A series LCR circuit is connected to an AC source of variable frequency and peak voltage 10 V . The circuit components are a resistor of 50 , an inductor of 40 mH , and a capacitor of 1 F . When the frequency of the source is tuned such that the circuit dissipates maximum power, the amplitude of the voltage across the inductor is _____ V .

Step-by-step solution

For maximum power dissipation, the circuit must be in resonance. At resonance, the impedance is purely resistive ( Z = R ). The peak current in the circuit is: I₀ = V₀ R = 10 50 = 0.2 A The resonant angular frequency is: ₀ = 1 LC = 1 40 10⁻³ 1 10⁻⁶ ₀ = 1 4 10⁻⁸ = 1 2 10⁻⁴ = 5000 rad/s The inductive reactance at resonance is: X_L = ₀ L = 5000 40 10⁻³ = 200 The amplitude of the voltage across the inductor is: V_ L0 = I₀ X_L = 0.2 200 = 40 V . Answer: 40