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electrical_engineering_and_electronics_1:block12 [2025/10/31 21:14] – angelegt mexleadminelectrical_engineering_and_electronics_1:block12 [2025/11/02 17:50] (aktuell) – [Learning objectives] mexleadmin
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-====== Block xx - xxx ======+====== Block 12 - Capacitors and Capacitance ======
  
 ===== Learning objectives ===== ===== Learning objectives =====
 <callout> <callout>
-After this 90-minute block, you  +After this 90-minute block, you can  
-  - Know what a capacitor is and how capacitance is defined, +  - define a **capacitor** and **capacitance** $C$ and use it for an ideal plate capacitor, including unit checks $[C]={\rm F}$.  
-  - Know the basic equations for calculating capacitance and be able to apply them, +  - relate fields and material.  
-  - Imagine a plate capacitor and give examples of its use. You also have an idea of what a cylindrical or spherical capacitor looks like and what examples of its use there are, +  - compute $C$ for key geometries (parallel plates, coaxial, spherical) and explain how $A$, $d$, $\varepsilon_{\rm r}$ scale $C$. 
-  - Know the characteristics of the E-field, D-field, and electric potential in the three types of capacitors presented here+
 </callout> </callout>
  
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 ===== 90-minute plan ===== ===== 90-minute plan =====
-  - Warm-up (x min):  +  - Warm-up (8 min): 
-    - ....  +    - Quick recall quiz: $C=\dfrac{Q}{U}$, $\vec{D}=\varepsilon\vec{E}$, units of $E$ (${\rm V/m}$), $D$ (${\rm C/m^2}$).  
-  - Core concepts & derivations (x min): +    - Estimate: how $C$ changes when $A$ doubles or $d$ halves (plate model).  
-    - ... +  - Core concepts & derivations (60 min): 
-  - Practice (x min): ... +    - From fields to $C$ (plate capacitor): $U=\int\vec{E}\cdot{\rm d}\vec{s}=E\,d$, $Q=\oint\vec{D}\cdot{\rm d}\vec{A}=D\,A$, $\Rightarrow C=\varepsilon_0\varepsilon_{\rm r}\dfrac{A}{d}$. Dimensional check: $[\varepsilon_0\varepsilon_{\rm r}A/d]={\rm F}$.  
-  - Wrap-up (x min): Summary box; common pitfalls checklist.+    - Other geometries: coaxial and spherical capacitor formulas; where fields are highest (edge intuition kept qualitative).  
 +  - Practice (20 min): 
 +    - Mini-calcs: (i) $C$ of given $A,d,\varepsilon_{\rm r}$; (ii) coaxial $C$ per length; (iii) allowable $U$ from $E_0$ and $d$; (iv) energy at given $U$.  
 +    - Discuss the provided “glass plate in capacitor” task. 
 +  - Wrap-up (2 min): Summary box + pitfalls checklist; connect to next block (capacitor circuits).
  
 ===== Conceptual overview ===== ===== Conceptual overview =====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
-  - ...+  - A **capacitor** is two conductors separated by a dielectric. It stores **charge** and **energy** in the electric field; no conduction current flows through the ideal dielectric. :contentReference[oaicite:15]{index=15} 
 +  - **Capacitance** measures how much charge per volt: $C=\dfrac{Q}{U}$. For parallel plates, $C=\varepsilon_0\varepsilon_{\rm r}\dfrac{A}{d}$ → increase $A$ or $\varepsilon_{\rm r}$, decrease $d$ to raise $C$. :contentReference[oaicite:16]{index=16} 
 +  - **Other geometries:** Closed forms exist for coaxial and spherical capacitors; useful as building blocks and for cables/sensors. :contentReference[oaicite:18]{index=18}
 </callout> </callout>
  
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 {{url>https://www.falstad.com/vector2de/vector2de.html?f=ChargedPlateDipole&fc=Floor%3A%20field%20magnitude&fl=Overlay%3A%20equipotentials&d=vectors&m=Mouse%20%3D%20Adjust%20Angle&st=20&vd=32&a1=63&a2=16&rx=77&ry=5&rz=107&zm=1.165 600,400 noborder}} {{url>https://www.falstad.com/vector2de/vector2de.html?f=ChargedPlateDipole&fc=Floor%3A%20field%20magnitude&fl=Overlay%3A%20equipotentials&d=vectors&m=Mouse%20%3D%20Adjust%20Angle&st=20&vd=32&a1=63&a2=16&rx=77&ry=5&rz=107&zm=1.165 600,400 noborder}}
 </WRAP></WRAP> </WRAP></WRAP>
 +
 +==== Symbols ====
 +
 +  * The symbol of a general capacitor is given be two parallel lines nearby each other. \\
 +  * Since **electrolytic capacitors** can only withstand voltage in one direction, the **polarisation** is often shown by a curved electrode (US) or a unfilled one (EU). \\ Be aware that electrolytic capacitors can explode, once used in the wrong direction.
 +
 +{{drawio>electrical_engineering_and_electronics_1:CapSymbols01.svg}}
  
 ==== Designs and types of capacitors ==== ==== Designs and types of capacitors ====
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 ===== Common pitfalls ===== ===== Common pitfalls =====
-  * ...+ 
 +  * **Mixing up geometry symbols.** Use $d$ (or $l$) strictly as **plate spacing** and $A$ as **active area** in $C=\varepsilon_0\varepsilon_{\rm r}\dfrac{A}{d}$. Check units to catch mistakes.  
 +  * **Forgetting the field relations.** $U=\int \vec{E}\cdot{\rm d}\vec{s}$ and $Q=\oint \vec{D}\cdot{\rm d}\vec{A}$; without them, layered-dielectric problems are guessed instead of solved.  
 +  * **Assuming conduction through the dielectric.** The apparent “current through a capacitor” is displacement-related; no charge carriers traverse the ideal dielectric. 
 +  * **Real-part issues.** Ignoring polarity of electrolytics and tolerance spreads ($\pm 10~\%$ and more) causes design errors; pick suitable component types. 
  
 ===== Exercises ===== ===== Exercises =====