Total carrent, \(I =(5+10 \sin \omega t )\)

\(\Rightarrow \quad I _{ eff }=\left[\frac{\int \limits_0^{ T } I ^2 dt }{\int \limits_0^{ T } dt }\right]^{1 / 2}\)

\(=\left[\frac{1}{ T } \int \limits _0^{ T }(5+10 \sin \omega t)^2 dt \right]^{1 / 2}\)

\(\frac{1}{ T } \int \limits _0^{ T } \sin ^2 \omega t . d t=\frac{1}{2}\)

So, \(I _{ eff }=\left[25+\frac{1}{2} \times 100\right]^{1 / 2}=5 \sqrt{3} A\)