Question

For a complete cycle of sinusoidal alternating current :

• A. The average value of current is zero.
• B. The average value of square of the current is zero.
• C. The average value of current is not zero.
• D. The direction of current changes continuously

Answer 1

Answer: (A), (D)

The direction of current changes continuously

A sinusoidal alternating current is given by,

$i=i_0\sin \omega t$


From the graph, we can say that this current continuously changes its direction.

From the definition of average current, we can write,

$i_{avg}=\frac{\text{The net area under i-t graph in one cycle}}{\text{Total time taken in one cycle}}$

Since, the net area for the given graph is zero for the complete cycle,

$\therefore i_{avg}=0$

The graph for the variation of square of a sinusoidal current with time can be drawn as :


From the graph, we can see that the average value of the square of the current is not zero.

Hence, options $\left(\text{A}\right)$ and $\left(\text{D}\right)$ are the correct answers.