If the voltage source is DC, the inductor will indeed short it out. You can only work out this type of problem with an AC voltage source. At t =0 when the switch is opened disconnecting the voltage source, I inductor (0+) = I inductor (0+) since current can't change instantly in an inductor, and Vc (0+) = Vc(0-) since the voltage across a capacitor can't change instantly For a parallel circuit Vc = Vr = Vl = V I ind = (1/L)(?V dt), Ir = V/R, Ic = C dV/dt I = I ind + Ir + Ic This can be solved with Laplace Transforms I(s) = V(s)(1/(sL) + 1/R + sC) - Vc(0+) + I inductor (0+)/s.
The battery is short circuited through the inductor, will not work.
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