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Q.

2.5πμF capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and 50sec−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=R2+12πνC2=(3000)2+12π×50×2.5π×10−62⇒Z=(3000)2+(4000)2=5×103ΩSo power factor cosφ=RZ=30005×103=0.6  and power  P=Vrmsirmscosφ=Vrms2cosφZ⇒P=(200)2×0.65×103=4.8W
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2.5πμF capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and 50sec−1 frequency. The power factor of the circuit and the power dissipated in it will respectively