If I = 2 Sin wt; but in a.c. circuit current I = I\(_0\) Sin wt; thus comparing the two equations, it implies that I\(_0\) = 2A; Again, the root means square (I(rms)) of an a.c. current is the value of the d.c. current that will dissipate the same amount of heat in a given resistance as the a.c.
and I(rms) = \(\frac{I_0}{\sqrt{2}}\) = \(\frac{2.0A}{\sqrt{2}}\) = \(\sqrt{2}\)A (by rationalizing the denominator \(\frac{2.0A}{\sqrt{2}}\))