xnzOJtbOaXb2A5psb1E2QAk2Fnk0oEnEFty1X3Fuwvgu0vlu4BNBVvnE1sGgZ6nOAq/BUHByHKOWRwGiExdtXKgg2rHBmLf1fNEblUK3Au0cQATs+V/E74
|
||||
|
||||
xQPJjRzu5YLvoPS2y7YNoqK4YpMMK4LyhwmJfvxYHy/uKaaq1Mgd+XEzNjmOnyWOXzWO2PF5Px+NBMiqu5ip/ye5Sre6gLyoQIB4qpB4CkaptHNjdpPSGNoyqFdM8Fx6oBtreseIj1XCbBseBPCledxPCESpIUoVoUYWB6ebqqLxXDdT83cdJB4JQix5hFJCON2oC2aL9T+Zsfuc+rRMBP5aF6FZhqJFxPV6Ltv1rXoBZQ5T5SFTFS3jkhlQVRVQ
|
||||
|
||||
1T7UV7Fb+j5N3Qwjdpbe5FnBbYFF9TtqXDXsXARLdrvuLwuKfDGr9Z1z4K90H4+jJBxbvBGPyZ9Sts0TqtQ04chkIeNyaFTNRloezMYcJubOEfQdaV4frNYeQ/EdGV7NkdU2QATlFuVUltwsVDe24C5RMfuyu5E71v01dS+b1hXs/0EyCelgUpTr3I2ISecFSekZQNfJzmQDyfwOKdDRNkq1Y8adQsYOQBYMiHMOTz6ciNi9lC/RLyGo3d6p3dhx
|
||||
|
||||
lBPftpryveDTvfBwOddxW7Occo2N25Y9ddO65eRM852b+cyqBfOb+5QKhdlc36o9JdgiryifyZa6NzeOpSZ7Jb+NG+hM9dY9RP9cxOV7DdlaJNjfJMQWSSJBsDitwAJ07A3gwBQCnD0BQDisIDoTKA7CkCXhKuDcasfQmLHdbBemNqby3U3TiOhw+kNxnDWqGtMU/fbYAcNKtHUqrZ9r7adqQet8nohkICYJlpA+yUg9xto1r0LM/bYdQ+4fgG73
|
||||
|
||||
xJw+VKZuk1Qe5uU0I7/Ps+bSa2ydltTVZNmV47MeE7gaddWU4sOKdpXANnybU8ggnCNojifdBXfNS2rkQAjsycImc/0a+VEYA2T7qp1QbLlNOX/EXgJkM54MJeNLHFEJjJSd98E3fbFghk7Ta9RouvG3IZjvj+9zMfvWTtl0syycuuYTAbkQL65+pwmq3IbmbxG4QCKsYAKrFywkCYA4AIUKUMwFwBSh4IRgFoBwHXA3h8AzgBOoqGqDH8kiapOY
|
||||
|
||||
IQAWDF9a+CGd4COEhAbAEMU+H6OTlhigdd41wbVDkTOAXcMQAcbEK40RCusuw4IYwbCFMFfdfWsSQfjPWH5uI3EY/RerB0CCr8tyiZAmtejn4npVm56WHhD08FEcCyiPHNsWS34UcAWKJWqgiUP6Zhgw+PU3vFBp6X9AUFKbBGYgGYNlzEhrbmoA0Pyhxr2+CBLo8g/5Dtv+rPSjOjw56vNJ2j0PqGvAqJ89ZOAvPhEuwyiOQWM+SG8KQGGCF8Xs
|
||||
|
||||
WAVetqXvajhYY3aJGLvE+Ag1YQ6g5wIjCA4nAciCGUcA4gZ7+gW+/sF4BTj1Y0pz8ujV0uYN4A+tLQ/rXqIGz1QfEwUf7X7o4JH4uCX8wPWGhAA8GYdghONaHov3w6z94eYQ4+qRxLLkc304VXfubBo7xCceAwk/hWROZVkuoWwfQY0IbK3t/6TlQoahjHAc03+4DX5pAyBbQMse//X4o0L1TvRYkoA/npC2hbFhhhVQAvraEoCng6REgBkXMU4B
|
||||
|
||||
QB5QhAIwDT1iQeZcguUC2LKG+iojAIwwiyEQGUBRxmUCAKUCMLbZQBzABACUSiGlFQBxSwRDkbgDTBMANyuWOkCiDTAEBmRmAA/BADZH+hcAQgdUQnXCDcjSwpIIQBVUgBjQEA1QY4YvBuCdCEqEgG8MMFIDBgjAQgYiOuEGHqlUix7fCraV0RhIYo0jbXJ92OKaC4YeQ9RPsA1y9RbhAIF6h4wuADYoQ+JI4Fth6ZoAzEA9QxsznJwxQdE/pb7q
