*What is Form Factor? Form Factor Formula & its Derivation*

*What is Form Factor? Form Factor Formula & its Derivation*

**What is Form Factor?**

The ratio of the root mean square value to the average value of an alternating quantity is called

**Form Factor.**The**Form Factor**is very important parameter for knowing the perfectness of the waveform. Any periodic waveform has varying magnitude with time. The waveform attains maximum or peak value at a point of time. The direct current has its maximum amplitude at all the times i,e. it has constant magnitude and the magnitude does not change with time. Contrary to this, the instantaneous value of AC varies with time and attains maximum or peak value and again the magnitude decrease. Before understanding**what is the Form Factor,**let us understand about the**crest factor of AC and its RMS and average value.****Crest Factor**

The

**crest factor**of an AC current or voltage waveform is the ratio of its peak value to root mean square(RMS) value.The crest factor of an AC voltage or current can be found by measuring its peak value and root mean square value.The root mean square value of an AC current is equal to the heating effect of the AC current that is equal to the heating effect of the DC current. The root mean square value of an perfect sinusoidal AC voltage or current has certain relationship with its peak or maximum value.The RMS value of an AC voltage is as given below.

**Mathematical derivation of AC RMS Value**

### Mathematical Derivation of Crest Factor

**What is form factor of AC waveform?**

The magnitude of the alternating current varies with time both in postive and negative half of the complete cycle. Form Factor shows how distorted is the waveform.The** rms value of AC** is equal to the **direct current **which when passed through the resistor for a given period of time will produce the same heating effect as produced by alternating current when passed through the same resistor for the same time. The rms value of the ac waveform, as derived above, **is equal to ****V _{p}/√2**. Where,

**V**is the peak value.

_{p}The

**average value of AC**is equal to the stady current which transfer the same amount of charge in a given time as transfered by an AC across the same circuit in the same circuit. The derivation of average value of AC is as given below.