In an LC circuit,the angular frequency at res | vedclass

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Question

(B) The resonant angular frequency of an $LC$ circuit is given by the formula $\omega = \frac{1}{\sqrt{LC}}$.Let the initial inductance be $L$ and cap

Vedclass · Accepted Answer

$\frac{\omega}{4 \sqrt{2}}$

Vedclass · Answer

(B) The resonant angular frequency of an $LC$ circuit is given by the formula $\omega = \frac{1}{\sqrt{LC}}$.Let the initial inductance be $L$ and capacitance be $C$. Then,$\omega = \frac{1}{\sqrt{LC}}$.According to the problem,the new inductance $L' = 4L$ and the new capacitance $C' = 8C$.The new resonant angular frequency $\omega'$ is given by $\omega' = \frac{1}{\sqrt{L'C'}} = \frac{1}{\sqrt{(4L)(8C)}} = \frac{1}{\sqrt{32LC}}$.Simplifying this,we get $\omega' = \frac{1}{\sqrt{16 	imes 2 	imes LC}} = \frac{1}{4 \sqrt{2} \sqrt{LC}}$.Since $\omega = \frac{1}{\sqrt{LC}}$,we can substitute this into the equation to get $\omega' = \frac{\omega}{4 \sqrt{2}}$.

In an $LC$ circuit,the angular frequency at resonance is $\omega$. What is the new angular frequency when the inductance is made four times and the capacitance is made eight times its original value?

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