Chapter 8, Problem 1RQ

For the circuit in Fig. 8.58, the capacitor voltage at t = 0⁻ (just before the switch is closed) is:

(a)    0 V

(b)    4 V

(c)    8 V

(d)    12 V

Figure 8.58

For Review Questions 8.1 and 8.2.

To determine

Choose the correct option to find the capacitor voltage at $t=0^{-}$ (just before the switch is closed).

Answer to Problem 1RQ

The correct option form the given choices is (a) 0 V.

Explanation of Solution

Calculation:

Redraw the given circuit as shown in Figure 1.

For the DC circuit, at the steady state condition when switch is open at $t=0^{-}$, the capacitor acts as open circuit and the inductor act as short circuit. Therefore, the Figure 1 becomes as shown in Figure 2.

Since, the capacitor is open circuited, the voltage across the capacitor at $t=0^{-}$ is 0 V.

Therefore, the capacitor voltage at $t=0^{-}$ is $v_{\text{C}}\left(0^{-}\right)$.

$v_{\text{C}}\left(0^{-}\right)=0\text{V}$

Therefore, the option (a) is correct and the options (b), (c), (d) are incorrect.

Conclusion:

Thus, the correct option from the given choices is (a) 0 V.