The switch in the circuit shown below has been opened for a long time before it is closed at t = 0. Find the current i(t) through the inductor for t ? 0. Assume R1 = 1 k?, R2 = 1 k?, R3 = 2 k?, R4 = 2 k?, Is = 6 mA, Vs = 6 V, L = 50 mH.
Ra = (R2 + R1) || R3 = 1 k?
i(0) = I0 = [Vs × Ra/(R4 + Ra)]/R3 = 1 mA
From Vs,
Iinf1 = 1 mA
From Is,
Rb = R3 || R4 = 1 k?
Rc = R2 + Rb = 2 k?
IR2(0) = Is × R1/(R1 + Rc) = 2 mA
Iinf2 = IR2(0) × R4/(R3 + R4) = 1 mA
Iinf = Iinf1 + Iinf2 = 2 mA
Req = R3 +[ R4 || (R2 + R1)] = 3 k?
? = L/Req = 16.6667 ?s, 1/? = 60000 (1/s)
i(t) = [Iinf + (I0 - Iinf)e-60000t] u(t) = [2 + (1 - 2)e-60000t] u(t) = [2 - e-60000t] u(t) mA
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