Question

A series LCR circuit with $R=20\Omega ,L=1.54\text{H}andC=35\mu \text{F}$ is connected to a variable frequency $200\text{V}$ ac supply. When the frequency of the supply equals the natural frequency of the circuit. What is the average power in $\text{kW}$ transferred to the circuit in one complete cycle?

Answer 1

Given a series LCR circuit - $V=200\text{V}$;
$R=20\Omega$;
$L=1.5\text{H}$ and
$C=35\mu F.$
When the frequency of the ac supply is equal to the natural frequency, then impedance is equal to the resistance.
$Z=R$ and $\phi =0$
We know that $I=\frac{V}{R}=\frac{200}{2}=10\Omega$
So, average power transferred
$P=VI\cos \phi$
$P=200\times 10\times 1$
$P=2000\text{W}$
$P=2\text{kW}.$