In an A.C. circuit containing L, C, R in seri | vedclass

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Question

(D) The true power in an $A.C.$ circuit is given by $P_{	ext{true}} = V_{	ext{rms}} I_{	ext{rms}} \cos \phi$,where $\cos \phi$ is the power factor.

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$\frac{R}{Z}$

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(D) The true power in an $A.C.$ circuit is given by $P_{	ext{true}} = V_{	ext{rms}} I_{	ext{rms}} \cos \phi$,where $\cos \phi$ is the power factor.The apparent power in an $A.C.$ circuit is given by $P_{	ext{apparent}} = V_{	ext{rms}} I_{	ext{rms}}$.The ratio of true power to apparent power is $\frac{P_{	ext{true}}}{P_{	ext{apparent}}} = \frac{V_{	ext{rms}} I_{	ext{rms}} \cos \phi}{V_{	ext{rms}} I_{	ext{rms}}} = \cos \phi$.In an $LCR$ series circuit,the power factor $\cos \phi$ is defined as the ratio of resistance to impedance,i.e.,$\cos \phi = \frac{R}{Z}$.Therefore,the ratio of true power to apparent power is $\frac{R}{Z}$.

In an $A.C.$ circuit containing $L, C, R$ in series,the ratio of true power to apparent power is ($Z=$ impedance of the circuit and $R$ is the resistance).

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