Question

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

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

Answer 1

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

$\overline{i^2}=\frac{\int i^{2}dt}{\int dt}=\frac{{\int }_2^4\left(4t\right)dt}{{\int }_2^{4}dt}=\frac{4{\int }_2^{4}tdt}{2}=2{\left[\frac{t^2}{2}\right]}_2^4=[t^2{]}_2^4=12\Rightarrow i_{max}=\sqrt{\overline{i^2}}=\sqrt{12}=2\sqrt{3}A$