A series LCR circuit is connected to an AC source of angular frequency 1000 rad s ⁻¹ . The circuit contains a resistor of 50 and an inductor of 20 mH. If the power factor of the circuit is exactly 1 , the required capacitance of the circuit is _____ F .

Step-by-step solution

For the power factor of a series LCR circuit to be exactly 1 , the circuit must be in resonance. At resonance, the inductive reactance equals the capacitive reactance: X_L = X_C L = 1 C Rearranging for capacitance C : C = 1 ^2 L Substituting the given values: = 1000 rad s ⁻¹ L = 20 10⁻³ H C = 1 (1000)^2 20 10⁻³ C = 1 10^6 20 10⁻³ = 1 20 10^3 C = 50 10⁻⁶ F Therefore, the capacitance is 50 F . Answer: 50