Last Updated on October 24, 2023 by Electricalampere

**Definition- **The ratio of RMS value to the average value of alternating quantities -voltage or current is called the form factor. The form factor term is used with alternating voltage and current because they have different RMS and average values. Let us first understand what is the alternating current.

## What is Alternating Current?

As its name suggests, alternating means charging its direction. The alternating current periodically changes its direction. On the other hand, the direct current flows in only one direction. The waveform of the alternating current is given below.

## The Form Factor of AC

The form factor represents the physical shape of the AC waveform. The factor changes with a change in the shape of the waveform because its RMS and average value change. Thus, the form factor is very important to understand AC waveform characteristics.

The form factor is a numerical value that is equal to the ratio between the root mean square (RMS) value and the average value of the waveform. The following mathematical formula can express it.

The RMS Value is the effective value of voltage and current, and It is calculated by taking the square root of the average of the squares of all the instantaneous values of the waveform over a complete cycle. In other words, the RMS value is equal to the arithmetic mean value of these instantaneous values.

The form factor of the perfect sinusoidal voltage or current can be calculated as follows.

Therefore,

You can calculate the form factor by dividing the RMS value of the waveform by its average value. If the RMS value of the AC wave is 25 volts and the average value is 22.52 volts, then the form factor of the AC wave is 25/22.52=1.11. If the form factor of a waveform is 1.11, then it is a perfect sinusoidal waveform, and it shows that the RMS value of the waveform is 1.11 times greater than its average value.

## Importance of Form Factor

The form factor of AC is important because of the following reasons

- The change in the form factor can be determined by analyzing the wave shape. The FF deviation from 1.11 shows the distorted waveform, and this contains the harmonics. The distorted waveform causes power losses in the transmission network and thus deteriorates the transmission efficiency.
- The losses in the electrical machines increase with distorted waveform.
- The measuring instrument for the perfect sinusoidal waveform read less or more for the waveshape with FF other than 1.11.
- The FF impacts the useful life of electrical equipment.

## How to Measure and Calculate Form Factor?

The following methods can be used to measure and calculate FF of AC.

- Cathode Ray Oscilloscope(CRO) is used to display the waveform on its screen visually. You can visually inspect the waveform for any distortion. The CRO also displays the RMS and average value, and by dividing the RMS by the average value, you can calculate the form factor of AC.
- You can use a True RMS multimeter to measure the RMS and average value. The meter directly outputs the FF of AC.

## The Form Factor of Various AC Waveforms

S.No. | Type of Wave | Form Factor(FF) |

1. | Sinusoidal wave | π/2√2 = 1.11072073 |

2. | Rectified sine wave (half-wave ) | π/2 = 1.5707963 |

3. | Rectified sine wave (full-wave ) | π/2√2 = 1.11072073 |

4. | Square wave | 1/1= 1 |

5. | Triangular waveform | 2/√3 = 1.15470054 |

6. | Sawtooth waveform | 2/√3 = 1.15470054 |

7. | Pulse wave | √D/D=√D |

8. | Gaussian noise | 1/√3/ 1/2=2/√3 |

## Solved Problem on Form Factor

The maximum or peak value of AC is 600 volts. Calculate the FF of voltage waveform.

The RMS value of AC

The Average value of AC

FF of AC

## Conclusion

The form factor of AC is a very important parameter and deviation of FF from its specified value deteriorates the power transmission efficiency, device performance, and useful life of equipment. The insightful knowledge of FF helps in designing and optimizing AC systems and equipment. Engineers and technicians can regularly monitor form factors( FF) to ensure AC power systems’ reliable and efficient operation.

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