The switch 1 in the circuit shown below has been closed for a long time before it is opened at t = 0 and the switch 2 has been opened for a long time before it is closed at t = 0. Find the voltage v(t) across the capacitor for t ? 0. Assume R1 = 6 k?, R2 = 3 k?, R3 = 1 k?, R4 = 2 k?, R5 = 1 k?, Is = 1 mA, Vs = 6 V, C = 0.4 ?F.
v(0) = V0 = (R3 + R4) × Is × R1/(R1 + R2 + R3 + R4) = 1.5 V
v(?) = Vinf = Vs × R4/(R4 + R5) = 4 V
Req = R3 + (R4 || R5) = 1.6667 k?
? = ReqC = 0.0006667 s, 1/? = 1500 (1/s)
v(t) = [Vinf + (V0 - Vinf)e-2500t] u(t) = [4 + (1.5 - 4)e-1500t] u(t) = [4 - 2.5e-1500t] u(t) V
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