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Alternating Current question

2025 · 7 Apr · Shift 1 · Q55

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Alternating Current
2025 · 7 Apr · Shift 1 · Q55

Alternating Current question

2025 · 7 Apr · Shift 1 · Q55

JEE MainPhysicsAlternating CurrentMCQ+4 / −1

An ac current is represented as

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

The r.m.s value of the current is

A
10 Amp
B
$5 \sqrt{2} \mathrm{~Amp}$
C
100 Amp
D
50 Amp

View written solutionFree

Correct answer: A

Given current

The current is

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

This has:

a DC component: $I_{dc} = 5\sqrt{2}$
an AC component: $i_{ac} = 10\cos\left(650\pi t + \frac{\pi}{6}\right)$

RMS of AC component

For a sinusoidal current $I_0\cos(\omega t+\phi)$ , the rms value is

I_{ac,\,rms} = \frac{I_0}{\sqrt{2}}

Here $I_0 = 10$ , so

I_{ac,\,rms} = \frac{10}{\sqrt{2}} = 5\sqrt{2}

Total RMS value

When DC and AC components are both present,

I_{rms} = \sqrt{I_{dc}^2 + I_{ac,\,rms}^2}

Substitute the values:

I_{rms} = \sqrt{(5\sqrt{2})^2 + (5\sqrt{2})^2}

= \sqrt{50 + 50}

= \sqrt{100} = 10 \text{ A}

Checking options

A: $10$ Amp ✅
B: $5\sqrt{2}$ Amp ❌
C: $100$ Amp ❌
D: $50$ Amp ❌

Therefore, the correct answer is Option A.

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