First slide

Alternating current and voltage

Question

If $i={t^2} \,\,\,0 < t < T$ then r.m.s. value of current is

Moderate

A

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

$\frac{{{T^2}}}{{ 2 }}$
C

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

None of these

Solution

${i_{rms}} = \sqrt {\frac{1}{T}\int_0^T {{i^2}dt} } = \frac{{{T^2}}}{{\sqrt 5 }}$

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