In a certain circuit current changes with tim | vedclass

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Question

(c)$\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}

Vedclass · Accepted Answer

$2\sqrt 3 A$

Vedclass · Answer

(c)$\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$

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

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