Question

In a given LC circuit, where frequency of AC source is $\omega =\frac{1}{\sqrt{LC}}$, choose the correct options.

• A. Power of source is zero
• B. $i_L=0$
• C. $i=0$
• D. $i_c\ne 0$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Power of source is zero
C $i=0$
D $i_c\ne 0$

$i_L=\frac{{ϵ}_0}{X_L}\sin (\omega t-\frac{\pi }{2})$ & $i_c=\frac{{ϵ}_0}{X_c}\sin (\omega t+\frac{\pi }{2})$
$i=i_c+i_L=\frac{{ϵ}_0}{X_c}\cos \omega t-\frac{{ϵ}_0}{X_L}cos\omega t$
$i={ϵ}_0\cos \omega t[\frac{1}{X_c}-\frac{1}{X_L}]={ϵ}_0\cos \omega t[\omega c-\frac{1}{\omega L}]=0$
since $\omega =1/\sqrt{LC}$

So, the total current supplied by the source is zero, hence the power delivered is alos zero.