The power factor of a CR circuit is 1 2 , If the frequency of a. c. signal is halved, then the power factor of the circuit will become

Step-by-step solution

The power factor in a CR circuit is defined as = R Z , where R is the resistance and Z = R^2 + X_C^2 is the impedance with capacitive reactance X_C = 1 C . Given the initial power factor ₁ = 1 2 , we equate: R R^2 + X_ C1 ^2 = 1 2 Squaring both sides yields R^2 R^2 + X_ C1 ^2 = 1 2 , which simplifies to R^2 = X_ C1 ^2 . Therefore R = X_ C1 . When the frequency is halved, f' = f/2 , so the new reactance becomes X_ C2 = 1 2 f' C = 1 2 (f/2) C = 2X_ C1 = 2R . The new power factor is: ₂ = R R^2 + X_ C2 ^2 = R R^2 + (2R