(Solved): 5.21 For the circuit shown in Figure P5.21, assume that switch \( S_{1} \) is always open and that ...

5.21 For the circuit shown in Figure P5.21, assume that switch \( S_{1} \) is always open and that switch \( S_{2} \) closes at \( t=0 \). 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 \( t \) : \( 0, \tau, 2 \tau, 5 \tau, 10 \tau \)