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 = 8 k?, R2 = 24 k?, R3 = 3 k?, Is = 0.5 mA, Vs = 3.2 V, C = 0.05 ?F.
v(0) = V0 = Is ×(R1 || R2) + Vs×R2/(R1 + R2) = 5.4 V
v(?) = Vinf = Vs×R2/(R1 + R2) = 2.4 V
Req = R3 + (R1 || R2) = 9 k?
? = ReqC = 0.00045 s
v(t) = [Vinf + (V0 - Vinf)e-2222.2222t] u(t) = [2.4 + (5.4 - 2.4)e-2222.2222t] u(t) = [2.4 + 3e-2222.2222t] u(t) V
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