For a series LCR circuit I = 100 sin ( 100 π t - π 3 ) mA and V = 100 sin ( 100 π t ) V , then calculate the resistance and reactance of the circuit.

The current I = 0 . 1 sin 100 π t - π 3 A and voltage V = 100 sin 100 π t V , The phase difference between current and voltage is π 3 and current is lagging. The impedance Z = V 0 I 0 ⇒ Z = 100 0 . 1 ⇒ Z = 1000 Ω From phasor diagram, the phase angle tan ϕ = X L - X C R ⇒ tan π 3 = X L - X C R ⇒ X L - X C = 3 R , The impedance Z = R 2 + ( X L - X C ) 2 ⇒ 1000 = R 2 + 3 R 2 ⇒ R = 500 Ω , The reactance of the circuit X L - X C = 500 3 Ω .

For a series LCR circuit I = 100 sin ( 100 π t - π 3 ) mA and V = 100 sin ( 100 π t ) volt , then find average power loss.

The current I = 0 . 1 sin 100 π t - π 3 A and voltage V = 100 sin 100 π t V The phase difference between current and voltage is π 3 and current is lagging. ⇒ ϕ = π 3 The peak current I 0 = 0 . 1 A The RMS current I RMS = I 0 2 = 0 . 1 2 A , The peak voltage V 0 = 100 V The RMS voltage V RMS = 100 2 = 50 2 V , The average power P avg = V RMS I RMS cos ϕ P a v g = 50 2 × 0 . 1 2 cos π 3 ⇒ P avg = 2 . 5 W