Question

An electrical circuit that only consists of a resistor R and a capacitor C, is connected to a voltage source V and follows the differential equation R dQ/dt + 1/C (Q) = V student submitted image, transcription available below where Q is the electric charge that moves in the circuit. Considering that R = 2 [Ω], C = 0.2[F] and V = cos 3t. Find the equation for the charge if initially V(0) = 0.

Answer 1

V = R dQ/dt + Q / C voltage across combination

Q = V C - C R dQ/dt charge on capacitor

Q = .2 cos 3t - .2 * 2 * dQ / dt

Q = .2 cos 3 t - .4 dQ / dt