An alternating current is given by i = i_1 si | vedclass

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(B) The given equation is $i = i_1 \sin \omega t + i_2 \cos \omega t$. We can rewrite this as $i = A \sin(\omega t + \phi)$,where $A$ is the amplitude

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$\sqrt{\frac{i_1^2 + i_2^2}{2}}$

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(B) The given equation is $i = i_1 \sin \omega t + i_2 \cos \omega t$. We can rewrite this as $i = A \sin(\omega t + \phi)$,where $A$ is the amplitude of the resultant current. To find $A$,we compare the coefficients: $i_1 = A \cos \phi$ and $i_2 = A \sin \phi$. Squaring and adding these equations: $i_1^2 + i_2^2 = A^2 \cos^2 \phi + A^2 \sin^2 \phi = A^2(\cos^2 \phi + \sin^2 \phi) = A^2$. Thus,the amplitude $A = \sqrt{i_1^2 + i_2^2}$. The root mean square (rms) value of a sinusoidal current $i = A \sin(\omega t + \phi)$ is given by $i_{rms} = \frac{A}{\sqrt{2}}$. Substituting the value of $A$,we get $i_{rms} = \sqrt{\frac{i_1^2 + i_2^2}{2}}$.

An alternating current is given by $i = i_1 \sin \omega t + i_2 \cos \omega t$. The rms current is given by

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