The r.m.s. value of the current i = 3 + 4 sin | vedclass

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(B) The given current is $i = 3 + 4 \sin(\omega t + \pi/3)$.To find the $r.m.s.$ value,we use the formula $I_{rms} = \sqrt{\langle i^2 \rangle}$.First

Vedclass · Accepted Answer

$\sqrt{17} \ A$

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(B) The given current is $i = 3 + 4 \sin(\omega t + \pi/3)$.To find the $r.m.s.$ value,we use the formula $I_{rms} = \sqrt{\langle i^2 \rangle}$.First,calculate $i^2 = (3 + 4 \sin(\omega t + \pi/3))^2 = 9 + 16 \sin^2(\omega t + \pi/3) + 24 \sin(\omega t + \pi/3)$.Taking the average over a full cycle,$\langle 9 \rangle = 9$,$\langle \sin^2(\omega t + \pi/3) \rangle = 1/2$,and $\langle \sin(\omega t + \pi/3) \rangle = 0$.Thus,$\langle i^2 \rangle = 9 + 16(1/2) + 24(0) = 9 + 8 = 17$.Therefore,$I_{rms} = \sqrt{17} \ A$.

The $r.m.s.$ value of the current $i = 3 + 4 \sin(\omega t + \pi/3)$ is:

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