Question

The mean value of current for half cycle for a current variation shown by the graph is

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

Answer 1

Answer: (A)

$I_{\text{mean }}=\frac{\underset{0}{\overset{T/2}{\int }}Idt}{T/2}$
From 0 to $\frac{T}{2}$ graph is straight line so the function (I) will be $=\frac{i_0}{(T/2)}t=\frac{2i_0}{T}t$
So $I_{\text{mean }}=\frac{2}{T}\underset{0}{\overset{T/2}{\int }}\frac{2i_0}{T}tdt=\frac{2}{T}\left(\frac{2}{T}\right)i_0{\left(\frac{t^2}{2}\right)}_0^{T/2}$
$=\frac{4}{T^2}{i}_0\left(\frac{1}{2}\right){\left(\frac{T^2}{4}-0\right)}^{\circ }=\frac{i_0}{2}$