Alternating Current

JEE Main level, numerical answer, medium

11 of 190

Question 11 of 190

A alternating current at any instant is given by i=[6+56sin⁡(100πt+π/3)]i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)] A. The rmsr m s value of the current is ________ A.

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Answer: 8

IDNs=∫i2dt∫dtIDns=(6)2+(56)22=36+28=64=8 A\begin{aligned} & I_{D N s}=\sqrt{\frac{\int i^2 d t}{\int d t}} \\ & I_{D n s}=\sqrt{(6)^2+\frac{(\sqrt{56})^2}{2}} \\ & =\sqrt{36+28} \\ & =\sqrt{64} \\ & =8 \mathrm{~A}\end{aligned}

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