Question

The voltage supplied to a circuit is given by $V=V_0{t}^{3/2}$, where $t$ is time in second. Find the $rms$ value of voltage for the period, $t=0$ to $t=1s$.

Answer 1

We know$V_{rms}=\sqrt{\frac{1}{T}{\int }_0^1{\left(V_0{t}^{3/2}\right)}^{2}dt}$ where T=0 to 1 s.

$=\sqrt{\frac{1}{1-0}{\int }_0^1{V_0}^2{t}^{3}dt}$

$=\sqrt{|\frac{{V_0}^2{t}^4}{4}{|}_0^1}=\frac{V_0}{2}$