Find the circuit differential equation in ilt and the, Electrical Engineering

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Find the circuit differential equation in ilt and the

The switch in Figure has been open for a long time and is closed at t = 0. The circuit parameters are R = 50 Ω, L = 250 mH, C = 0.5 μF, and V_A = 1000 V.

(a) Find the circuit differential equation in iL(t) and the initial conditions i_L(0) and v_C(0).

(b) Use Laplace transforms to solve for i_L(t) for t ≥ 0.

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