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Q.

A 750 Hz, 20 V (rms) source is connected to a resistance of 100  Ω, an inductance of 0.1803 H and a capacitance of  10    μF all in series. The time in which the resistance (heat capacity 2 J/ºC) will get heated by 10ºC. (assume no loss of heat to the surroundings) is close to :

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a

418 s

b

348 s

c

365 s

d

245 s

answer is B.

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Detailed Solution

ω=2πf⇒ω=2π×750=1500πImpedance =Z=R2+Lω-1Cω2 ⇒Z=1002+0.18031500π-110×10-61500π2=834Ω Power consumed by resistance=P=Vrmsirmscosθ=Vrms.VrmsZ.RZ=20×20×100834×834=0.058WHeat dissipated=Pt=Sθ⇒t=SθP=2×100.058=348s
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