Alternating Current

JEE Main level, single correct, medium

6 of 190

Question 6 of 190

An ac current is represented as
i=52+10cos⁡(650πt+π6)Amp\mathrm{i}=5 \sqrt{2}+10 \cos \left(650 \pi \mathrm{t}+\frac{\pi}{6}\right) \mathrm{Amp}
The r.m.s value of the current is

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Answer: (C) 10 Amp

i=52+10cos⁡(650πt+π6)i=5 \sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right)
i2=50+100cos⁡2(650πt+π6)\mathrm{i}^2=50+100 \cos ^2\left(650 \pi \mathrm{t}+\frac{\pi}{6}\right)
+(2)(52)(10)cos⁡(650πt+π6)+(2)(5 \sqrt{2})(10) \cos \left(650 \pi t+\frac{\pi}{6}\right)
⟨i2⟩=50+1002+0\left\langle\mathrm{i}^2\right\rangle=50+\frac{100}{2}+0
<i2⟩=100\left. \lt \mathrm{i}^2\right\rangle=100
<i>=10Amp \lt \mathrm{i} \gt =10 \mathrm{Amp}

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