Question

If rms value of given semi-circular current wave is $i_{rms}=\sqrt{x}a$ , then x is

Answer 1

By given wave form $i^2+t^2=a^2\Rightarrow i^2=a^2-t^2$
$<i^2>=\frac{{\int }_0^a{i}^{2}dt}{{\int }_0^{a}dt}=\frac{{\int }_0^a(a^2-t^2)dt}{a}=\frac{2}{3}{a}^2$
$i_{rms}=\sqrt{<i^2>}=\sqrt{\frac{2}{3}}a$