Question

In a certain circuit current changes with time according to $i=2\sqrt{t}$. rms. value of current between t= $2$ to t= $4$ s will be

• A. $3$ A
• B. $3\sqrt{3}A$
• C. $2\sqrt{3}$ A
• D. $(2-\sqrt{2})A$

Answer 1

The correct option is C $2\sqrt{3}$ A

As we know,

$\overline{i^2}=\frac{\int i^{2}dt}{\int dt}$
$=\frac{4{\int }_2^{4}rdt}{2}=2{\left[\frac{t^2}{2}\right]}_2^4={\left[t^2\right]}_2^4=12$

$\Rightarrow i_{rms}=\sqrt{\overline{i^2}}=\sqrt{12}=2\sqrt{3}A$