A 750Hz,20V source is connected to a resistance of 100Ω, an inductance of 0.1803H and a capacitance of 10μF, all are in series. The time in which the resistance will get heated by 10∘C is-
[ Use, thermal capacity=2J/∘C]
A
349s
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B
328s
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C
248s
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D
228s
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Solution
The correct option is A349s Given, Voltage of source ,Vrms=20VFrequency of source =750HzR=100Ω;L=0.1803H;C=10μFThermal capacity=2J/∘CΔT=10∘C
The impedance,
Z=√R2+(ωL−1ωC)2
XL=ωL=2×3.14×750×0.1803≈850Ω
XC=1ωC=12×3.14×750×10−5=21.2Ω
∴Z=√(100)2+(850−21.2)2≈835Ω
∴H=I2Rt=msΔT
(VrmsZ)2×Rt=2×10
(20835)2×100t=2×10
∴t=20(0.023)2×100≈349s
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Hence, (A) is the correct answer.