Question

A series $LCR$ circuit containing a resistor of resistance $120\Omega$ has resonant frequency $4\times {10}^5\text{rad/s}$. At resonance, the voltage across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively. Find the value of $L$.

• A. ${10}^{-4}\text{H}$
• B. ${10}^{-6}\text{H}$
• C. $4\times {10}^{-8}\text{H}$
• D. $2\times {10}^{-4}\text{H}$

Answer 1

The correct option is D $2\times {10}^{-4}\text{H}$

In a series $LCR$ circuit, at resonance,

$X_L=X_C$ and $Z=R$

Also, current,

$i=\frac{\Delta V_R}{R}=\frac{60}{120}=0.5\text{A}$

Voltage across inductor,

$\Delta V_L=i{X}_L=i\omega L$

$\Rightarrow 40=0.5\times 4\times {10}^5\times L$

$\Rightarrow L=2\times {10}^{-4}\text{H}$

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