Alternating current

What is RMS Voltage?

What-is-RMS-Voltage

The RMS Voltage stands for Root Mean Square voltage. RMS voltage is defined as the square root of the square of the instantaneous signals. RMS is also known as quadratic mean. RMS can also be expressed in continuous variable value depending on the combination of squares of rapid values ​​during the cycle.
The term of RMS is most important in alternating current. Alternating current is varies continuously with time. In calculation we cannot use directly instantaneous value of voltage.

How to Calculate RMS Voltages

The RMS value is only calculated for alternating current because alternating current is a time varying current and direct current is fixed amplitude current.
For calculating of RMS voltage we use two methods which are given below;

  • Graphical Method
  • Analytical Method

Graphical Method of RMS Voltage

In graphical method we use the graph of signal to calculating RMS voltage. When the signal is not symmetrical the graphical method is more useful. The accuracy of in this method is depends on the how much point are taken. Few points show low accuracy and more point show high accuracy.
Let us see the example in graphical method to find out the rms value.

Graphical-Method

Step 1:- first we find square of each value
Step 1:- find out the average of these square values.
Step 1:- and last take the square of these average value
Thorough these step we find out the RMS value of alternating current.

Analytical Method of RMS Voltage

In this way, the voltage of the RMS can be calculated by mathematical process. This method is more accurate in the pure sinusoidal waveform.

Let us assume the sinusoidal voltage waveform is VmCos(ωt) with a period of T.

Where,
Vm = Peak value of voltage or Maximum value waveform
ω = Angular frequency which value is 2π/T
we are going to calculation of  RMS value of voltage.

vrms-formula

So, RMS value of pure sinusoidal wave are derive from the peak (maximum) value.

RMS Voltage Formula

RMS voltage can be calculated from the maximum value, maximum value to maximum value and the average value.

Peak-Voltage

In the formulas below the sinusoidal waveform is used to calculate the RMS voltage.

From peak voltage (VP);

VRMS = VRMS / √2
VRMS= 0.7071 VP

From peak to peak voltage (VPP);

VRMS = VRMS / 2√2
VRMS= 0.353 VP-P

From average voltage (VAVG);

VRMS = ( π / √2) VAVG
VRMS= 1.11 VAVG

RMS-Voltage-Formula

RMS Voltage and Average Voltage

The RMS is important for various calculations in AC circuits. Similarly, peak voltage, peak-to-peak voltage, and average voltage are also required.

Peak Voltage

Peak-to-peak voltage is the distance from the lowest negative amplitude, or curve, to the highest positive amplitude, or crest, of AC voltage waveform. In other words, we can say the peak-to-peak voltage is full height of the waveform.
Considering the sinusoidal waveform, the voltage rises from the reference axis and reaches the highest waveform on the positive side. The difference between these two points gives us a higher voltage.

Peak-Voltage

From a very high point, the voltage begins to decrease and reaches the reference axis. After that, it begins to expand on the negative side and reaches a very high point. This point is a negative high point.
We can calculate the maximum voltage from the RMS , peak-to-peak , and the average value.

Average Voltage

The method for obtaining the average volt is the same as the RMS. The only difference is that faster values ​​are not a square function and do not form a square root.

Average-Voltage

The middle value is the average value. And the area above the horizontal line is same as the area below horizontal line. This is known as voltage modes.

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