|
||||
|
||||
gHsHVIJmUlJ4ePxeHod426NGfhIDUrLN1mAQlmsDg+G7EQMLNTfgc0PpHM3OOBJjA4hRH5CAG9zKrgDAQxIwXmPZBTo0ObB6ocRFQvEaj1BG1CqhBItnoeMpFtDqRQvPfpj1k7bkNo+5e2psGmpSgnBYgYwmvB4FaEhoHNM8ikHFDQhySWwClm7V/LjUfGd9RyJmiqT8kmWC1QOqy2WrhEo+rA9ADeFOCnhqgkkXAGwHoBhjDqxfcYbVzjGfAvxj
|
||||
|
||||
ieYaCGrS9QCYndTtP1H7SbCz0qie6Nol+A3AOKTaJou3z9Zto3oiMYOBfmiwsZ++9YsNjPUmYti3BbY0Hh2On4g4exR1fwXjSCE+DcyIQ14f8PDCjjIh447ZpOKN44FPEVwUUW2z44pwK6xkzDN214DbdmCHNNcXAwAF1wqCqeMyeUMk6MDohu/H/oSPlqtCES7Qy8eCLiEnNbxVQbAKCgxa+Q3yr7fFpbToRqExAkIbVI2GwA9R1gxAdYPeUPJA
|
||||
|
||||
TR4P5alhNS5J0tHI6ERllUGZbqg2WsFZgfXmQkQAOApwX8NUD6DMAYAbAXCbkw1bGoqKwnXeENkBpkTxhTGVnEEiDY2CthjE4lkRW6iNwsQhrEsQ8zBDEsimLGZwbvFrF2CRJsHUMs2JQ7PCck7Yqfl4PXqqUlm8k0AopK3or92kWbTYkjyBEo81J7yWEblnhH8dxwW2a5t6Cr5c0Fxlk0TscGRhfF6hG4g+NixjiBVcRzPP5hfU8nVCdOOmYqn5
|
||||
|
||||
IvFadqOQU3LCFIkCJAiSdtF8hix4C2EeAPVLEsah6jEBMEmMtsvEGfHXUUBBqbKTgypY/lPadHKag0BKn+FYJLLcoBVJDpVT4KNU4iL+GurkgcIUoNqRGILo3QNcmqWDFCCdYR4DBd7fCsDFhgV9HoTYbou+3CRtEXojJWsjajUEcS/qe2LqfWGNQttDgjiQSRDVErjNRJ20qcpGVbF7SpJB0+FkdO7EnTPhC/G6RdKHEGVrpazCIafVLIwjaaz0
|
||||
|
||||
nAv9JNRoiTJqBeceiPubTTG4A2MocSOFxYi8Eg0Qdh5EdHOiAwB4kFviKEIniC5LohGfOyRlf9ApeovPOjPQAZSUx6UqUIcFhBElCWewBAJ0R4HtRsA+5eIDwP1a9QbUyhOmaNUZk0tsehU86G5j5TQTSpHM8qQhI5aVZwApsGiHADgCKgAUuXaAEiGyBVBJRaIJYAwEIAIAKAL8R2RJJyQMgpQN82+eyAgBwIQIf8OcPoEVAw0r5Tg0fkfMfk7p
|
||||
|
||||
gwL88+QvRjbuD5w38kQL/Jfm5RvB6bJNg/LAXPysgb8lNjDy5lwLbML8xBVAWUkZtIAP8+BfoATrqSocsCp+WgqyBPgtJZ9YoMQvAVZBcoHIwUVfHwAijQFJCqAH/NoUciuRPIg0FTGoV4KTRPqSUdKOCByj75uC0ha/ID4h8OMfCiReuCoEhoaBXWNbjgtQVsKX5waU8GqTZhiK1F7C/QLlAmQELLQfODUGKTlD/hSxL0VXo4lYmSNVEn0MxWSD
|
||||
|
||||
lA3gUMY4BIPBgQyU4HEEIIchACMBsADApvBgAQCdGAdEYVtFRqlFkXqKsgBCx6fjgekCh75vIEgFwt5FHzUlxARUAgDCKOKslDQNgPbHkV0lggeIvOSQGexrQX4NIDaKQGUCcgAAFGnGoC8BuorSlpfWJMQABKdULaOUDJhaIyrBpbgGaUa4Ol4y3gJMuaa9LJSMSjBQgHIWKjOAxzT1FeOyC2j0wpAEgWtByClK/YOc4IvMG4CHKjQHAVHCctIB
|
||||
|
||||
OitY1o10ZcuuVGhe8pASkKQFGAXK0Apy/0E8peUlLNAZS+5UwOiV2AcI1JPIPKHOVwBClxS85X8ogY0RVWhARgKeECWKsXcgENUmEGCAIqTkwReBOqP0BaKvYiM8AYL2RmVUDA8oTINiqjg0jOMZ8CyAiqRUorKp5YcAExE2g1VCwrK8sEAA
