For an R-L series circuit, the power factor is 3 2 , for R-L frequency f Hz. If the frequency doubles, the new power factor will be

Step-by-step solution

The initial power factor is given by = R R^2 + X_L^2 = 3 2 Squaring both sides, we get: R^2 R^2 + X_L^2 = 3 4 4R^2 = 3R^2 + 3X_L^2 R^2 = 3X_L^2 X_L = R 3 The inductive reactance is X_L = 2 f L . When the frequency is doubled ( f' = 2f ), the new inductive reactance becomes: X_L' = 2X_L = 2R 3 The new power factor is: ' = R R^2 + (X_L')^2 ' = R R^2 + ( 2R 3 )^2 ' = R R^2 + 4R^2 3 ' = R 7R^2 3 = 3 7 Answer: 3 7