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 current amplitude is maximum? Also, find the maximum value of current.

• A. $500.5\text{Hz},19.1\text{A}$
• B. $663.5\text{Hz},14.1\text{A}$
• C. $809.9\text{Hz},22.5\text{A}$
• D. $700.5\text{Hz},18.1\text{A}$

Answer 1

The correct option is B $663.5\text{Hz},14.1\text{A}$

Maximum current in the circuit is achieved at resonance.

The resonant angular frequency,

${\omega }_0=\frac{1}{\sqrt{\left(LC\right)}}$

$\Rightarrow {\omega }_0=\frac{1}{\sqrt{\left(0.12\right)(480\times {10}^{-9})}}$

$\Rightarrow {\omega }_0\approx 4167\text{rad/s}$

The resonant frequency $f_0$ is given as,

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

At resonance, maximum current amplitude is given as,

$i_{max}=\frac{V_0}{R}=\frac{\sqrt{2}\times 230}{23}=14.1\text{A}$

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