|
||||
```
|
||||
%%
|
||||
|
|
@ -80,6 +80,8 @@ $\overrightarrow{AB}=b(\cos{\alpha_2}\overrightarrow{x}+\sin{\alpha_2}\overright
|
|||
![[MG.pdf#page=11]]
|
||||
|
||||
# Cinématique
|
||||
Formule Babar = ![[Pasted image 20251001143754.png]]
|
||||
|
||||
$\overrightarrow{V}_{M\in S_s/R_0}=\frac{d}{dt}\overrightarrow{O_0M}(t)|_{B_0}$
|
||||
|
||||
![[TD-Ven. 26 septembre 2025|1000]]
|
||||
|
|
@ -103,3 +105,236 @@ $\Omega_{1/0}=\dot{\theta} \overrightarrow{z}$
|
|||
$xyzxyz$
|
||||
Pour calculer le produit vectoriel de $x$ et $y$, on prend le suivant ($z$)
|
||||
Vers la droite, c'est positif ($x • y = z$) et vers la gauche c'est négatif ($y • x = -z$)
|
||||
|
||||
|
||||
|
||||
$\overrightarrow{v}_{O_1}\in{1/0}=\frac{d}{dt}\overrightarrow{O_0O_1}|_O$
|
||||
$\overrightarrow{O_0O_1}=\overrightarrow{O_0I}+\overrightarrow{IO_1}=X\overrightarrow{x_0}+R\overrightarrow{y_0}$
|
||||
$\frac{d}{dt}\times X\overrightarrow{x_0}+R\overrightarrow{y_0}|_O=\dot{X}\overrightarrow{x_0}\times\frac{d\overrightarrow{x_0}}{dt}|_O+\dot{R}\overrightarrow{y_0}+R\frac{d\overrightarrow{y_0}}{dt}|_O=\dot{X}\overrightarrow{x_0}$
|
||||
$\overrightarrow{V_{I\in{1/0}}}=\overrightarrow{V_{O_1\in{1/0}}}+\overrightarrow{IO_1}\overrightarrow{\Omega_{1/0}}$
|
||||
$=\dot{X}\overrightarrow{x_0}+R\dot{\theta}\overrightarrow{x_0}=(\dot{X}+R\dot{\theta})\overrightarrow{x_0}$
|
||||
|
||||
Roulement à bille
|
||||
![[Drawing 2025-10-01 14.27.18.excalidraw]]
|
||||
Repère fix ($0$) $\rightarrow (\overrightarrow{e_x}, \overrightarrow{e_y})$
|
||||
Repère se déplaçant avec la bille $\rightarrow (\overrightarrow{e_\theta}, \overrightarrow{e_r})$
|
||||
Vitesse de la bague intérieure par rapport à $0$: $\Omega_{i/0}=\dot{\theta}_i\overrightarrow{e_z}$
|
||||
Vitesse de la bague extérieure par rapport à $0$: $\Omega_{e/0}=\dot{\theta}_e\overrightarrow{e_z}$
|
||||
|
||||
Calculer la vitesse du point $I\in{\color{red}i}$ Par rapport à $O$:
|
||||
