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(B) The root mean square $(RMS)$ current is defined as $I_{rms} = \sqrt{\frac{1}{T_2 - T_1} \int_{T_1}^{T_2} i^2 dt}$.Given $i = 2\sqrt{t}$,so $i^2 =

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$2\sqrt{3}\,A$

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(B) The root mean square $(RMS)$ current is defined as $I_{rms} = \sqrt{\frac{1}{T_2 - T_1} \int_{T_1}^{T_2} i^2 dt}$.Given $i = 2\sqrt{t}$,so $i^2 = 4t$.The time interval is from $T_1 = 2\,s$ to $T_2 = 4\,s$,so $T_2 - T_1 = 4 - 2 = 2\,s$.Now,calculate the integral: $\int_{2}^{4} 4t \,dt = [2t^2]_{2}^{4} = 2(4^2 - 2^2) = 2(16 - 4) = 2(12) = 24$.Substitute these values into the $RMS$ formula:$I_{rms} = \sqrt{\frac{24}{2}} = \sqrt{12} = \sqrt{4 	imes 3} = 2\sqrt{3}\,A$.

In a circuit,current varies with time as $i = 2\sqrt{t}$. The root mean square value of current for the interval $t = 2\,s$ to $t = 4\,s$ is:

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