Question

The electric current in a circuit is given by $i=i_0\left(\frac{t}{\tau }\right)$ for some time. Then the $r.m.s.$ current for the period $t=0$ to $t=\tau$ is

• A. $\frac{i_0}{\sqrt{3}}$
• B. $\frac{i_0}{\sqrt{2}}$
• C. $\sqrt{3}{i}_0$
• D. $\frac{i_0}{\sqrt{5}}$

Answer 1

The correct option is A $\frac{i_0}{\sqrt{3}}$

Given current $i=\frac{i_{o}t}{\tau }$

We know RMS current $=i_{rms}=\sqrt{\frac{{\int }_0^{\tau }{i}^{2}dt}{{\int }_0^{\tau }dt}}$

Substituting value and doing simple integration, we get RMS current $=\frac{i_o}{\sqrt{3}}$