The electric current in a circuit is given by i = 3t. Find the rms current for the period t = 0 to t = 1 sec

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$\sqrt{3} a m p$

$\sqrt{2} a m p$

5 Amp

3 amp

answer is C.

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Detailed Solution

$i = 3 t i^{2} = 9 t^{2}$

$i_{r M S}^{2} = \frac{\int_{0}^{t} i^{2} d t}{\int_{0}^{t} d t} = \frac{\int_{0}^{t} d t^{2} d t}{\int_{0}^{t} d t} = \frac{9 t^{3}}{3 t} = {[3 t^{2}]}_{0}^{1} = 3$

$i_{r M S} = \sqrt{3} a m r$

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