Find the steady state current for a circuit in which L 500H

Find the steady state current for a circuit in which L = 500H, R = 150 ohm, C = 0.0020 F and E = 10sin5t if q = 0 and I = 2 amp for t = 0.

Solution

X_L = wL = 5 x 0.5 = 2.5 ohm

X_C = 1/wC = 1/(5*0.02) = 10 ohm

R = 150 ohm

Z = sqrt(150² + (10-2.5)²) = 150.1874 ohm

steady state current = (10sin5t)/150.1874 A = 0.066583489sin5t ampere