Find the effective value of current i = 2sin( | vedclass

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(C) Given the current equation: $i = 2\sin(100\pi t) + 2\cos(100\pi t + 30^{\circ})$.Using the trigonometric identity $\cos(A + B) = \cos A \cos B - \

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$\sqrt{2}\,A$

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(C) Given the current equation: $i = 2\sin(100\pi t) + 2\cos(100\pi t + 30^{\circ})$.Using the trigonometric identity $\cos(A + B) = \cos A \cos B - \sin A \sin B$,we expand the second term:$i = 2\sin(100\pi t) + 2[\cos(100\pi t)\cos(30^{\circ}) - \sin(100\pi t)\sin(30^{\circ})]$.Substitute $\cos(30^{\circ}) = \frac{\sqrt{3}}{2}$ and $\sin(30^{\circ}) = \frac{1}{2}$:$i = 2\sin(100\pi t) + 2[\cos(100\pi t) \cdot \frac{\sqrt{3}}{2} - \sin(100\pi t) \cdot \frac{1}{2}]$.$i = 2\sin(100\pi t) + \sqrt{3}\cos(100\pi t) - \sin(100\pi t)$.$i = \sin(100\pi t) + \sqrt{3}\cos(100\pi t)$.This is in the form $i = I_m \sin(100\pi t + \phi)$,where the amplitude $I_m = \sqrt{1^2 + (\sqrt{3})^2} = \sqrt{1 + 3} = \sqrt{4} = 2\,A$.The effective value ($RMS$ value) is given by $I_{	ext{rms}} = \frac{I_m}{\sqrt{2}}$.$I_{	ext{rms}} = \frac{2}{\sqrt{2}} = \sqrt{2}\,A$.

Find the effective value of current $i = 2\sin(100\pi t) + 2\cos(100\pi t + 30^{\circ})$.

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