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(D) The given current is $i = i_1 + i_2$,where $i_1 = 2\sin(100\pi t)$ and $i_2 = 2\sin(100\pi t + 30^\circ)$.Using the phasor addition method,the res

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(D) The given current is $i = i_1 + i_2$,where $i_1 = 2\sin(100\pi t)$ and $i_2 = 2\sin(100\pi t + 30^\circ)$.Using the phasor addition method,the resultant current $i = I_0 \sin(100\pi t + \phi)$.The amplitude $I_0$ is given by $I_0 = \sqrt{I_{01}^2 + I_{02}^2 + 2I_{01}I_{02}\cos(	heta)}$,where $I_{01} = 2$,$I_{02} = 2$,and $	heta = 30^\circ$.$I_0 = \sqrt{2^2 + 2^2 + 2(2)(2)\cos(30^\circ)} = \sqrt{4 + 4 + 8(\frac{\sqrt{3}}{2})} = \sqrt{8 + 4\sqrt{3}}$.$I_0 = \sqrt{4(2 + \sqrt{3})} = 2\sqrt{2 + \sqrt{3}}$.The $RMS$ value (effective value) $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{2\sqrt{2 + \sqrt{3}}}{\sqrt{2}} = \sqrt{2}\sqrt{2 + \sqrt{3}} = \sqrt{4 + 2\sqrt{3}} = \sqrt{(\sqrt{3}+1)^2} = \sqrt{3} + 1 \, A$.Since this value is not among the options,the correct choice is $D$.

The effective value ($RMS$ value) of the current $i = 2\sin(100\pi t) + 2\sin(100\pi t + 30^\circ)$ is:

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