Question

In a certain circuit current changes with time according to i = 2$\sqrt{t}$ 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

$\stackrel{-}{i^2}=\frac{\int i^{2}dt}{\int dt}=\frac{{\int }_2^4\left(4t\right)dt}{{\int }_2^{4}dt}=\frac{4{\int }_2^{4}tdt}{2}=2{\left[\frac{t^2}{2}\right]}_2^4={\left[t^2\right]}_2^4=12$

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