Question

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

• A. $3\text{A}$
• B. $3\sqrt{3}\text{A}$
• C. $2\sqrt{3}\text{A}$
• D. $\sqrt{3}\text{A}$

Answer 1

The correct option is C $2\sqrt{3}\text{A}$

Given, $i=2\sqrt{t}$

As we know that the r.m.s. value of current is given by,

$I_{rms}=\sqrt{I^2}$

$I_{rms}=\sqrt{\frac{{\int }_2^4(2\sqrt{t}{)}^{2}dt}{{\int }_2^{4}dt}}$

$I_{rms}=2\sqrt{\frac{{\left[\frac{t^2}{2}\right]}_2^4}{[t{]}_2^4}}=2\sqrt{\frac{[4^2-2^2]}{2[4-2]}}$

$\therefore I_{rms}=2\sqrt{3}\text{A}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.