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

The correct option is A $\frac{i_0}{2}$

$i_{mean}=\frac{{\int }_o^{\frac{T}{2}}i.d}{{\int }_0^{\frac{T}{2}}dt}$

$\frac{i-i_o}{t-\frac{T}{2}}=\frac{-i_o}{\frac{-T}{2}}$

$i-i_o=\frac{2i_0}{T}(t-\frac{T}{2})$

$\left(\frac{2i_o}{T}\right)t-i_o$

$I=\left(\frac{2i_o}{T}\right)t$

$i_{mean}=\frac{{\int }_0^{\frac{T}{2}}\frac{2i_o}{T}.t.dt}{\frac{T}{2}}$

$=\frac{2i_o\times 2}{T.T}{\left[\frac{t^2}{2}\right]}_0^{T/2}$

$=\frac{4i_o}{T^2}\times \frac{T^2}{8}$

$i_{mean}=\frac{i_o}{2}$