How to Calculate RMS Voltage
The RMS value is only calculated for time-varying waveforms in which the magnitude of a quantity fluctuates with time.
There are two approaches or methods to calculate RMS value.
- Graphical Method
- Analytical Method
Graphical Method
It can be used to find the RMS value of any non-sinusoidal time-varying waveform by drawing a number of mid-ordinates onto the waveform. The effectiveness of this approach is contingent upon the quantity of data points extracted from the waveform.
In the graphical method, several mid-ordinates are selected, and their instantaneous values are Recorded. Each mid-ordinate’s value in a waveform is squared and added consecutively. The sum of the squared values is divided by the total number of mid-ordinates, and taking the square root of this result provides the RMS value.
Let us consider an example, V1 ,V2 ,….,V12 are the instantaneous values of voltages.
VRMS = √(V12+V22+V32+.....+V122)/12
Analytical Method
The analytical method, on the other hand, is a mathematical procedure that utilizes calculus to find the effective or RMS value of any periodic voltage or current. This method is more accurate for pure sinusoidal waveforms. It involves integrating the squared waveform function with respect to time and then simplifying the equation to derive the RMS value.
where,
Vm is the maximum value or peak value of the waveform.
ω is the angular frequency which is equal to 2Л/T.
Now, we can calculate the rms value of a sinusoidal voltage as:
VRMS = √1/T∫0T Vm2 cos2 (ωt)dt
Integrating through with limits taken from 0 to 360o or T, the period gives:
VRMS = √Vm2 /2T[t + sin(2ωt)/2ω]0T
The above equation is reduces down to:
VRMS = √V m2 /2
VRMS = V m /√2
VRMS = V m x 0.7071
RMS Voltage
Root Mean Square is referred to as RMS. The square root of the average of the squares of the values or the square of the function defining the continuous waveform is the Root Mean Square (RMS) of a collection of values or a continuous-time waveform. In this article, we will be going through what is RMS Voltage, How to calculate RMS Voltages using Graphical and Analytical Methods, Then we will see Different RMS Voltage Formula, At last we will conclude our Article with Applications, Advantages, Disadvantages and Some Applications.
Table of Content
- What is RMS Voltage?
- How to Calculate RMS Voltage
- Formula
- Significance
- Derivation
- Applications
- Advantages and Disadvantages