Question

A coil has an inductance of $\frac{22}{\pi }$ $H$ and is joined in series with a resistance of $220$ $\Omega$. When an alternate e.m.f. of $220$ $V$ at $50$ is applied to it, then watt less component of the rms current in the circuit.

• A. $5$ $ampere$
• B. $0.5$ $ampere$
• C. $0.7$ $ampere$
• D. $7$ $ampere$

Answer 1

The correct option is B $0.5$ $ampere$

$X_L=2\pi \times 50\times \frac{2.2}{\pi }$

$\Rightarrow X_L=220$ $\Omega$

$I=\frac{220\angle 0^o}{220+j220}$

$\Rightarrow I=\frac{1}{1+j}\frac{(1-j)}{(1-j)}=\frac{1-j}{2}$

Imaginary part is watt-less component of $I$

$\Rightarrow I=0.5$ $A$