question_answer

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:

A)  5.5 mH

B)  0.55 mH

C)   55 mH

D)  0.55 H

Correct Answer: D

Solution :

\[V=100V\] \[i=1amp\] \[V=iR\] \[R=\frac{100}{1}\] \[=100\Omega \] \[Va.c.=100V\] \[Z=\sqrt{{{R}^{2}}+X_{L}^{2}}\] \[i=0.5amp.\] \[V=\sqrt{({{R}^{2}}+X{{L}^{2}})}\] \[\frac{1000}{5}=\sqrt{{{R}^{2}}+X_{L}^{2}}\] \[{{(200)}^{2}}={{100}^{2}}+X{{L}^{2}}\] \[40,000-10,000=X_{L}^{2}\] \[\sqrt{30,000}={{X}_{L}}\] \[{{X}_{L}}=173.2\Omega \] \[{{X}_{L}}=2\pi f\,L\] \[173.2=2\pi \times 50L\] \[L=0.551H\]