A resistance R draws power P when connected to an AC source. If an inductance is now placed in series with…

1. $\mathrm{P}{\left(\frac{\mathrm{R}}{\mathrm{Z}}\right)}^2$
2. $\mathrm{P}\sqrt{\frac{\mathrm{R}}{\mathrm{Z}}}$
3. $\mathrm{P}\left(\frac{\mathrm{R}}{\mathrm{Z}}\right)$
4. $\mathrm{P}$

Solution

We know
$P=\frac{V^2}{R} ; P^{\prime }=\frac{V.V}{z}\cos \mathrm{\Phi }$
${ V}^2=PR \& \cos \mathrm{\Phi }=\frac{R}{z}$
$P^{\prime }=\frac{V^2}{z} \frac{R}{z}$
$\Rightarrow \frac{P^{}R}{z^2} R=P\left(\frac{R^2}{z^2}\right)$
$=P^{}{\left(\frac{R}{z}\right)}^2$

Asked in: NEET 2015 (Phase 1)

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