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. Given: v = v_m sin ω t , where v_m = 141.4 V , R = 50 Ω . RMS voltage: V = (v_m/√(2)) = (141.4/√(2)) = 100 V . RMS current: I = (V/R) = (100/50) = 2 A . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P