$\overrightarrow{V_{I\in{i/0}}}=\overrightarrow{V_{0\in{i/0}}}+\overrightarrow{IO_1}\overrightarrow{\Omega_{i/0}}$
|
||||
$=\overrightarrow{0}-r_i\overrightarrow{e_r}\wedge\dot{\theta_i}\overrightarrow{e_z}$
|
||||
$=-r_i\dot{\theta_i}\overrightarrow{e_r}\wedge\overrightarrow{e_z}=r_i\dot{\theta_i}\overrightarrow{e_\theta}$
|
||||
|
||||
$\overrightarrow{V_{J\in{e/0}}}=r_e\dot{\theta_e}\overrightarrow{e_\theta}$
|
||||
|
||||
$\overrightarrow{V_{C\in{bi/0}}}=\overrightarrow{V_{I\in{bi/0}}}+\overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}}$
|
||||
$\overrightarrow{V_{C\in{bi/0}}}=\overrightarrow{V_{J\in{bi/0}}}+\overrightarrow{CJ}\wedge\overrightarrow{\Omega_{bi/0}}=\overrightarrow{V_{J\in{bi/0}}}-\overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}}$
|
||||
|
||||
$2\overrightarrow{V_{C\in{bi/0}}}=\overrightarrow{V_{I\in{bi/0}}}+\overrightarrow{V_{J\in{bi/0}}}$
|
||||
|
||||
$I \in bi \quad I \in i$
|
||||
|
||||
pas de glissement en $I$ :
|
||||
|
||||
$\overrightarrow{V_{I \in bi/i}} = \overrightarrow{V_{I \in bi/0}} + \overrightarrow{V_{I \in 0/i}} = \overrightarrow{0}$
|
||||
|
||||
$\overrightarrow{V_{I \in bi/0}} = - \overrightarrow{V_{I \in 0/i}} = \overrightarrow{V_{I \in ci/0}} = a \, \dot{\theta}_i \, \overrightarrow{e_\theta}$
|
||||
|
||||
$\overrightarrow{V_{J \in bi/0}} = \overrightarrow{V_{J \in ee/0}} = R_e \, \dot{\theta}_e \, \overrightarrow{e_\theta}$
|
||||
|
||||
$2 \, \overrightarrow{V_{C \in bi/0}} = \overrightarrow{V_{I \in bi/0}} + \overrightarrow{V_{J \in bi/0}}$
|
||||
|
||||
$\overrightarrow{V_{C \in bi/0}} = \tfrac{1}{2} \big( n_i \, \dot{\theta}_i + n_e \, \dot{\theta}_e \big) \, \overrightarrow{e_\theta}$
|
||||
|
||||
$\overrightarrow{V_{I\in{bi/0}}}-\overrightarrow{V_{J\in{bi/0}}}+\overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}} + \overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}}$
|
||||
|
||||
Or, $\overrightarrow{A}\wedge\overrightarrow{X}=\overrightarrow{B}$ $\implies\boxed{\overrightarrow{X}=\overrightarrow{B}\wedge\frac{\overrightarrow{A}}{\overrightarrow{A}•\overrightarrow{A}}+\lambda\overrightarrow{A}}$
