## Alternating Current

Component | Symbol |
---|---|

AC Voltage Source |

Until now, the power source for every circuit in this tutorial has been a battery which is a form of Direct Current (DC). A DC power source provides a stable, easy to understand voltage for a circuit. However, it's not the only type of power source you will encounter. Alternating Current (AC) is a very common source as well. Household current is an example of AC. The major advantage of AC over DC is that AC can be transmitted over a much longer distance then DC with very little loss.

The dynamics of AC are a little harder to understand then DC. A graph of a DC voltage source versus time shows a simple linear function (see figure 13). The DC source puts out a constant voltage. AC is a bit more complex. It follows a sinusoidal wave form. The voltage starts at zero and increases until it reaches a peak value, then decreases until reaching zero. It then reverses direction and increases until it reaches the peak value again (but in the opposite direction), then decreases until reaching zero once again. This process marks one complete AC cycle (see figure 13). It then begins the next identical cycle.

## Frequency

Frequency is the rate at which an AC waveform repeats itself. It is measured in units called *hertz*. One hertz represents one cycle per second. Common household AC has a rate of 60 hertz meaning it completes 60 full cycles within one second. That means a single cycle takes about 16.6 milliseconds (ms) to complete.

## Amplitude

Determining the value of DC voltage is straightforward. The voltage is constant so anytime you measure it, you will get the same result. Determining AC voltage is not at all straightforward, since it varies in magnitude and direction over time. Taking the average value is no good. The two half-cycles of the sine wave are mirror images of each other. They would cancel each other out leaving an average voltage of zero. You would never get the bread toasted with zero voltage! Using the peak voltage is interesting, but the wave is only that high for an instant so it is not very representative of what's going on. So what value is used?

It turns out that the best value is something called the *Root Mean Square* (RMS). This is calculated by taking the peak value of the AC wave and dividing it by the square root of two. Why is RMS the best value to use? Well, an AC voltage with an RMS of some value will heat up a resistor to the same temperature that a DC voltage of that same value would heat the resistor. Thus they have the same power. An AC voltage source with a RMS value of 12 volts produces the same power as a 12 volt DC source.

Since dividing the peak value by the square root of two is the same as multiplying the peak value by the inverse of the square root of two, and the inverse of the square root of two is approximated by 0.7071, you can simply multiply the peak AC voltage by 0.7071 to get the Root Mean Square value.