Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
Beide Seiten der vorigen Revision Vorhergehende Überarbeitung | Letzte Überarbeitung Beide Seiten der Revision | ||
electrical_engineering_1:dc_circuit_transients [2023/12/02 00:55] mexleadmin [Exercises] |
electrical_engineering_1:dc_circuit_transients [2023/12/02 01:08] mexleadmin [Exercises] |
||
---|---|---|---|
Zeile 538: | Zeile 538: | ||
2. At a distinct time $t_1$, the voltage $u_C$ is charged up to $4/5 \cdot U_1$. | 2. At a distinct time $t_1$, the voltage $u_C$ is charged up to $4/5 \cdot U_1$. | ||
- | At this point, the switch $S_2$ will be closed. \\ Calculate $t_1$! | + | At this point, the switch $S_1$ will be opened. \\ Calculate $t_1$! |
# | # | ||
We can derive $u_{C}$ based on the exponential function: $u_C(t) = U_1 \cdot (1-e^{-t/ | We can derive $u_{C}$ based on the exponential function: $u_C(t) = U_1 \cdot (1-e^{-t/ | ||
- | Therefore we get $t_1$ by: | + | Therefore, we get $t_1$ by: |
\begin{align*} | \begin{align*} | ||
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 $S_1$ is open and $S_2$ is closed. |
- | In this case, we can " | + | |
{{drawio> | {{drawio> | ||
- | We see that for the time constant, we now need to use $R=R_1 || R_3 + R_2$. | + | We see that for the time constant, we now need to use $R=R_3 + R_2$. |
\begin{align*} | \begin{align*} | ||
\tau_2 &= R\cdot C \\ | \tau_2 &= R\cdot C \\ | ||
- | & | + | & |
- | & | + | |
\end{align*} | \end{align*} | ||
Zeile 586: | Zeile 584: | ||
# | # | ||
\begin{align*} | \begin{align*} | ||
- | \tau_2 & | + | \tau_2 & |
\end{align*} | \end{align*} | ||