A series combination of resistor ' R ' and capacitor ' C ' is connected to an a.c. source of angular frequency ' '. Keeping the voltage same, if the frequency is changed to 3 the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

Step-by-step solution

Initial current I = V Z and Final current I ^ = V Z ^ I ^ = I 2 Z^ =2 Z R ^2+ X _ c ^2 R ^2+ X _ c ^ 2 = 1 4 4 R^2+4 X_c^2=R^2+X_c^2 aligned & 3 R^2=X_c^ 2 -4 X_c^2 & X_c= 1 C , X_c^ = 3 C & X_c ^ =3 X_c aligned From (1) 3 R^2=9 X_c^2-4 X_c^2=5 X_c^2 X _ c ^2 R ^2 = 3 5 =0.6 X _ c R = 0.6