The switch in the circuit shown below 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 = 8 k?, R2 = 4 k?, R3 = 8 k?, R4 = 12 k?, R5 = 6 k?, Is = 2.4 mA, Vs = 13.5 V, C = 0.05 ?F.
v(0) = V0 = Vs × R4/(R4 + R5) = 9 V
Ra = R2 + R3 + (R4 || R5) = 16 k?
Rb = R4 || (R3 + R2 + R1) = 7.5 k?
Vinf1 = Vs×[Rb/(R5 + Rb)] × (R1 + R2)/(R1 + R2 + R3) = 4.5 V
Vinf2 = (R4 + (R4 || R5)) × Is × R1/(R1 + Ra) = 9.6 V
Vinf = Vinf1 + Vinf2 = 14.1 V
Req = (R2 + R1) || [R3 + (R4 || R5)] = 6 k?
? = ReqC = 0.0003 s, 1/? = 3333.3333 (1/s)
v(t) = [Vinf + (V0 - Vinf)e-2500t] u(t) = [14.1 + (9 - 14.1)e-3333.3333t] u(t) = [14.1 - 5.1e-3333.3333t] u(t) V
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