JEE MainPhysicsAlternating Current
A series LCR circuit is connected to an AC voltage source described by the equation V = 200 (1000 t) V. The circuit contains a resistance of 50 and a capacitance of 40 F . If the circuit operates at unity power factor, the required value of inductance is ______ mH.
Correct answer
25
Step-by-step solution
The circuit operates at unity power factor, which means it is in a state of resonance. At resonance, the inductive reactance equals the capacitive reactance, so L = 1 C . From the given voltage equation V = 200 (1000 t) , the angular frequency is = 1000 rad/s. Substituting the values of and C : 1000 L = 1 1000 40 10⁻⁶ L = 1 10^6 40 10⁻⁶ = 1 40 H L = 0.025 H = 25 mH. Answer: 25