Chapter 21, Problem 1QAP

To determine

The reason why ac voltage is often described using the root mean square value rather than average voltage

Answer to Problem 1QAP

Because many AC voltages are sinusoidal, average voltage is often zero. So root mean square value is used to not to cancel off negative values from positive values.

Explanation of Solution

Introduction:

The graph of an AC voltage versus time

Many AC voltages are sinusoidal. Therefore the average voltage is zero because equal amounts of voltages lie above and below the x axis. Therefore negative and positive values will cancel off when calculating the average value. If we take the square of each and every voltage before averaging, all the square voltages will be positive. So the negative values do not cancel out the positive values. Therefore ac voltage is often described using the root mean square value rather than average voltage.

Conclusion:

Because many AC voltages are sinusoidal, average voltage is often zero. So root mean square value is used to not to cancel off negative values from positive values.