|
||||
|
||||
$2\overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}}=\overrightarrow{V_{J\in{bi/0}}}-\overrightarrow{V_{I\in{bi/0}}}$
|
||||
$2\overrightarrow{CI}\wedge\overrightarrow{\Omega_{bi/0}}=R_e \, \dot{\theta}_e \, \overrightarrow{e_\theta}-R_i \, \dot{\theta}_i \, \overrightarrow{e_\theta}$
|
||||
$$
|
||||
\overrightarrow{\Omega_{bi/0}}=
|
||||
(r_e \, \dot{\theta}_e
|
||||
-r_i \, \dot{\theta}_i)\overrightarrow{e_\theta}
|
||||
\wedge
|
||||
\frac
|
||||
{
|
||||
2\overrightarrow{CI}
|
||||
}
|
||||
{
|
||||
2\overrightarrow{CI}•2\overrightarrow{CI}
|
||||
}
|
||||
+\lambda2\overrightarrow{CI}
|
||||
$$
|
||||
$$
|
||||
\overrightarrow{\Omega_{bi/0}}=
|
||||
(r_e \, \dot{\theta}_e
|
||||
-r_i \, \dot{\theta}_i)\overrightarrow{e_\theta}
|
||||
\wedge
|
||||
\frac
|
||||
{
|
||||
-(r_e-r_i)\overrightarrow{e_r}
|
||||
}
|
||||
{
|
||||
(r_e-r_i)^2
|
||||
}
|
||||
+\lambda(r_i-r_e)\overrightarrow{e_r}
|
||||
$$
|
||||
$$
|
||||
\overrightarrow{\Omega_{bi/0}}=
|
||||
\frac
|
||||
{
|
||||
-(r_e \, \dot{\theta}_e
|
||||
-r_i \, \dot{\theta}_i)
|
||||
}
|
||||
{
|
||||
r_i-r_e
|
||||
}
|
||||
\overrightarrow{e_\theta}
|
||||
\wedge
|
||||
\overrightarrow{e_r}
|
||||
+\lambda(r_i-r_e)\overrightarrow{e_r}
|
||||
$$
|
||||
$$
|
||||
\overrightarrow{\Omega_{bi/0}}=
|
||||
\frac
|
||||
{
|
||||
r_i \, \dot{\theta}_i
|
||||
-r_e \, \dot{\theta}_e
|
||||
}
|
||||
{
|
||||
r_i-r_e
|
||||
}
|
||||
\overrightarrow{e_z}
|
||||
+\lambda(r_i-r_e)\overrightarrow{e_r}
|
||||
$$
|
||||
|
||||
# Statique
|
||||
À savoir:
|
||||
$\cos(-\alpha)=\cos(\alpha)$, et $\sin(-\alpha)=-\sin(\alpha)$
|
||||
|
||||
![[Drawing 2025-10-02 09.54.32.excalidraw|1000]]
|
||||
|
||||
Avec $\color{#AC46C5}\overrightarrow{p}$ le poids, $\color{#8888FF}I$ et $\color{#8888FF}J$ les points de contact entre le chariot et la pente.
|
||||
Avec $m$ la masse du chariot, et $g$ la constante gravitationnelle.
