An alternating current is given by the equation i = i1 sin ω t + i2 cos ω t. The rms current will be: (a) 1/√(2)(i₁² + i₂²)1/2 (b) 1/√(2)(i₁ + i₂) (c) 1/√(2)(i₁ + i₂)² (d) 1/2(i₁² + i₂²)1/2

Answer: (a). irms² = i² = i₁²sin ²ω t + i₂²cos ²ω t + 2i₁i₂sin ω tcos ω t = (i₁²)/(2) + (i₂²)/(2) + 0 irms = 1/√(2)(i₁² + i₂²)1/2 So the answer is (a).

An alternating current is given by the equation i = i1 sin ω t + i2… | JEE Main 2021 (26 Feb, Shift 1)

Q36JEE Main 2021 · 26 FEB · SHIFT 1Medium

AC Basics: Peak, RMS & Average Values

An alternating current is given by the equation i = i1 sin $\omega$ t + i2 cos $\omega$ t. The rms current will be:

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Answer: (a)

$i_{rms}^2 = \langle i^2 \rangle = i_1^2\langle\sin^2\omega t\rangle + i_2^2\langle\cos^2\omega t\rangle + 2i_1i_2\langle\sin\omega t\cos\omega t\rangle$
$= \frac{i_1^2}{2} + \frac{i_2^2}{2} + 0$
$i_{rms} = \frac{1}{\sqrt{2}}\left(i_1^2 + i_2^2\right)^{1/2}$
So the answer is (a).

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