Alternating current equation |AlternatingCurrentJEEMain2021

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JEE MAIN 2021

26-02-2021 S1

Question

An alternating current is given by the equation $\mathrm{i}=\mathrm{i}_1 \sin \omega \mathrm{t}+\mathrm{i}_2 \cos \omega \mathrm{t}$. The rms current will be

Select the correct option:

A

$\frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$

B

$\frac{1}{\sqrt{2}}\left(i_1+i_2\right)^2$

C

$\frac{1}{2}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$

D

$\frac{1}{\sqrt{2}}\left(i_1+i_2\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & i=i_1 \sin \omega t+i_2 \sin (\omega t+90) \\ & i=\sqrt{i_1^2+i_2^2} \sin (\omega t+\phi) \\ & i_{\text {rms }}=\frac{i_0}{\sqrt{2}} \frac{\sqrt{i_1^2+i_2^2}}{\sqrt{2}}\end{aligned}$

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