Question

For the circuit shown in Figure P5.21, assume that switch $S_1$ is always open; switch $S_2$ has been closed for a long time, and opens at $f=0$. a. Find the capacitor voltage, $v_C(t)$, at $t=0^{+}$. b. Find the time constant, $\tau$, for $t \geq 0$. c. Find an expression for $v_c(t)$ and sketch the function. d. Find $v_c(t)$ for each of the following values of $t$ : $0, \tau, 2 \pi, 5 \tau, 10 \tau$.

    For the circuit shown in Figure P5.21, assume that switch $S_1$ is always open; switch $S_2$ has been closed for a long time, and opens at $f=0$.
a. Find the capacitor voltage, $v_C(t)$, at $t=0^{+}$.
b. Find the time constant, $\tau$, for $t \geq 0$.
c. Find an expression for $v_c(t)$ and sketch the function.
d. Find $v_c(t)$ for each of the following values of $t$ : $0, \tau, 2 \pi, 5 \tau, 10 \tau$.

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Principles and Applications of Electrical Engineering

Principles and Applications of Electrical Engineering

Giorgio Rizzoni 4th Edition

Chapter 5, Problem 22

Instant Answer

Step 1

Since switch S₁ is always open, we can ignore it. We're told that switch S₂ has been closed for a long time and opens at t = 0. This means that before t = 0, the circuit is in steady state with S₂ closed, and after t = 0, S₂ is open. Show more…

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For the circuit shown in Figure P5.21, assume that switch $S_1$ is always open; switch $S_2$ has been closed for a long time, and opens at $f=0$. a. Find the capacitor voltage, $v_C(t)$, at $t=0^{+}$. b. Find the time constant, $\tau$, for $t \geq 0$. c. Find an expression for $v_c(t)$ and sketch the function. d. Find $v_c(t)$ for each of the following values of $t$ : $0, \tau, 2 \pi, 5 \tau, 10 \tau$.

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