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

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Find the circuit differential equation in vct and the

The switch in Figure P9-53 has been open for a long time and is closed at t = 0. The circuit parameters are R = 500 Ω, L = 2.5 H, C = 2.5 μF, and VA = 500 V.

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

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

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