Question 5.14: Initial and Final Voltage and Current Consider the circuit s...

Electrical Engineering: Concepts and Applications

Initial and Final Voltage and Current

Consider the circuit shown in Figure 5.36. Find $v_{C}\left(0^{+}\right), i_{C}\left(0^{+}\right)$ , and $v_{C}(\infty)$ .

5.14

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The equivalent circuit at $t=0^{+}$ (after the switch is closed) corresponds to Figure 5.36(b). Here:

\begin{aligned}&v_{C}\left(0^{+}\right)=0 \\&i_{C}\left(0^{+}\right)=\frac{50}{R_1+R_2}=\frac{50}{4}=12.5  mA\end{aligned}

The equivalent circuit at t = ∞ corresponds to Figure 5.36(c). In this case, the voltage across the capacitor is equal to the voltage across $R_3$ . Using the voltage divider rule;

\begin{aligned}v_{C}(\infty) &=50 \frac{R_3}{R_1+R_3} \\&=50 \frac{2}{4}=25  V\end{aligned}

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