|
||||
|
||||
$\overrightarrow{IJ}=a\overrightarrow{i}$
|
||||
$\overrightarrow{HG}=h\overrightarrow{j}$
|
||||
$\overrightarrow{IG}=\overrightarrow{IH}+\overrightarrow{HG}=\frac{a}{2}\overrightarrow{i}+h\overrightarrow{j}$
|
||||
|
||||
$\color{red}\overrightarrow{F_{N1}}\color{white}=F_{N1}\color{red}\overrightarrow{j}$
|
||||
$\color{orange}\overrightarrow{F_{T1}}\color{white}=F_{T1}\color{red}\overrightarrow{i}$
|
||||
$\color{red}\overrightarrow{F_{N2}}\color{white}=F_{N2}\color{red}\overrightarrow{j}$
|
||||
$\color{orange}\overrightarrow{F_{T2}}\color{white}=F_{T2}\color{red}\overrightarrow{i}$
|
||||
|
||||
![[Drawing 2025-10-02 10.15.02.excalidraw|250]]
|
||||
$\color{red}\theta\color{white}=-\alpha+\frac{3\pi}{2}-2\pi=-(\alpha+\frac{\pi}{2})$
|
||||
$\cos{\color{red}\theta}=\cos{(-(\alpha+\frac{\pi}{2}))}=\cos{(\alpha+\frac{\pi}{2})}=-\sin{\alpha}$
|
||||
$\sin{\color{red}\theta}=\sin{(-(\alpha+\frac{\pi}{2}))}=-\sin{(\alpha+\frac{\pi}{2})}=-\cos{\alpha}$
|
||||
|
||||
$\color{#AC46C5}\overrightarrow{p}\color{white}=mg(\cos{\color{red}\theta}\color{red}\overrightarrow{i}\color{white}+\sin{\color{red}\theta}\color{red}\overrightarrow{j}\color{white})$
|
||||
$\color{#AC46C5}\overrightarrow{p}\color{white}=mg(-\sin{\alpha}\color{red}\overrightarrow{i}\color{white}-\cos{\alpha}\color{red}\overrightarrow{j}\color{white})$
|
||||
$\color{#AC46C5}\overrightarrow{p}\color{white}=-mg(\sin{\alpha}\color{red}\overrightarrow{i}\color{white}+\cos{\alpha}\color{red}\overrightarrow{j}\color{white})$
|
||||
|
||||
$$
|
||||
_I\cases{F_{N_1}\overrightarrow{j}+F_{T_1}\overrightarrow{i} \\ \overrightarrow{0}}
|
||||
+ _J\cases{
|
||||
F_{N_2}\overrightarrow{j}+F_{T_2}\overrightarrow{i} \\
|
||||
\overrightarrow{0}
|
||||
}
|
||||
+ _G\cases{
|
||||
-mg(\sin{\alpha}\color{red}\overrightarrow{i}\color{white}+\cos{\alpha}\color{red}\overrightarrow{j}\color{white}) \\
|
||||
\overrightarrow{0}
|
||||
}
|
||||
=\cases{\overrightarrow{0} \\ \overrightarrow{0}}
|
||||
$$
|
||||
|
||||
Comment transporter un torseur:
|
||||
$$
|
||||
_I\cases{
|
||||
\overrightarrow{R} \\
|
||||
\overrightarrow{O}=\overrightarrow{M_{\overrightarrow{R}/I}}
|
||||
}$$ $$
|
||||
_M\cases{
|
||||
\overrightarrow{R} \\
|
||||
\overrightarrow{M_{\overrightarrow{R}/M}} = \overrightarrow{M_{\overrightarrow{R}/I}} +\overrightarrow{MI}\wedge\overrightarrow{R}
|
||||
}
|
||||
$$
|
||||
$$
|
||||
_I\cases{
|
||||
\overrightarrow{F_1} \\
|
||||
\overrightarrow{M_{\overrightarrow{F_1}/I}}
|
||||
}
|
||||
+_J\cases{
|
||||
\overrightarrow{F_2} \\
|
||||
\overrightarrow{M_{\overrightarrow{F_2}/J}}
|
||||
}
|
||||
+_G\cases{
|
||||
\overrightarrow{p} \\
|
||||
\overrightarrow{0}
