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Q.

An inductor 20 mH, a capacitor 100μF  and a resistor 50 Ω are connected in series across a source of emf, V=10 sin 314 t. The power loss in the circuit is

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a

0.79 W

b

0.43 W

c

2.74 W

d

1.13 W

answer is A.

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Detailed Solution

Impedance  Z in an ac circuit isZ=R2+XC-XL2; where XC= capacitive reactance                                                   and XL= inductive reactance.  Also XC=1ωC and XL=ωL∴Z=(50)2+1314×100×10-6-314×20×10-32      or   Z=56Ω The power loss in the circuit is Pav=VrmsZ2R∴Pav=10(2)562×50=0.79 W
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