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 = 4s will be

Moderate

A

3 A
B

$3\sqrt{3}A$
C

$2\sqrt{3}A$
D

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

Solution

$\overline {{i^2}} = \frac{{\int_{}^{} {{i^2}dt} }}{{\int_{}^{} {dt} }} = \frac{{\int_2^4 {(4t)} dt}}{{\int_2^4 {dt} }} = \frac{{4\int_2^4 {t\;dt} }}{2}$ $= 2\left[ {\frac{{{t^2}}}{2}} \right]_2^4 = \left[ {{t^2}} \right]_2^4 = 12$
$\Rightarrow {i_{rms}} = \sqrt {\overline {{i^2}} } = \sqrt {12} = 2\sqrt 3 \;A$

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