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electrical_engineering_and_electronics_1:block13 [2025/11/02 17:47] – mexleadminelectrical_engineering_and_electronics_1:block13 [2026/01/10 12:51] (aktuell) – mexleadmin
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 ====== Block 13 - Capacitor Circuits and Energy ====== ====== Block 13 - Capacitor Circuits and Energy ======
  
-===== Learning objectives =====+===== 13.0 Intro ===== 
 + 
 +==== 13.0.1 Learning Objectives ====
 <callout> <callout>
 After this 90-minute block, you can After this 90-minute block, you can
   * identify series vs. parallel connections of capacitors from a circuit diagram,   * identify series vs. parallel connections of capacitors from a circuit diagram,
-  * compute equivalent capacitance $C_{\rm eq}$ for series $\left(\displaystyle \frac{1}{C_{\rm eq}}=\sum_k \frac{1}{C_k}\right)$ and parallel $\left(\displaystyle C_{\rm eq}=\sum_k C_k\right)$ networks, +  * compute equivalent capacitance $C_{\rm eq}$ for series and parallelnetworks, 
-  * use the key sharing rules: in **series** $Q_k=\text{const.}$ and voltages divide $\left(U_k=\dfrac{Q}{C_k}\right)$; in **parallel** $U_k=\text{const.}$ and charges divide $\left(Q_k=C_k\,U\right)$, +  * use the key sharing rules: in **series** $Q_k=\text{const.}$ and voltages divide; in **parallel** $U_k=\text{const.}$ and charges divide, 
-  * apply the capacitor divider relation (two series capacitors) $\,U_1=\dfrac{C_2}{C_1+C_2}\,U\,,\;U_2=\dfrac{C_1}{C_1+C_2}\,U\,$, +  * apply the capacitor divider relation (two series capacitors), 
-  * determine and check stored energy with $W=\dfrac{1}{2}C U^2=\dfrac{1}{2}Q U=\dfrac{Q^2}{2C}$, including a dimensional check to $\rm J$.+  * determine stored energy, including a dimensional check to $\rm J$.
 </callout> </callout>
  
-===== Preparation at Home =====+==== 13.0.2 Preparation at Home ====
  
 Well, again  Well, again 
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 For checking your understanding please do the following exercises: For checking your understanding please do the following exercises:
-  * ...+  * 5.9.5
  
-===== 90-minute plan =====+==== 13.0.3 90-minute plan ====
   - Warm-up (10 min):   - Warm-up (10 min):
     - Quick quiz (2–3 items): series or parallel? which rule applies (constant $U$ or constant $Q$)?     - Quick quiz (2–3 items): series or parallel? which rule applies (constant $U$ or constant $Q$)?
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     - Common-pitfalls checklist and one exit-ticket calculation.     - Common-pitfalls checklist and one exit-ticket calculation.
  
-===== Conceptual overview =====+==== 13.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **What stays the same?** In **series** all capacitors carry the **same charge** $Q$; in **parallel** all capacitors see the **same voltage** $U$.   - **What stays the same?** In **series** all capacitors carry the **same charge** $Q$; in **parallel** all capacitors see the **same voltage** $U$.
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 </callout> </callout>
  
-===== Core content =====+===== 13.1 Core content =====
  
-==== Series Circuit of Capacitor ====+==== 13.1.1 Series Circuit of Capacitor ====
  
 If capacitors are connected in series, the charging current $I$ into the individual capacitors $C_1 ... C_n$ is equal. If capacitors are connected in series, the charging current $I$ into the individual capacitors $C_1 ... C_n$ is equal.
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   * The capacitors can be discharged again via the lamp.   * The capacitors can be discharged again via the lamp.
  
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 </WRAP> </WRAP>
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Parallel Circuit of Capacitors ====+==== 13.1.2 Parallel Circuit of Capacitors ====
  
 If capacitors are connected in parallel, the voltage $U$ across the individual capacitors $C_1 ... C_n$ is equal. If capacitors are connected in parallel, the voltage $U$ across the individual capacitors $C_1 ... C_n$ is equal.
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 In the simulation below, again, besides the parallel connected capacitors $C_1$, $C_2$,$C_3$, an ideal voltage source $U_q$, a resistor $R$, a switch $S$, and a lamp are installed. In the simulation below, again, besides the parallel connected capacitors $C_1$, $C_2$,$C_3$, an ideal voltage source $U_q$, a resistor $R$, a switch $S$, and a lamp are installed.
  
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 </WRAP> </WRAP>
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Energy in the electric Field ====+==== 13.1.3 Energy in the electric Field ====
  
 Now we want to see how much energy is stored in a capacitor during charging. Now we want to see how much energy is stored in a capacitor during charging.
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Common pitfalls =====+===== 13.2 Common pitfalls =====
   * Mixing up the rules: writing $C_{\rm eq}=C_1+C_2$ for **series** (wrong) or $\dfrac{1}{C_{\rm eq}}=\dfrac{1}{C_1}+\dfrac{1}{C_2}$ for **parallel** (wrong).   * Mixing up the rules: writing $C_{\rm eq}=C_1+C_2$ for **series** (wrong) or $\dfrac{1}{C_{\rm eq}}=\dfrac{1}{C_1}+\dfrac{1}{C_2}$ for **parallel** (wrong).
   * Forgetting which quantity is equal: **series $\Rightarrow Q_k=\text{const.}$**, **parallel $\Rightarrow U_k=\text{const.}$**.   * Forgetting which quantity is equal: **series $\Rightarrow Q_k=\text{const.}$**, **parallel $\Rightarrow U_k=\text{const.}$**.
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   * Dropping units or mixing forms of energy: always keep $W=\tfrac12 C U^2=\tfrac12 Q U=\dfrac{Q^2}{2C}$ and check $\rm J$.   * Dropping units or mixing forms of energy: always keep $W=\tfrac12 C U^2=\tfrac12 Q U=\dfrac{Q^2}{2C}$ and check $\rm J$.
  
-===== Exercises =====+===== 13.3 Exercises =====
  
 <panel type="info" title="Task 5.8.1 Calculating a circuit of different capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Task 5.8.1 Calculating a circuit of different capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics_2:task_5.9.3_with_calculation&nofooter}} +{{page>electrical_engineering_and_electronics:task_5.9.3_with_calculation&nofooter}} 
- +{{page>electrical_engineering_and_electronics:task_k4wrrhf8v46gct49_with_calculation&nofooter}} 
 +{{page>electrical_engineering_and_electronics:task_y7dozgdsljqvnqge_with_calculation&nofooter}}
  
 ===== Embedded resources ===== ===== Embedded resources =====