Practice question

**Capacitive reactance** X_C =1/(ω C)=1/(2π f C) (Ω), C capacitance (F), current leads voltage by 90°, I_rms = V_rms/X_C = V_rms ω C, I_peak = V_peak ω C, impedance Z = X_C for pure C. For 45 μF, 60 Hz, X_C=1/(2π×60×45×10⁻⁶)=58.9 Ω, V_rms=110 V, I_rms=1.867 A, I_peak=2.64 A. X_C = (1/ω C) , ω = 2π × 50 = 314 rad/s . C = 25 × 10⁻⁶ F . X_C = (1/314 × 25 × 10⁻⁶) ≈ 127.4 Ω . RMS current: I = (V/X_C) = (230/127.4) ≈ 1.805 A . Peak current: i_m = √(2) I = 1.414 × 1.805 ≈ 2.55 A .