What is the r.m.s. value of the current i = t | vedclass

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(C) The $r.m.s.$ value of a current $i(t)$ over a time interval $T$ is given by the formula: $i_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} i^2 dt}$.Given

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$\frac{T^2}{\sqrt{5}}$

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(C) The $r.m.s.$ value of a current $i(t)$ over a time interval $T$ is given by the formula: $i_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} i^2 dt}$.Given $i = t^2$,we have $i^2 = t^4$.Substituting this into the formula:$i_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} t^4 dt}$.Evaluating the integral: $\int_{0}^{T} t^4 dt = \left[ \frac{t^5}{5} \right]_{0}^{T} = \frac{T^5}{5}$.Now,substitute back into the expression:$i_{rms} = \sqrt{\frac{1}{T} \cdot \frac{T^5}{5}} = \sqrt{\frac{T^4}{5}} = \frac{T^2}{\sqrt{5}}$.

What is the $r.m.s.$ value of the current $i = t^2$ for the time interval $0 < t < T$?

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