Root Mean Square (RMS) Values

The value of an AC voltage is continually changing from zero up to the positive peak, through zero to the negative peak and back to zero again. Clearly for most of the time it is less than the peak voltage, so this is not a good measure of its real effect.

Instead we use the root mean square voltage (V_RMS) which is 0.7 of the peak voltage (V_peak):

V_RMS = 0.7 × V_peak   and   V_peak = 1.4 × V_RMS

These equations also apply to current.
They are only true for sine waves (the most common type of AC) because the 0.7 and 1.4 are different values for other shapes. 

The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect.

For example a lamp connected to a 6V RMS AC supply will light with the same brightness when connected to a steady 6V DC supply. However, the lamp will be dimmer if connected to a 6V peak AC supply because the RMS value of this is only 4.2V (it is equivalent to a steady 4.2V DC).

You may find it helps to think of the RMS value as a sort of average, but please remember that it is NOT really the average! In fact the average voltage (or current) of an AC signal is zero because the positive and negative parts exactly cancel out!

What do AC meters show, is it the RMS or peak voltage?

AC voltmeters and ammeters show the RMS value of the voltage or current.

What does '6V AC' really mean, is it the RMS or peak voltage?

If the peak value is meant it should be clearly stated, otherwise assume it is the RMS value. In everyday use AC voltages (and currents) are always given as RMS values because this allows a sensible comparison to be made with steady DC voltages (and currents), such as from a battery.

For example a '6V AC supply' means 6V RMS, the peak voltage is 8.6V. The UK mains supply is 230V AC, this means 230V RMS so the peak voltage of the mains is about 320V!

So what does root mean square (RMS) really mean?

First square all the values, then find the average (mean) of these square values over a complete cycle, and find the square root of this average. That is the RMS value. Confused? Ignore the maths (it looks more complicated than it really is), just accept that RMS values for voltage and current are a much more useful quantity than peak values.