|
||||
}
|
||||
=_I\cases{
|
||||
\overrightarrow{F_1} \\
|
||||
\overrightarrow{M_{\overrightarrow{F_1}/I}}
|
||||
}
|
||||
+_I\cases{
|
||||
\overrightarrow{F_2} \\
|
||||
\overrightarrow{M_{\overrightarrow{F_2}/I}}
|
||||
}
|
||||
+_I\cases{
|
||||
\overrightarrow{p} \\
|
||||
\overrightarrow{M_{\overrightarrow{p}/I}}
|
||||
}
|
||||
$$
|
||||
Avec $\overrightarrow{M_{\overrightarrow{F_2}/I}} = \overrightarrow{M_{\overrightarrow{F_2}/J}} + \overrightarrow{IJ}\wedge\overrightarrow{F_2}$ , avec $\overrightarrow{M_{\overrightarrow{F_2}/J}}=\overrightarrow{0}$. Donc,
|
||||
$\overrightarrow{M_{\overrightarrow{F_2}/I}} = \overrightarrow{IJ}\wedge(F_{N_2}\overrightarrow{j}+F_{T_2}\overrightarrow{i})=a\overrightarrow{i}\wedge(F_{N_2}\overrightarrow{j}+F_{T_2}\overrightarrow{i})=aF_{N2}k$ (car $i\wedge j \rightarrow k$)
|
||||
|
||||
Avec $\overrightarrow{M_{\overrightarrow{p}/I}} =\overrightarrow{M_{\overrightarrow{p}/G}} + \overrightarrow{IG}\wedge\overrightarrow{p}=0 + (\frac{a}{2}\overrightarrow{i}+h\overrightarrow{j})\wedge(-mg(\sin{\alpha}\overrightarrow{i}+\cos{\alpha}\overrightarrow{j}))=mg(-\frac{a}{2}\cos{\alpha}+h\sin{\alpha})T_2$
|
||||
|
||||
Quand il y a frottement, On a ![[Drawing 2025-10-02 11.54.47.excalidraw]] $||\overrightarrow{F_T}||=\lambda_f||\overrightarrow{F_N}||$
|
||||
$||\overrightarrow{F_T}||≤\lambda_a||\overrightarrow{F_N}||$
|
||||
|
||||
$F_{N2}=0$
|
||||
$-\frac{a}{2}\cos{\alpha_c}+h\sin{\alpha_c}=0$
|
||||
$h\sin{\alpha_c}=\frac{a}{2}\cos{\alpha_c}$
|
||||
$\tan{\alpha_c}=\frac{a}{2h}$
|
||||
$\boxed{\alpha=\tan^{-1}{(\frac{a}{2h})}}$
|
||||
|
||||
|
||||
![[Drawing 2025-10-02 12.14.37.excalidraw]]
|
||||
|
||||
Les translations bloquées génèrent des forces,
|
||||
les rotations bloquées génèrent des moments.
|
||||
|
||||
$\overrightarrow{p}=mg\overrightarrow{x_0}$
|
||||
$\overrightarrow{R_x}=R_x\overrightarrow{x_0}$
|
||||
$\overrightarrow{R_y}=R_y\overrightarrow{y_0}$
|
||||
|
||||
Torseur statique $\rightarrow _G\cases{mg\overrightarrow{x_0}\\\overrightarrow{0}}+_{O_0}\cases{R_x\overrightarrow{x_0}+R_y\overrightarrow{y_0}\\\overrightarrow{0}}$
|
||||
|
||||
|
||||
```functionplot
|
||||
---
|
||||
title: Hope over time
|
||||
xLabel: Time (days)
|
||||
yLabel: Hope (percentage)
|
||||
bounds: [0,30,0,1]
|
||||
disableZoom: true
|
||||
grid: true
|
||||
---
|
||||
hope(x)=0.85(1-x/30)^0.1
|
||||
```
|
||||
|
||||
```functionplot
|
||||
---
|
||||
title: Understanting over time
|
||||
xLabel: Time (days)
|
||||
yLabel: Understanting (percentage)
|
||||
bounds: [0,30,-5,1]
|
||||
disableZoom: true
|
||||
grid: true
|
||||
---
|
||||
hope(x)=0.65(1-(x/26)^100)
|
||||
```
|
||||
|
||||