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Q.

$\frac{{2.5}}{\pi }\mu F$ capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and $50se{c^{ - 1}}$ frequency. The power factor of the circuit and the power dissipated in it will respectively

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a

0.6, 0.06 W

b

0.06, 0.6 W

c

0.6, 4.8 W

d

4.8, 0.6 W

answer is C.

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Detailed Solution

$Z=\sqrt{R^2+\left ( \frac{1}{2\pi\,vC} \right )^2}=\sqrt {(3000)^2+\frac{1}{\left ( 2\pi\, \times50\times\frac{2.5}{\pi}\times10^-6 \right )^2}}$ $\Rightarrow Z = \sqrt {{{(3000)}^2} + {{(4000)}^2}} = 5 \times {10^3}\Omega$

So power factor $\cos \varphi = \frac{R}{Z} = \frac{{3000}}{{5 \times {{10}^3}}} = 0.6$ and power $P = {V_{rms}}{i_{rms}}\cos \varphi = \frac{{V_{rms}^2\cos \varphi }}{Z}$ $\Rightarrow P = \frac{{{{(200)}^2} \times 0.6}}{{5 \times {{10}^3}}} = 4.8W$

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capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and frequency. The power factor of the circuit and the power dissipated in it will respectively