Question

A series ac circuit consist of an inductor and a capacitor. The inductance and capacitance is respectively $1$ henry and $25\mu F$. If the current is maximum in circuit, then angular frequency will be

• A. $100rad/s$
• B. $200rad/s$
• C. $50rad/s$
• D. $200/2\pi rad/s$

Answer 1

The correct option is B $200rad/s$

Calculation of angular frequency:
We know that the current will be maximum at resonant frequency.
Now, at resonance $X_L=X_C$
$\omega L=\frac{1}{\omega C}$
${\omega }^2=\frac{1}{LC}$
Given $L=1H,C=25\times {10}^{-6}F$
$\omega =\frac{1}{\sqrt{\left(1\right)\times (25\times {10}^{-6}})}$
$=\frac{1}{(5\times {10}^{-3})}$
$\omega =200rad{s}^{-1}$
Hence, the correct option is $\left(A\right)$.