Question

For an AC circuit, calculate the average value of the current per cycle, for which time function of the current is shown in the figure.

• A. $\frac{I_0}{2}$
• B. $\frac{I_0}{\sqrt{2}}$
• C. $\frac{2I_0}{3}$
• D. $\frac{3I_0}{4}$

Answer 1

The correct option is D $\frac{3I_0}{4}$

The average value of current per cycle is given as

$<I>=\frac{{\int }_0^{T}Idt}{T}$

$=\frac{\text{Area Under Curve from}0\to T}{T}$

$=\frac{(\frac{1}{2}\times \frac{T}{2}\times I_0)+(\frac{T}{2}\times I_0)}{T}$

$\therefore <I>=\frac{3I_0}{4}$

Hence, $\left(\text{D}\right)$ is the correct option.