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If impedance is $\sqrt{3}$ times of resistance, then find phase difference.
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Verified Answer
The correct answer is:
$60^{\circ}$
Using relation, $\tan \theta=\frac{X_{L}-X_{C}}{R}$
$$
\Rightarrow \quad \theta=\tan ^{-1}\left(\frac{X_{L}-X_{C}}{R}\right)=\tan ^{-1}\left(\frac{Z}{R}\right)
$$
Here, $Z=\sqrt{3} R$
$\Rightarrow \quad \theta=\tan ^{-1}\left(\frac{\sqrt{3} \pi}{n}\right)=\tan ^{-1}(\sqrt{3})=60^{\circ}$
$$
\Rightarrow \quad \theta=\tan ^{-1}\left(\frac{X_{L}-X_{C}}{R}\right)=\tan ^{-1}\left(\frac{Z}{R}\right)
$$
Here, $Z=\sqrt{3} R$
$\Rightarrow \quad \theta=\tan ^{-1}\left(\frac{\sqrt{3} \pi}{n}\right)=\tan ^{-1}(\sqrt{3})=60^{\circ}$
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