Alternating Current

JEE Main level, numerical answer, medium

28 of 190

Question 28 of 190

As shown in the figure an inductor of inductance 200mH200mH is connected to an ACAC source of emf 220V220Vand frequency 50Hz50Hz. The instantaneous voltage of the source is 0V0V when the peak value of current is aπA\dfrac{\sqrt{a}}{\pi }A. The value of aa is _____ .

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Answer: 242

The reactance of the given inductor is,
XL=ωL=2πfL=2π×50×0.2=20πΩ{X}_{L}=\omega L=2\pi fL=2\pi \times 50\times 0.2=20\pi \Omega.
The maximum current in the given circuit will be,
i0=2VrmsXL=2×22020π=242πA{i}_{0}=\dfrac{\sqrt{2}{V}_{rms}}{{X}_{L}}=\dfrac{\sqrt{2}\times 220}{20\pi }=\dfrac{\sqrt{242}}{\pi }A
Therefore, a=242a=242

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