A series LCR circuit with inductance 10 mH , capacitance 100 F , and resistance 50 is connected to an AC source of voltage V = 100 2 (1000t) volt. The RMS current and the power factor of the circuit are respectively:

Step-by-step solution

From the given voltage equation V = 100 2 (1000t) , the peak voltage is V₀ = 100 2 V and the angular frequency is = 1000 rad s ⁻¹ . The RMS voltage is V_ rms = V₀ 2 = 100 V . The resonant angular frequency of the circuit is: ₀ = 1 LC = 1 10 10⁻³ 100 10⁻⁶ = 1 10⁻⁶ = 1000 rad s ⁻¹ Since = ₀ , the circuit is in resonance. At resonance, the impedance Z is equal to the resistance R ( Z = 50 ) and the phase difference between voltage and current is zero. The power factor is = (0) = 1 . The RMS current is I_ rms = V_ rms