Direct current (DC) circuits involve current flowing in one direction. In alternating current (AC) circuits the voltage oscillates in a sine wave pattern:

V(t) = V_o sin(wt)

In a household circuit, the frequency is 60 Hz. The angular frequency is related to the frequency, f, by:

w = 2pf

V_o represents the maximum voltage, which in a household circuit in North America is about 170 volts. We talk of a household voltage of 120 volts, though; this number is a kind of average value of the voltage. The particular averaging method used is called root mean square (square the voltage to make everything positive, find the average, take the square root), or rms. Voltages and currents for AC circuits are generally expressed as rms values. For a sine wave, the relationship between the peak and the rms average is:

rms value = 0.707 peak value

RMS averaging

RMS stands for root-mean-square.

Consider the numbers -1, 1, 3, and 5.

The average is this set of numbers is 2.

What is the rms average of these numbers (-1, 1, 3, and 5)? First square the numbers, then find the average of the squares, and then take the square root of that average.

The rms average is 3.

Root mean square averaging turns everything positive, and weights larger numbers more than smaller numbers.

A similar process is done to determine the rms average of sin(q) over one period. First square it and then find the mean (this can be done by integrating), which works out to 1/2.

Then take the square root:

The rms average of a sine wave of amplitude 1 is

1

=

0.707