Question

R.M.S value of circular current wave, which is varying as shown in the figure in amperes (where $a=\frac{3}{\sqrt{2}}$) is(answer upto two decimals points)

Answer 1

$<I^2>=\frac{\int I^{2}dt}{\int dt}$ where $I^2+t^2=a^2$

$<I^2>=\frac{{\int }_0^a(a^2-t^2)dt}{{\int }_0^{a}dt}$

= $\frac{{(a^{2}t-\frac{t^3}{3})}_0^a}{a}=\frac{2}{3}{a}^2$

$I_{rms}=\sqrt{<I^2>}=\sqrt{\frac{2}{3}}.a=\sqrt{\frac{2}{3}}\cdot \frac{3}{\sqrt{2}}=\sqrt{3}$