A series LCR circuit containing a resistance of 20 , an inductance of 10 mH, and a capacitance of 1 F is connected to a variable frequency AC source of RMS voltage 50 V. The frequency of the source is tuned until the power dissipated in the circuit is maximum. The RMS voltage across the inductor at this frequency is ______ V.

Step-by-step solution

The power dissipated in the circuit is maximum at resonance. At resonance, the impedance of the circuit is purely resistive, so Z = R = 20 . The RMS current in the circuit is: I_ rms = V_ rms R = 50 20 = 2.5 A The resonant angular frequency is: ₀ = 1 LC = 1 10 10⁻³ 1 10⁻⁶ = 1 10⁻⁸ = 10^4 rad/s The inductive reactance at resonance is: X_L = ₀ L = 10^4 10 10⁻³ = 100 The RMS voltage across the inductor is: V_L = I_ rms X_L = 2.5 100 = 250 V. Answer: 250