Question

A current of $1.1A$ flows through a coil when connected to a $110-V$ dc source. When $110-50Hz$ ac is supplied to the same coil, only $0.5A$ current flows. Calculate the resistance, impedance and inductance of the coil

Answer 1

For dc,

$I=1.1A$

$V=110V$

$V=IR$

therefore, $R=\frac{110}{1.1}=100\Omega$

For ac,

$V=110V$

$R=100\Omega$

$I=0.5A$

$Z=\frac{V}{I}=\frac{110}{0.5}=220\Omega$

Frequency $\nu =50Hz$

wkt

$\begin{array}{c}Z=\sqrt{R^2+\omega L^2}=\sqrt{R^2+4{\pi }^2{\nu }^2{L}^2}\\ 220=\sqrt{{100}^2+4{\pi }^2{\left(50\right)}^2{L}^2}\\ L=0.389H\end{array}$