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electrical_engineering_1:aufgabe_7.2.6_mit_rechnung [2021/10/30 10:32]
tfischer 		electrical_engineering_1:aufgabe_7.2.6_mit_rechnung [2023/02/11 23:08]
mexleadmin
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-<panel type="info" title="Excercise 5.2.6: Charging and Discharging of RC elements (exam task, ca. 11% of a 60 minute exam, WS2020)"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 5.2.6: Charging and Discharging of RC elements (exam task, ca. 11% of a 60 minute exam, WS2020)"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 <WRAP right> {{:elektrotechnik_1:schaltung_klws2020_3_2_1.jpg?400|schaltung_klws2020_3_2_1.jpg}}</WRAP> <WRAP right> {{:elektrotechnik_1:schaltung_klws2020_3_2_1.jpg?400|schaltung_klws2020_3_2_1.jpg}}</WRAP>
  
-The adjacent circuit with the following data is given:+The circuit shown right is given with the following data:
  
   * $U = 10 V$   * $U = 10 V$
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   * $C = 40 nF$   * $C = 40 nF$
  
-At first the capacitor is empty and all switches are open. The switsch S1 will be closed at t=0.+At first the voltage drop on the capacitor $u_C=0$ and all switches are open. The switch S1 will be closed at $t=0$. 
 + 
 +<button size="xs" type="link" collapse="Loesung_7_2_6_6_Simu">{{icon>eye}} Simulation</button><collapse id="Loesung_7_2_6_6_Simu" collapsed="true">  
 + 
 +<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjOB0AMt-CwFMC0B2E1IGYAsBOaPAJnwFY1cA2MADlzCpDIjJF22dTDACgA3EMWK4Q2MsSEjwaJtEzt5YeSsyQyvAM5TRYWUNq0Zc8CABmAQwA2mpLwBOBo3qbZ6xhcugOx7l79FiMhNabwBjAKFgyPFJeVxUIxVeAHcYiR0xDO9tN119XFCPJXNrWx9CpQKi2IUybzS8rMlK5sxU9hqMilds3gBLZn1iNEketpUYaFwfcZGx-TBiJPAGoaYlowIN5fbtDklN9nwdlYhLGzs0g-BdpqO1+7u-fW8Ae3ZTJWJsaDip6AQLBwIFCT6cACuAH0AMK8IA noborder}} </WRAP> 
 + 
 +</collapse>
  
 1. Determine the time constant $\tau$ for this charging process. 1. Determine the time constant $\tau$ for this charging process.
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 <button size="xs" type="link" collapse="Loesung_7_2_6_1_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_1_Endergebnis" collapsed="true"> \begin{align*} \tau = 7,2 µs \end{align*} \\ </collapse> <button size="xs" type="link" collapse="Loesung_7_2_6_1_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_1_Endergebnis" collapsed="true"> \begin{align*} \tau = 7,2 µs \end{align*} \\ </collapse>
  
-2. How high is the voltage at the capacitor $C$ when $t=10 µs$?+2. What is the value of the voltage $u_C(t)$ drop over the capacitor $C$ at $t=10 µs$?
  
 <button size="xs" type="link" collapse="Loesung_7_2_6_2_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_2_Lösungsweg" collapsed="true"> <button size="xs" type="link" collapse="Loesung_7_2_6_2_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_2_Lösungsweg" collapsed="true">
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 <button size="xs" type="link" collapse="Loesung_7_2_6_2_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_2_Endergebnis" collapsed="true"> \begin{align*} U_C(t) = 7,506 V -> 7,5 V \end{align*} \\ </collapse> <button size="xs" type="link" collapse="Loesung_7_2_6_2_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_2_Endergebnis" collapsed="true"> \begin{align*} U_C(t) = 7,506 V -> 7,5 V \end{align*} \\ </collapse>
  
-3. How high is the energy when the capacitor is fully charged?+3. What is the value of the energy, when the capacitor is fully charged?
  
 <button size="xs" type="link" collapse="Loesung_7_2_6_3_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_3_Lösungsweg" collapsed="true"> <button size="xs" type="link" collapse="Loesung_7_2_6_3_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_3_Lösungsweg" collapsed="true">
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 <button size="xs" type="link" collapse="Loesung_7_2_6_3_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_3_Endergebnis" collapsed="true"> \begin{align*} W_C = 2 µJ \end{align*} \\ </collapse> <button size="xs" type="link" collapse="Loesung_7_2_6_3_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_3_Endergebnis" collapsed="true"> \begin{align*} W_C = 2 µJ \end{align*} \\ </collapse>
  
-4. Determine the new time constant when the capacitor is fully charged. The switch S1 will be opened whereas the switch S2 will be closed simultaneously.+4. Determine the new time constant when the switch $S_1$ will be opened and the switch $S_3$ will be closed simultaneously. 
  
 <button size="xs" type="link" collapse="Loesung_7_2_6_4_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_4_Lösungsweg" collapsed="true"> <button size="xs" type="link" collapse="Loesung_7_2_6_4_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_7_2_6_4_Lösungsweg" collapsed="true">
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 <button size="xs" type="link" collapse="Loesung_7_2_6_4_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_4_Endergebnis" collapsed="true"> \begin{align*} \tau = 5,2 µs \end{align*} \\ </collapse> <button size="xs" type="link" collapse="Loesung_7_2_6_4_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_7_2_6_4_Endergebnis" collapsed="true"> \begin{align*} \tau = 5,2 µs \end{align*} \\ </collapse>
  
-5. When the capacitor is empty all switches will be opend. The switch S4 will be closed at $t = 1μs$. \\ How high is the voltage at the capacitor C?+5. When the capacitor is empty all switches will be opened. The switch $S_4$ will be closed at $t= 0$. \\ What is the voltage $u_C$ at the capacitor C after $t = 1μs$?
  
 <button size="xs" type="link" collapse="Loesung_7_2_6_5_Tipps">{{icon>eye}} Tips</button><collapse id="Loesung_7_2_6_5_Tipps" collapsed="true"> <button size="xs" type="link" collapse="Loesung_7_2_6_5_Tipps">{{icon>eye}} Tips</button><collapse id="Loesung_7_2_6_5_Tipps" collapsed="true">