Question

What is the average value of the AC voltage over one complete cycle
A. Zero
B. ${{V}_{\max }}$
C. $\dfrac{2{{V}_{\max }}}{\pi }$
D. $2{{V}_{\max }}$

Answer 1

Hint:In contrast to direct current (DC), which travels exclusively in one direction, alternating current (AC) is an electric current that occasionally switches direction and varies its amplitude constantly over time. Alternating current is the type of electricity that is provided to companies and homes, and it is the type of electricity that is used by consumers when they plug in kitchen appliances, televisions, fans, and electric lamps to a wall outlet.

Complete answer:
When an alternator generates AC power, the voltage changes polarity over time in a very specific way. When this voltage of alternating polarity from an alternator is graphed over time, the "wave" drawn by it takes on a unique form known as a sine wave.

The transition from one polarity to the other is smooth in an electromechanical alternator's voltage plot, with the voltage level moving most rapidly at the zero ("crossover") point and most slowly at the peak. We would see the same pattern if we graphed the trigonometric function of "sine" across a horizontal range of 0 to 360 degrees. The AC voltage's average value throughout one complete cycle is zero.

One cycle of sine wave occurs when a waveform achieves a complete set of positive and negative values, such as when a sinusoidal wave completes one set of positive and negative values. The angular measure of 360 degrees corresponds to one cycle. The waveform may not rotate 360 degrees in a complete cycle. However, there should be one positive and one negative half cycle.

Hence option A is correct.

Note:The area above the horizontal axis of a periodic waveform is positive, whereas the area below the horizontal axis is negative. Because the area above the horizontal axis (the positive half cycle) is equal to the area below the axis (the negative half cycle), the average or mean value of a symmetrical alternating quantity is zero, (0). This is due to the fact that when the two areas are added together, the negative area cancels out the positive area, resulting in zero average voltage.