Question

In a $LC$ circuit. Angular frequency at resonance is $w$. What will be the new angular frequency when inductor's introduces is made $2$ times and capacitance is made $4$ times?

• A. $\frac{w}{\sqrt{2}}$
• B. $\frac{w}{2\sqrt{2}}$
• C. $2w$
• D. $\frac{2w}{\sqrt{2}}$

Answer 1

Answer: (B)

$\frac{w}{2\sqrt{2}}$

$w=\frac{1}{\sqrt{LC}}$
Now if $L^1=2L{C}^1=4C$
$w^1=\frac{1}{\sqrt{2L.4C}}$
$w^1=\frac{1}{2\sqrt{2}}\cdot \frac{1}{\sqrt{LC}}=\frac{w}{2\sqrt{2}}$