Ok, so now that
you think you've had enough with math, you find that AC has more
complicated math than DC does. But the fun isn't quite over yet.
You've got to be able to convert AC voltage to their DC equivalent
voltages, and visa versa. The main problem is with Voltage. DC Voltage
is straightforward. If it's 10 Volts, it's 10 Volts  period.
But with AC, Voltage becomes more difficult to define. Looking at an AC wave, we actually have 3 different voltages to compare. The voltage from the 0 line to the positive peak of the AC curve is called the PEAK VOLTAGE. If we measure the Voltage from the top of the positive peak, to the bottom of the Negative peak, we call it the PEAK TO PEAK VOLTAGE, which is equal to 2 times the peak voltage. Finally, when we try to do work with an AC Voltage, we find out that a 10 Volt peak voltage wont turn a motor as fast as a 10 Volt DC Voltage. Reason? Because 10 Volts DC is 10 Volts all the time. A 10 Volt peak AC Voltage is only 10 Volts for an instant. The rest of the time it is swinging higher and lower in Voltage level. So at what Voltage level does the AC wave do as much work as a pure DC Voltage?
Where E_{peak} equals the peak voltage of an AC signal and E_{eff} equals its effective (RMS) DC equivalent.
Just when you thought it was safe to get back into the water, I'm gonna throw one more formula at you. What happens if we take all the instantaneous voltage values of a sine wave, add them all up, and then take the average of them? Well, it doesn't quite come up to the effective voltage. When working with rectifier circuits (we'll discuss them in a later section), we must sometimes use what is known as the AVERAGE VOLTAGE of a given AC sine wave. The average voltage is found by the following formula:
Now at this point, one might pose the question  WHY do we go into such
detail about different voltage levels (peak, RMS, and average). The
reason is because you ABSOLUTELY need to know which you are working with
at any particular time. For instance  100 Volts PEAK voltage may be
the threshold at which your $30,000 piece of lab equipment (say a 6
trace digital oscilloscope)gets destroyed. If you measure it with a
multimeter first, and it shows 90 Volts, then think you can put your
scope on it  you just blew the front end of your scope. Why? Because
90 Volts RMS is greater than 100 Volts Peak by 27 Volts!!! Multimeters
measure in RMS typically, and most aren't accurate enough to measure in
"True RMS". You have to know the parameters of the device being tested,
as well as the limitations of your equipment, or you'll wind up doing a
lot of expensive damage!
But with AC, Voltage becomes more difficult to define. Looking at an AC wave, we actually have 3 different voltages to compare. The voltage from the 0 line to the positive peak of the AC curve is called the PEAK VOLTAGE. If we measure the Voltage from the top of the positive peak, to the bottom of the Negative peak, we call it the PEAK TO PEAK VOLTAGE, which is equal to 2 times the peak voltage. Finally, when we try to do work with an AC Voltage, we find out that a 10 Volt peak voltage wont turn a motor as fast as a 10 Volt DC Voltage. Reason? Because 10 Volts DC is 10 Volts all the time. A 10 Volt peak AC Voltage is only 10 Volts for an instant. The rest of the time it is swinging higher and lower in Voltage level. So at what Voltage level does the AC wave do as much work as a pure DC Voltage?

It was found that it takes a 141 Volt AC wave to do the same amount of work as a 100 Volt DC source. The EFFECTIVE value of a 141 Volt AC source then is only 100 Volts. Another term for EFFECTIVE voltage is RMS, which stands for Root Mean Square.
Often, electricians and electronics technicians find that they need to be able to convert AC voltages to DC voltages. They need to know what the effective voltage is. Based on the 141:100 ratio of AC to DC, the following formulae were conceived:
Just when you thought it was safe to get back into the water, I'm gonna throw one more formula at you. What happens if we take all the instantaneous voltage values of a sine wave, add them all up, and then take the average of them? Well, it doesn't quite come up to the effective voltage. When working with rectifier circuits (we'll discuss them in a later section), we must sometimes use what is known as the AVERAGE VOLTAGE of a given AC sine wave. The average voltage is found by the following formula: