Question

An $\text{AC}$ circuit consists of an inductor of inductance $0.5\text{H}$ and a capacitor of capacitance $8\mu \text{F}$ in series. The current in the circuit is maximum when the angular frequency of $\text{AC}$ source is,

• A. $500\text{Hz}$
• B. $2\times {10}^5\text{Hz}$
• C. $4000\text{Hz}$
• D. $5000\text{Hz}$

Answer 1

The correct option is A $500\text{Hz}$

For $\text{LC}$ circuit,

$X_C=\frac{1}{\omega C}=\left(\frac{{10}^6}{8\omega }\right)\text{and}{X}_L=\omega L=\left(\frac{\omega }{2}\right)$

Now, $i_{rms}=\frac{V_{rms}}{Z}$

So, for $i_{rms}$ to be maximum,

Impedance, $Z=|X_L-X_C|=0$

$\Rightarrow X_L=X_C$

$\Rightarrow \omega L=\frac{1}{\omega C}$

$\Rightarrow \frac{\omega }{2}=\frac{{10}^6}{8\omega }$

$\Rightarrow {\omega }^2=250000$

$\Rightarrow \omega =500\text{Hz}$

Hence, option $\left(A\right)$ is correct.