The switch in the circuit shown below has been closed for a long time before it is opened at t = 0. Find the voltage v(t) across the capacitor for t ? 0. Assume R1 = 3 k?, R2 = 6 k?, R3 = 2 k?, R4 = 2 k?, R5 = 4 k?, Is = 0.6 mA, Vs = 6 V, C = 0.08 ?F.
Ra = R2 || (R4 + R5) = 3 k?
Rb = R1 || R2
v(0) = V0 = Rb ×Is × R5/(R5 + R4 + Rb) + Vs×Ra/(R1 + Ra) = 3.6 V
v(?) = Vinf = R2 ×Is × R5/(R5 + R4 + R2) = 1.2 V
Req = R3 + (R2 || (R4+ R5)) = 5 k?
? = ReqC = 0.0004 s
v(t) = [Vinf + (V0 - Vinf)e-2500t] u(t) = [1.2 + (3.6 - 1.2)e-2500t] u(t) = [1.2 + 2.4e-2500t] u(t) V
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