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Q.

Power dissipated in an LCR series circuit connected to an AC source of emf $ε$ is

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a

$\frac{ε^{2} R}{[R^{2} + {(Lω - \frac{1}{Cω})}^{2}]}$

b

$\frac{ε^{2} \sqrt{R^{2} + {(Lω - \frac{1}{Cω})}^{2}}}{R}$

c

$\frac{ε^{2} [R^{2} + {(Lω - \frac{1}{Cω})}^{2}]}{R}$

d

$\frac{ε^{2} R}{\sqrt{R^{2} + {(Lω - \frac{1}{Cω})}^{2}}}$

answer is A.

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Detailed Solution

Power dissipated in series LCR circuit,

$P = I_{rms}^{2} R = \frac{ε_{rms}^{2} R}{| Z |^{2}} = \frac{ε^{2} R}{[R^{2} + {(ωL - \frac{1}{ωC})}^{2}]}$

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