In an A.C. circuit I_rms and I_0 are related as:

The correct answer is Option (3) → \( I_{\mathrm{rms}} = I_{0}/\sqrt{2} \)

The rms value is the square root of the mean of \( i^{2} \) over a cycle. For \( i = I_0\sin\omega t \), the mean of \( \sin^{2}\omega t \) over a cycle is \( 1/2 \).

    \( \displaystyle I_{\mathrm{rms}} = \sqrt{\overline{i^{2}}} = \sqrt{I_0^{2}\,\overline{\sin^{2}\omega t}} = \sqrt{\frac{I_0^{2}}{2}} = \frac{I_0}{\sqrt{2}} \approx 0.707\,I_0 \)

NCERT (2026-27):
Summary – “… To express it in the same form as the dc power (P = I²R), a special value of current is used. It is called root mean square (rms) current and is donoted by I:

    \( \displaystyle I = \frac{i_m}{\sqrt{2}} = 0.707\, i_m \)”