| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung Nächste ÜberarbeitungBeide Seiten der Revision |
| electrical_engineering_1:aufgabe_7.2.6_mit_rechnung [2021/10/24 00:57] – 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 7.2.6: 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%> |
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| <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> |
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| The adjacent circuit with the following data is given: | The circuit shown right is given with the following data: |
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| * $U = 10 V$ | * $U = 10 V$ |
| * $C = 40 nF$ | * $C = 40 nF$ |
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| 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 $t=0$. |
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| | <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"> |
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| | <WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjOB0AMt-CwFMC0B2E1IGYAsBOaPAJnwFY1cA2MADlzCpDIjJF22dTDACgA3EMWK4Q2MsSEjwaJtEzt5YeSsyQyvAM5TRYWUNq0Zc8CABmAQwA2mpLwBOBo3qbZ6xhcugOx7l79FiMhNabwBjAKFgyPFJeVxUIxVeAHcYiR0xDO9tN119XFCPJXNrWx9CpQKi2IUybzS8rMlK5sxU9hqMilds3gBLZn1iNEketpUYaFwfcZGx-TBiJPAGoaYlowIN5fbtDklN9nwdlYhLGzs0g-BdpqO1+7u-fW8Ae3ZTJWJsaDip6AQLBwIFCT6cACuAH0AMK8IA noborder}} </WRAP> |
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| | </collapse> |
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| 1. Determine the time constant $\tau$ for this charging process. | 1. Determine the time constant $\tau$ for this charging process. |
| <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> |
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| 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 $t=10 µs$? |
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| <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"> |
| <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> |
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| 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? |
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| <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"> |
| <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> |
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| 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. |
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| <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"> |
| <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> |
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| 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 $t = 1μs$? |
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| <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"> |