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In a L-C circuit, angular frequency at resonance is $\omega$. What will be the new angular frequency when inductor's inductance is made two times and capacitor's capacitance is made four times?
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Verified Answer
The correct answer is:
$\frac{\omega}{2 \sqrt{2}}$
$\because$ Angular frequency at resonance,
$\omega=\frac{1}{\sqrt{\mathrm{LC}}}$ ...(i)
According to question, when inductor's inductance is made 2 times and capacitance is 4 times, then
$\omega^{\prime}=\frac{1}{\sqrt{\mathrm{LC}}}$
or $\quad \omega^{\prime}=\left(\frac{1}{2 \sqrt{2}}\right) \frac{1}{\sqrt{\mathrm{LC}}}$
$=\frac{\omega}{2 \sqrt{2}} \quad$ [From Eq. (i)]
$\omega=\frac{1}{\sqrt{\mathrm{LC}}}$ ...(i)
According to question, when inductor's inductance is made 2 times and capacitance is 4 times, then
$\omega^{\prime}=\frac{1}{\sqrt{\mathrm{LC}}}$
or $\quad \omega^{\prime}=\left(\frac{1}{2 \sqrt{2}}\right) \frac{1}{\sqrt{\mathrm{LC}}}$
$=\frac{\omega}{2 \sqrt{2}} \quad$ [From Eq. (i)]
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