MCQ
In a certain circuit current changes with time according to $i=2 \sqrt{t}$. r.m.s. value of current between $t=2$ to $t=4 s$ will be
- A$3\ A$
- B$3 \sqrt{3}\ A$
- ✓$2 \sqrt{3}\ A$
- D$(2-\sqrt{2})\ A$
✓
Answer
Correct option: C.
$2 \sqrt{3}\ A$
$\overline{i^2} =\frac{\int i^2 d t}{\int d t}=\frac{\int_2^4(4 t) d t}{\int_2^4 d t}=\frac{4 \int_2^4 t d t}{2}=2\left[\frac{t^2}{2}\right]_2^4=\left[t^2\right]_2^4=12$
$ \Rightarrow i_{m s}=\sqrt{i^2}=\sqrt{12}=2 \sqrt{3} \mathrm{~A}$
$ \Rightarrow i_{m s}=\sqrt{i^2}=\sqrt{12}=2 \sqrt{3} \mathrm{~A}$
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