Question

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

Impedance for AC LC circuit is given by $Z=|X_L-X_C|$.

• A. $800\text{rad/s}$
• B. $600\text{rad/s}$
• C. $700\text{rad/s}$
• D. $500\text{rad/s}$

Answer 1

The correct option is D $500\text{rad/s}$

For an AC LC circuit,

$X_C=\frac{1}{\omega C}=\frac{{10}^6}{8\omega }$

$X_L=\omega L=\frac{\omega }{2}$

So, impedance,

$Z=|X_L-X_C|...\left(1\right)$

Now,

$i_0=\frac{V_0}{Z}$

For $i_0$ to be maximum, $Z\to 0$

$\therefore X_L=X_C\left[\text{From}\right(1\left)\right]$

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

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

$\Rightarrow \omega =500\text{rad/s}$

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