Question

The electric current in a circuit is given by $i=\frac{i_0}{T}t$, where $t$ is time and $T$ is time period. Calculate the rms current for the period $t=0$ to $t=T$.

• A. $i_0$
• B. $i_0^2$
• C. $\frac{i_0}{\sqrt{2}}$
• D. $\frac{i_0}{\sqrt{3}}$

Answer 1

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

The square of the current is $i^2=\frac{i_0^2}{T^2}{t}^2$.

The mean of the square of the current is,

$i_{avg}^2=\frac{1}{T}{\int }_0^T\frac{i_0^2}{T^2}{t}^{2}dt=\frac{i_0^2}{T^3}{\int }_0^T{t}^{2}dt=\frac{i_0^2}{3}$

Thus, the rms current is,

$i_{rms}=\sqrt{i_{avg}^2}=\frac{i_0}{\sqrt{3}}$