Question

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

Answer 1

$R=10\Omega$ L= 0.4 Henny
E=6.5 V $f=\frac{30}{\pi }Hz$
$Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+{\left(2\pi fL\right)}^2}$
$Power=V_{rms}{I}_{rms}\cos \varphi$
$=6.5\times \frac{6.5}{Z}\times \frac{R}{Z}=\frac{6.5\times 6.5\times 10}{{\left[\sqrt{R^2+{\left(2\pi fL\right)}^2}\right]}^2}=\frac{6.5\times 6.5\times 10}{{10}^2{(2\pi \times \frac{30}{\pi \times 0.4})}^2}=\frac{6.5\times 6.5\times 10}{100+576}=0.625=\frac{5}{8}W$