Question

A coil has a resistance of $10\Omega$ and an inductance of $0.4$ henry. It is connected to an $AC$ source of $6.5\, V, \frac{30}{\pi} Hz$ the average power (in watt) consumed in the circuit.

Answer 1

Average power consumed is given by
$P = \frac{V^2_{rms} R}{Z^2}$
where $Z = \sqrt{R^2 + (\omega L)^2}$
$ = \sqrt{10^2 + (2\pi \times \frac{30}{\pi} \times 0.4)^2}$
$ = 26\,\Omega$
$\therefore P = \frac{6.5^2 \times 10}{26^2} = 0.625\,W$