Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen Revision Vorhergehende Überarbeitung
Nächste Überarbeitung 		Vorhergehende Überarbeitung
Nächste Überarbeitung Beide Seiten der Revision
electrical_engineering_1:dc_circuit_transients [2023/12/02 00:50]
mexleadmin [Exercises] 		electrical_engineering_1:dc_circuit_transients [2023/12/02 00:55]
mexleadmin [Exercises]
Zeile 483: Zeile 483:
   * $R_3 = 3 \rm k\Omega$   * $R_3 = 3 \rm k\Omega$
   * $C   = 1 \rm \mu F$   * $C   = 1 \rm \mu F$
-  * $S_1$ and $S_2$ are opened (open-circuit)+  * $S_1$ and $S_2$ are opened in the beginning (open-circuit)
  
 {{drawio>electrical_engineering_1:Exercise522setup.svg}} {{drawio>electrical_engineering_1:Exercise522setup.svg}}
Zeile 569: Zeile 569:
 Again the time constant $\tau$ is given as: $\tau= R\cdot C$. \\ Again the time constant $\tau$ is given as: $\tau= R\cdot C$. \\
 Again, we try to determine which $R$ and $C$ must be used here. \\ Again, we try to determine which $R$ and $C$ must be used here. \\
-To find this out, we have to look at the circuit when both $S_1$ and $S_2$ are closed.+To find this out, we have to look at the circuit when both $S_1$ and $S_2$ are closed. \\ 
 +In this case, we can "fold" over the resistor $R_3$ to the left-side of the capacitor $C$.
  
 {{drawio>electrical_engineering_1:Exercise522sol4.svg}} {{drawio>electrical_engineering_1:Exercise522sol4.svg}}
Zeile 578: Zeile 579:
 \tau_2 &= R\cdot C \\ \tau_2 &= R\cdot C \\
        &= (R_1 || R_3 + R_2) \cdot C \\        &= (R_1 || R_3 + R_2) \cdot C \\
-       &= {{\rm  1 ~k\Omega \cdot 3 ~k\Omega }\over{\rm  1 ~k\Omega + 3 ~k\Omega}} + 2 ~{\rm k\Omega}) \cdot 1 ~{\rm \mu F} \\+       &= \left({{\rm  1 ~k\Omega \cdot 3 ~k\Omega }\over{\rm  1 ~k\Omega + 3 ~k\Omega}} + 2 ~{\rm k\Omega}\right) \cdot 1 ~{\rm \mu F} \\
 \end{align*} \end{align*}