The alternating current is given by i = left{ | vedclass

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(A) The given current is $i = i_1 + i_2$,where $i_1 = \sqrt{42} \sin \left(\frac{2 \pi}{T} t\right)$ and $i_2 = 10$.The $r.m.s.$ value of a composite

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$11$

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(A) The given current is $i = i_1 + i_2$,where $i_1 = \sqrt{42} \sin \left(\frac{2 \pi}{T} tight)$ and $i_2 = 10$.The $r.m.s.$ value of a composite current $i = i_1 + i_2$ is given by $I_{rms} = \sqrt{I_{1,rms}^2 + I_{2,rms}^2}$.For the sinusoidal component $i_1$,the $r.m.s.$ value is $I_{1,rms} = \frac{I_0}{\sqrt{2}} = \frac{\sqrt{42}}{\sqrt{2}} = \sqrt{21}$.For the constant component $i_2 = 10$,the $r.m.s.$ value is $I_{2,rms} = 10$.Therefore,$I_{rms} = \sqrt{(\sqrt{21})^2 + 10^2} = \sqrt{21 + 100} = \sqrt{121} = 11 	ext{ A}$.

Currents	$r.m.s.$ values
$(A) \ x_0 \sin \omega t$	$(i) \ x_0$
$(B) \ x_0 \sin \omega t \cos \omega t$	$(ii) \ \frac{x_0}{\sqrt{2}}$
$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$	$(iii) \ \frac{x_0}{2\sqrt{2}}$

The alternating current is given by $i = \left\{\sqrt{42} \sin \left(\frac{2 \pi}{T} t\right) + 10\right\} \text{ A}$. The $r.m.s.$ value of this current is $\text{A}$.

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