An LCR series circuit is connected to a variable-frequency AC source. It is observed that the current amplitude in the circuit reaches its maximum value when the angular frequency of the source is 5000 rad/s . If the capacitance in the circuit is 4 F , what is the inductance of the inductor?

Step-by-step solution

The current amplitude in an LCR series circuit is maximum at the resonant angular frequency. The resonant angular frequency is given by = 1 LC . Squaring both sides gives ^2 = 1 LC . Rearranging for inductance L , we get L = 1 ^2 C . Substituting the given values = 5000 rad/s and C = 4 F = 4 10⁻⁶ F : L = 1 (5000)^2 4 10⁻⁶ L = 1 25 10^6 4 10⁻⁶ L = 1 100 H L = 0.01 H = 10 mH Answer: 10 mH