A series LCR circuit with R = 10 and C = 10 F is connected to an a.c. source of RMS voltage 20 V and variable frequency. If the RMS voltage across the capacitor at resonance is 400 V , the value of the inductance L is _______ mH .

Step-by-step solution

At resonance, the inductive reactance and capacitive reactance are equal ( X_L = X_C ), so the total impedance of the circuit is purely resistive ( Z = R ). The RMS current in the circuit at resonance is: I = V R = 20 10 = 2 A The RMS voltage across the capacitor is given by V_C = I X_C . Therefore, the capacitive reactance at resonance is: X_C = V_C I = 400 2 = 200 At resonance, we also know that X_C = L C . Squaring both sides and rearranging for L : L = C X_C^2 Substituting C = 10 F = 10 10⁻⁶ F and X_C = 200 : L