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Q.
In a certain circuit, current changes with time according to $i=2 \sqrt{t}$. R.m.s. value of current between $t=2 s$ to $t=4$ s will be
Alternating Current
Solution:
$\overline{i^{2}}=\frac{\int i^{2} d t}{\int d t}=\frac{\int\limits_{2}^{4}(4 t) d t}{\int\limits_{2}^{4} d t}=\frac{4 \int\limits_{2}^{4} t d t}{2}$
$=2\left[\frac{t^{2}}{2}\right]_{2}^{4}=\left[t^{2}\right]_{2}^{4}=12$
$\Rightarrow i_{ rms }=\sqrt{i^{2}}=\sqrt{12}=2 \sqrt{3} A$