Problem 4 (20 points)
The switch in the circuit shown in Fig. 4 has been in position a for a long time. At t = 0, the switch is moved to position b.
400 kW
20 Ω
+
90 V
40 V
0.5 F
Fig. 4
a) Draw the circuit and find the value of v for t < 0.
b) Draw the circuit for t > 0 and determine the final value of v.
c) Find the time constant of the circuit when the switch is in position b.
d) Write the expression for v_c(t).
e) How long after the switch is in position b does the capacitor voltage equal zero?