Question

An inductor of $1\text{H}$ and a capacitor of $1\mu \text{F}$ have equal reactance when connected to the same AC source at the same condition. The value of reactance is -

• A. ${10}^4\Omega$
• B. ${10}^2\Omega$
• C. ${10}^3\Omega$
• D. ${10}^5\Omega$

Answer 1

The correct option is C ${10}^3\Omega$

It is given that, $X_L=X_C$

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

$\Rightarrow {\omega }^2=\frac{1}{LC}=\frac{1}{1\times {10}^{-6}}$

$\therefore \omega ={10}^3\text{rad/s}$

Now,

$X_L=\omega L={10}^3\times 1={10}^3\Omega$

$\therefore X_L=X_C={10}^3\Omega$

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