It is difficult to imagine a discussion of electricity that does not include some reference to voltage, current or both. Indeed, these quantities represent two of the three legs of the foundation described by Ohm’s Law. Although references to voltage and current are common, the values in an AC system can be expressed in a number of different ways, each of which can have a special significance in electrical design.

This article focuses on AC voltage, but the same principles also apply to current (amps) and power (watts or volt-amps).

**Peak Voltage**

Peak values represent the peak or maximum voltage as measured from the zero reference. Though this is not used much in everyday calculations, peak values can be important in some calculations. For example, peak voltage is an important consideration when considering insulation and peak currents create peak flux values. These values are important in the design of equipment.

Sometimes AC values are stated as peak-to-peak values indicating the voltage or current deviation between the peak positive and peak negative value. Typically, the peak-to-peak value is double the peak value, though in rare cases the positive and negative deviation is asymmetrical.

**Instantaneous Voltage**

Although not used much for practical calculations, understanding instantaneous voltage is important when studying other aspects of circuits. The instantaneous value is simply the value at a particular instant of time and can fall anywhere from zero to the peak value.

**RMS or Effective Voltage**

RMS (Root Mean Square) is a popular method for expressing AC voltage because it models the equivalent energy of a DC circuit with the same voltage. The RMS value of a true sine wave is the peak value times 0.7071 (1/√2). Many low-cost meters assume the sine wave is undistorted and simply read the peak and display the calculated value. Unfortunately, if this type of meter is used for testing a non-sinusoidal waveform — either intentionally generated or due to harmonic distortion — the reading will by off by a significant margin.

The example below is a pure sine wave. The arrows indicate instantaneous voltage measurement points. The readings are taken at 10° increments. The RMS calculation is based on 36 readings taken over one cycle. The waveform peaks are 100v and -100v. Instantaneous measurements (rounded to one decimal point) are shown at the base of each arrow. Since the waveform is a sine wave, the expected RMS voltage should be 100v × 0.7071, or 70.71v.

Instantaneous Voltage 1st Semi-Cycle |
Square of Instantaneous Voltage |
Instantaneous Voltage 2nd Semi-Cycle |
Square of Instantaneous Voltage |

17.4 | 302.76 | -17.4 | 302.76 |

34.2 | 1169.64 | -34.2 | 1169.64 |

50.0 | 2500.00 | -50.0 | 2500.00 |

64.3 | 4134.49 | -64.3 | 4134.49 |

76.6 | 5867.56 | -76.6 | 5867.56 |

86.6 | 7499.56 | -86.6 | 7499.56 |

94.0 | 8836.00 | -94.0 | 8836.00 |

98.5 | 9702.25 | -98.5 | 9702.25 |

100 | 10000.00 | -100 | 10000.00 |

98.5 | 9702.25 | -98.5 | 9702.25 |

94.0 | 8836.00 | -94.0 | 8836.00 |

86.6 | 7499.56 | -86.6 | 7499.56 |

76.6 | 5867.56 | -76.6 | 5867.56 |

64.3 | 4134.49 | -64.3 | 4134.49 |

50.0 | 2500.00 | -50.0 | 2500.00 |

34.2 | 1169.64 | -34.2 | 1169.64 |

17.4 | 302.76 | -17.4 | 302.76 |

0.0 | 0.00 | 0.0 | 0.00 |

This measured value is very close to the 70.71v that we would expect with a peak value of 100v. Increasing the number of sample points would increase the accuracy. Though this is not necessary for a sine wave, this system makes it possible to make accurate RMS measurements on non-sinusoidal waveforms.

The following illustration shows a simplified example of a Triac-Switched sine wave. Triacs are used for incandescent dimmers and work by using a control voltage to switch the voltage on at a point after the beginning of each semi-cycle. They turn off when the voltage drops to near zero. Once again, the RMS calculation is based on 36 readings taken over one cycle. The waveform peaks are 100v and -100v.

Instantaneous Voltage 1st Semi-Cycle |
Square of Instantaneous Voltage |
Instantaneous Voltage 2nd Semi-Cycle |
Square of Instantaneous Voltage |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.00 | 0.00 | 0.00 |

98.5 | 9702.25 | -98.5 | 9702.25 |

100 | 10000.00 | -100 | 10000.00 |

98.5 | 9702.25 | -98.5 | 9702.25 |

94.0 | 8836.00 | -94.0 | 8836.00 |

86.6 | 7499.56 | -86.6 | 7499.56 |

76.6 | 5867.56 | -76.6 | 5867.56 |

64.3 | 4134.49 | -64.3 | 4134.49 |

50.0 | 2500.00 | -50.0 | 2500.00 |

34.2 | 1169.64 | -34.2 | 1169.64 |

17.4 | 302.76 | -17.4 | 302.76 |

0.0 | 0.00 | 0.0 | 0.00 |

This example make it obvious that a standard Non-RMS volt meter reading be off by a substantial amount when attempting to read a non-sinusoidal voltage. For some applications, the error will not matter, but it is important to choose the correct instrument for the application.

**Average Voltage**

Since the sum of the positive and negative alternations in a symmetrical AC sine wave is zero, technically the average voltage of a sine wave is also zero . Therefore, average voltage is calculated using twice the peak of a half cycle or by using the peak-to-peak voltage. The average voltage for a sine wave with a 1v peak is as follows:

As you can see, the average voltage is slightly less than the RMS voltage.

**Form Factor**

While not technically a type of AC voltage measurement, form factor, the ratio of the RMS and average voltages, is useful in some types of electrical calculations. For example, form factor is used when calculating the number of turns required for a specific transformer core. Since a sine wave is the expected input some sources express form factor as the “constant” 1.11, but this only holds for a sine wave.

Form factor for other waveforms will yield other multipliers, for example, a in a square wave the RMS and Average voltage are the same so the form factor is 1.0.

References and related links:

- Lowdon, Eric (1989).
*Practical Transformer Design Handbook (2nd Ed)*. Tab Books. - http://www.electronics-tutorials.ws/accircuits/rms-voltage.html
- http://www.electronics-tutorials.ws/accircuits/average-voltage.html