For the circuit shown in Figure P5.41, assume that switches S1 and S2 have been held closed for a long time prior to t = 0. S1 then opens at t = 0; however, S2 does not open until t = 48 s. Also assume
R1 = 5?, R2 = 4?, R3 = 3?, R4 = 6?, and C1 = C2 = 4F.
a. Find the capacitor voltage vC at t = 0.
b. Find the time constant ? for 0 < t < 48 s.
c. Find vC for 0 < t < 48 s.
d. Find ? for t > 48 s.
e. Find vC for t > 48 s.
f. Sketch vC for all time.
Analysis:
The approach here is to find the transient solution in the interval 0 < t < 48 seconds and use that solution to determine the initial condition (the capacitor voltage) for the new transient after the switch S2 opens.
a) and have been closed for a long time and in DC steady state the capacitors can be replaced with open circuits. Thus, by node analysis and voltage division
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