An inductor coil takes current 8 ~A when connected to a 100 ~V and 50 ~Hz AC source. A pure resistor under the same condition takes current of 10 ~A . If inductor coil and resistor are connected in series to a 100 ~V and 40 ~Hz AC supply, then the current in the series combination of above resistor and inductor is

Step-by-step solution

Inductive reactance when 100 ~V , 50 ~Hz source is connected is given by X _ L = V I = 100 8 =12.5 Resistance R = V 1 = 100 10 =10 Inductive reactance at new frequency of 40 ~Hz aligned & X _ L ^ X _ L = 2 f ^ L 2 fL = 40 50 = 4 5 & X _ L ^ = 4 5 X _ L = 4 5 12.5=10 aligned When they are connected in series the impedance will be given by aligned & Z= R^2+X_L^ 2 = (10)^2+(10)^2 =10 2 A & I= V Z = 100 10 2 =5 2 ~A aligned