The alternating current is given by, i = \ 42 ((2π)/(T)t) + 10\ A ....

The given function of current is, $i = \left\{\sqrt{42}\sin \left(\dfrac{2\pi}{T}t\right) + 10\right\}A$

It means, ${i}^{2} = 42\sin^{2}\left(\dfrac{2\pit}{T}\right) + 100 + 20\sqrt{42}\sin \left(\dfrac{2\pit}{T}\right)$

$⇒ \left<{i}^{2}\right> = \dfrac{42}{2} + 100$

RMS value of the current is, ${i}_{rms} = \sqrt{\left<{i}^{2}\right>} = \sqrt{121} = 11A$