Question

Current is given as $i=2\sqrt{t}$. RMS value of current between t = 0 to t = 2 sec is

Answer 1

$i^2=4t,<i^2>=\frac{{\int }_0^{2}4tdt}{{\int }_0^{2}dt}=\frac{\frac{4}{2}(t^2{)}_0^2}{(t{)}_0^2}$

$<i^2>=\frac{2\times 2^2}{2}=2^2$

$\Rightarrow i_{rms}=\sqrt{<i^2>}=2A$