First slide

Alternating current and voltage

Question

In a certain circuit, current changes with time according to $i = 2 \sqrt{t} .$ R.m.s. value of current between t = 2s to t = 4s will be

Moderate

A

3 A
B

$3 \sqrt{3} A$
C

$2 \sqrt{3} A$
D

$(2 - \sqrt{2}) A$

Solution

$\bar{i^{2}} = \frac{\int i^{2} dt}{\int dt} = \frac{\int_{2}^{4} (4 t) dt}{\int_{2}^{4} dt} = \frac{4 \int_{2}^{4} tdt}{2}$
$= 2 {[\frac{t^{2}}{2}]}_{2}^{4} = {[t^{2}]}_{2}^{4} = 12$
$\Rightarrow i_{rms} = \sqrt{\bar{i^{2}}} = \sqrt{12} = 2 \sqrt{3} A$

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