Practice question

**Power factor** cos φ = R/Z, 0≤cos φ≤1, at resonance cos φ=1 maximum power, pure L or C cos φ=0 zero average power, current wattless because energy stored returned. Instantaneous power when current maximum in pure L: I=I_peak, V=0 because V leads 90°, so P= V I =0 at that instant, average zero. Z = √(R² + (X_L - X_C)²) = √(40² + (65 - 25)²) = √(1600 + 1600) = √(3200) ≈ 56.57 Ω . Power factor: cos Φ = (R/Z) = (40/56.57) ≈ 0.707 . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P