Question

A choke coil of $100\, ohm$ and $1 \,H$ is connected to a generator of $E =200 \sin (100\, t$ ) volt. The average power dissipated will be ?

Answer 1

$E =200 \sin (100\, t )$
$R =100\, \Omega, L =1 \,H$
$Z =\sqrt{ R ^{2}+(\omega L )^{2}}$
$Z =\sqrt{100^{2}+(100 \times 1)^{2}}=100 \sqrt{2}$
$I _{\text {runs }}=\frac{200}{\sqrt{2}} \times \frac{1}{100 \sqrt{2}}$
$I _{\text {runs }}=1\, A$
cos $\phi=\frac{ R }{ Z }=\frac{100}{100 \sqrt{2}}=\frac{1}{\sqrt{2}}$
Power $= E _{\text {rms }} I _{ rms } \cos \phi .$
$=\frac{200}{\sqrt{2}} \times 1 \times \frac{1}{\sqrt{2}}=100$ watt