An ac current is represented as i=5 2 +10 (650 π t+(π)/(6)) Amp The r.m.s value of the current is

Correct answer: C. 10 Amp i=5 2 +10 (650 π t+(π)/(6)) i^2=50+100 ^2(650 π t+(π)/(6)) +(2)(5 2 )(10) (650 π t+(π)/(6)) ^2 =50+(100)/(2)+0 . i^2 =100 i =10 Amp

JEE Main 20257 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Morning Shift
Subject: Physics
Chapter: Alternating Current

JEE Main 2025 · 7 April · Morning Shift · Physics · Alternating Current

An ac current is represented as i=5 2 +10 (650 π t+(π)/(6)) Amp The...

An ac current is represented as

\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

Options

A50 Amp
B100 Amp
C10 Amp
D $5 \sqrt{2} \mathrm{Amp}$

Correct answer

C. 10 Amp

Step-by-step solution

i=5 \sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right)

\mathrm{i}^2=50+100 \cos ^2\left(650 \pi \mathrm{t}+\frac{\pi}{6}\right)

+(2)(5 \sqrt{2})(10) \cos \left(650 \pi t+\frac{\pi}{6}\right)

\left\langle\mathrm{i}^2\right\rangle=50+\frac{100}{2}+0

<br/>\left. \lt \mathrm{i}^2\right\rangle=100

\lt \mathrm{i} \gt =10 \mathrm{Amp}

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