Practice question

**AC through capacitor** voltage lags current by 90°, Q= C V, I= dQ/dt = C dV/dt, V(t)=V_peak sin ωt, I(t)=I_peak sin(ωt+90°), average power zero because energy stored in electric field ½ C V² returned each cycle, capacitor blocks DC but passes AC, X_C decreases with f. X_L = ω L , ω = 2π × 50 = 314 rad/s . L = 50 × 10⁻³ H . X_L = 314 × 0.05 = 15.7 Ω . RMS current: I = (V/X_L) = (220/15.7) ≈ 14.01 A . Peak current: i_m = √(2) I = 1.414 × 14.01 ≈ 19.81 A . Applying X_L = ωL,