A series LCR circuit is connected to an AC source of variable frequency. At a particular frequency, the current in the circuit is in phase with the applied voltage. If the inductive reactance at this frequency is 50 and the capacitance of the circuit is 20 F , the frequency of the AC source is :

Step-by-step solution

The current is in phase with the voltage when the circuit is at resonance. At resonance, the inductive reactance ( X_L ) equals the capacitive reactance ( X_C ): X_L = X_C Given X_L = 50 , we have X_C = 50 . The capacitive reactance is given by X_C = 1 C . Substituting the given values ( C = 20 F = 20 10⁻⁶ F ): 50 = 1 20 10⁻⁶ = 1 50 20 10⁻⁶ = 1 1000 10⁻⁶ = 1 10⁻³ = 1000 rad/s The linear frequency f is related to the angular frequency by f = 2 : f = 1000 2 = 500 Hz Answer: 500 Hz