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 $t = 2$ to $t = 4 s$ will be

Moderate

A

3A
B

$3 \sqrt{3} A$
C

$2 \sqrt{3} A$
D

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

Solution

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

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