Question

A series $RLC$ circuit has inductance of $0.12\text{H}$, capacitance of $480\text{nF}$ and resistance of $23\Omega$ is connected to a $230\text{V}$ AC supply whose frequency can be varied. What is the source frequency for which average power absorbed by the circuit is maximum? Also, find the value of maximum power.

• A. $500.3\text{Hz},1400\text{W}$
• B. $580.2\text{Hz},2000\text{W}$
• C. $663.5\text{Hz},2300\text{W}$
• D. $753.5\text{Hz},2800\text{W}$

Answer 1

The correct option is C $663.5\text{Hz},2300\text{W}$

Maximum average power is absorbed by the circuit at resonance.

The resonant angular frequency,

${\omega }_0=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{\left(0.12\right)(480\times {10}^{-9})}}\approx 4167\text{rad/s}$

Also, resonant frequency,

$f_0=\frac{{\omega }_0}{2\pi }=\frac{4167}{2\times 3.14}=663.5\text{Hz}$

Now, average power absorbed by the circuit,

$P=V_{rms}{i}_{rms}\cos \varphi$

$=\frac{V_{rms}^2}{Z}\cos \varphi$

At resonance, $\varphi =0^{\circ }$ and $Z=R$, so,

$P_{max}=\frac{V_{rms}^2}{R}=\frac{{230}^2}{23}$

$=2300\text{W}$

Hence, option $\left(C\right)$ is the correct answer.