An alternating current is given by the equation i = i 1 sin ω t + i 2 cos ω t . The rms current will be:

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An alternating current is given by the equation

i = i_{1} \sin ω t + i_{2} \cos ω t

. The rms current will be:

PhysicsAlternating CurrentJEE MainJEE Main 2021 (26 Feb Shift 1)

Options:

A $\frac{1}{\sqrt{2}} {(i_{1} + i_{2})}^{2}$
B $\frac{1}{\sqrt{2}} (i_{1} + i_{2})$
C $\frac{1}{2} {(i_{1}^{2} + i_{2}^{2})}^{\frac{1}{2}}$
D $\frac{1}{\sqrt{2}} {(i_{1}^{2} + i_{2}^{2})}^{\frac{1}{2}}$

Solution:

1219 Upvotes Verified Answer

The correct answer is:

\frac{1}{\sqrt{2}} {(i_{1}^{2} + i_{2}^{2})}^{\frac{1}{2}}

$i = i_{1} \sin ω t + i_{2} \sin (ω t + 90)$

$i = \sqrt{i_{1}^{2} + i_{2}^{2}} \sin (ω t + ϕ)$

$i_{rms} = \frac{i_{0}}{\sqrt{2}} = \frac{\sqrt{i_{1}^{2} + i_{2}^{2}}}{\sqrt{2}}$

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