Effective Value or Root Means Square Explained

The effective value of an AC is that value that will produce the same heating effect as a specific value of a steady DC. In other words, an AC has an effective value of 1 ampere if it produces heat at the same rate as the heat produced by 1 ampere of DC, both flowing in the same value of resistance.

Another name for the effective value of an AC or voltage is the root-mean-square (rms) value. This term was derived from one method used to compute the value. The rms is calculated as follows: The instantaneous values for one cycle are selected for equal periods of time. Each value is squared, and the average of the squares is calculated. (Values are squared because the heating effect varies as the square of the current or voltage.) The square root of this answer is the rms value.

A more accurate method requires the use of calculus. Either method shows that the effective or rms value is 0.707 times the maximum or peak (p) value. A simple equation for calculating the effective value is shown as follows:

where subscript “p” refers to the peak value

When an AC or voltage is specified, it is always the effective value that is meant, unless otherwise stated. Standard AC meters indicate effective or rms values.