An a.c. source of 15 ~V , 50 ~Hz is connected across an inductor (L) and resistance (R) in series R.M.S. current of 0.5 ~A flows in the circuit. The phase difference between applied voltage and current is ( 3 ) radian. The value of resistance (R) is ( 60^ = 3 )

Step-by-step solution

Given data: E =15 ~V , f =50 ~Hz , I =0.5 ~A , = 3 rad Impedance is given as Z= E I = 15 0.5 =30 aligned & = X _ L R & 3 = X _ L R & 3 = X _ L R & X _ L = 3 R aligned The formula for impedance is array rl Z & = R^2+X_L^2 Z & = R^2+( 3 R)^2 Z & = 4 R^2 2 & R=Z R & = Z 2 = 30 2 =15 array