Consider the two circuits shown below:

If the bulbs light with the same brightness (that is, they are working at the same power), then it would be logical to regard the current I_ac as being equivalent to the current I_dc.

However, the simple mathematical average value of I_ac is, of course, equal to zero.

We therefore use a different method of finding an "average" or effective value of an alternating current (or voltage).

In general, if an a.c. generator is connected to a component of resistance R, the instantaneous power dissipated in the component is equal to i²R

Therefore, the mean power is given by

The root mean square value of the current is therefore

Similarly, to calculate the r.m.s. value of the voltage of an a.c. supply, we have

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