**What is Peak Value, Average Value and RMS Value?**

**What is Peak Value, Average Value and RMS Value?**

**Peak Value**

**peak value**.The peak value is also termed as crest value.The peak value of symmetrical alternating voltage and current waveform can also be determined by measuring the peak to peak value of waveform.

**Average Value**

The sinusoidal waveform has different magnitude of voltage or current at different instant of waveform. The magnitude of the current or voltage at particular instant is called instantaneous value of the waveform.The average of all the instantaneous values of an alternating voltage and current over one complete cycle is known as **average value**.

For a symmetrical sinusoidal waveform, the positive half cycle is symmetrical to the negative half cycle. Therefore, the average value of one complete cycle is zero.However, the average value is calculated without considering the signs.Therefore, only positive half cycle is considered for determining the average value of the alternating waveform.

In above diagram, Let i1, i2, i3…….. in be the mid ordinates.

The average value(Iav) of the sinusoidal waveform,

= Mean Value of the mid ordinates

**Formula Derivation of Average Value of Sinusoidal Waveform**

The average value of sinusoidal waveform is obtained by adding instantaneous values of voltage or current over one half cycle only.

_{av = 0.637 x 300}

V_{av} =191.1 Volts

**RMS Value**

## The ‘RMS Value’ stands Root Mean Squared value.The RMS value of an alternating current is given by that steady (D.C) current which when flowing through a given time produces the same amount of heat as produced by the A.C when flowing through the same circuit for the same time.It is also known as effective value of A.C.

**DC Value Equivalent of RMS Value**

**Graphical Method**

Let the peak value of AC voltage is 25 volts and the instantaneous value at mid-ordinates of half cycle of AC are as follows.

The RMS value of the AC voltage is calculated as follows.

The RMS value of the AC wave is 17.68 volts.

**Analytical Method of RMS Value Calculation**

For symmetrical sinusoidal voltage or current waveform analytical method can be used to find out the RMS value.

For symmetrical sinusoidal voltage or current waveform analytical method can be used to find out the RMS value.

**Formula Derivation of RMS Value of Sinusoidal Waveform**

If the peak value of AC voltage is 25 volts its RMS value will be;**Vrms = 25/1.414 = 17.68 Volts**

**RMS Voltage Equations**

Vrms = 0.707 Vm

Vrms = 1.11 Vavg.

The ratio of the rms value and the average value of pure sinusoidal waveform is equal to 1.11.If the RMS to average value ratio is other than 1.11 the waveform is said to be distorted.