When (100 ~V ) d.c. is applied across a coil, a current of 1 A flows through it. When (100 ~V ) a.c. of (50 ~Hz ) is applied to the same coil only 0.5 A flows. The inductance of the coil is

Step-by-step solution

For dc, V=I R ( R is resistance of inductor) 100=1 R R=100 . For ac, Z= R^2+X_L^2 aligned & V=I Z & 100=0.5 R^2+X_L^2 & 100=0.5 (100)^2+X_L^2 aligned aligned & 100= 5 10 (100)^2+X_L^2 & X_L^2=(200)^2-(100)^2=300 100 & X_L= 3 (100)^2 =100 3 & L=100 3 2 v L=100 3 & 2 50 L=100 3 & 100 L=100 3 & L= 3 = 3 3.14 L=0.55 H . aligned