An inductor of ( 100 ) mH , capacitor of capacitance ( 10⁻³ 2 ) F and resistance of 10 are connected in series with an AC voltage source of 110 ~V , 50 ~Hz supply. The tangent of the phase angle ' ' between voltage and current is

Step-by-step solution

The tangent of the phase angle between voltage and current in a series RLC circuit is determined by the inductive and capacitive reactances relative to the resistance. Given: R = 10 , L = 100 10⁻³ , H , C = 10⁻³ 2 , F , and f = 50 , Hz . The angular frequency is = 2 f = 100 rad/s . Inductive reactance is X_L = L = (100 ) ( 100 10⁻³ ) = 10 , . Capacitive reactance is X_C = 1 C = 1 100 10⁻³ 2 = 1 0.05 = 20 , . The phase angle satisfies = X_L - X_C R = 10 - 20 10 = -1 . Taking the magnitude gives | | = 1 . The tangent