The switch in the circuit shown below has been closed for a long time before it is opened at t = 0. Find the current i(t) through the inductor for t ? 0. Assume R1 = 3 k?, R2 = 6 k?, R3 = 2 k?, Is = 6 mA, L = 80 mH.
Ra = R1 || R2 || R3 = 1 k?
VR2(0) = Is × Ra = 6 V
i(0) = I0 = VR2(0)/R3 = 3 mA
Req = R3 + (R1 || R2) = 4 k?
? = L/Req = 20 ?s, 1/? = 50000 (1/s)
i(t) = 3 e-50000t u(t) mA
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