Question

An inductance of $1mH$ and a capacitance of $10\mu F$ are connected in a circuit. The angular frequency of circuit will be

• A. $10^{3}rad/s$
• B. $10^{4}rad/s$
• C. $10^{2}rad/s$
• D. $10^{5}rad/s$

Answer 1

Answer: (B)

At resonance,
inductive reactance $\left(X_L\right)$ is equal to capacitive reactance
$\left(X_C\right).$ Therefore,
$X_L=X_C$
$\omega L=\frac{1}{\omega C}\Rightarrow \omega =\frac{1}{\sqrt{LC}}$
Given, $L=1mH=1\times 10^{-3}H,$
$C=10\mu F=10\times 10^{-6}F$
$\therefore \omega =\frac{1}{\sqrt{10^{-3}\times 10\times 10^{-6}}}$
$\Rightarrow \omega =10^{4}rad/s$