Question

The self inductance of a choke coil is $10mH$. When it is connected to a $10VDC$ source, the loss of power is $20W$. When it is connected to a $10VAC$ source, the loss of power is $10W$. The frequency of $AC$ source (in $Hz$ ) will be (Answer to be given in nearest integer)

Answer 1

Answer: 80

For $DC:R=\frac{V^2}{P}\left(\therefore X_L=0\right)$
$R=\frac{10\times 10}{20}=5\Omega$
For $AC:P_{\text{loss }}=VI\cos \varphi$
$P_{\text{loss }}=V\times \frac{V}{Z}\times \frac{R}{Z}$
$P_{\text{loss }}=\frac{V^2\times R}{Z^2}$
$Z^2=\frac{V^{2}R}{P_{\text{loss }}}=\frac{10\times 10\times 5}{10}=50\Omega$
Now, $Z^2=R^2+X_L^2$
$50=25+X_L^2$
$\Rightarrow X_L=5\Omega$
$2\pi fL=5$
$\Rightarrow f=\frac{5}{2\pi L}=\frac{5}{2\pi \times 10\times 10^{-3}}$
$f=80Hz$