Question

A series $LCR$ with $R=20\Omega ,L=1.5H$ and $C=35\mu F$ is connected to a variable frequency $200V$ a.c. supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

• A. $100\text{Watt}$
• B. $200\text{Watt}$
• C. $1000\text{Watt}$
• D. $2000\text{Watt}$

Answer 1

The correct option is D $2000\text{Watt}$

Average power transferred
$P_{avg}=\frac{1}{2}{I}_0{V}_0\cos \varphi$


From the phasor diagram,
$\cos \varphi =\frac{R}{Z}$
At resonance, $X_L=X_C$
and therefore, $Z=R$
$\cos \varphi =1$
and $P_{avg}=\frac{1}{2}{I}_0{V}_0\cos \varphi$
$=V_{rms}{I}_{rms}\cos \varphi$
$=V_{rms}{I}_{rms}$

Given $V_{rms}=200V$
$I_{rms}=\frac{V_{rms}}{Z}=\frac{V_{rms}}{R}$
$=\frac{200V}{20\Omega }=10A$

$\therefore P_{avg}=200\times 10=2000\text{Watt}$