## RMS Output Voltage for Phase Controller Solution

STEP 0: Pre-Calculation Summary
Formula Used
RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter)))
Vrms(full) = sqrt(((Vm)^2/pi)*int((sin(x))^2,x,(60+αf(thy)),(120+αf(thy))))
This formula uses 1 Constants, 3 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)
Variables Used
RMS Output Voltage Full Converter - (Measured in Volt) - RMS Output Voltage Full Converter is defined as the root mean square value of the voltage at output terminal of a full converter circuit.
Peak Voltage - (Measured in Volt) - Peak Voltage is the peak or maximum voltage of a circuit/ rectifier.
Firing Angle of Thyristor Converter - (Measured in Radian) - Firing Angle of Thyristor Converter refers to the Angle at which the Thyristor is triggered to start Conducting Current in an AC (alternating current) Circuit.
STEP 1: Convert Input(s) to Base Unit
Peak Voltage: 10 Volt --> 10 Volt No Conversion Required
Firing Angle of Thyristor Converter: 27.5 Degree --> 0.47996554429835 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vrms(full) = sqrt(((Vm)^2/pi)*int((sin(x))^2,x,(60+αf(thy)),(120+αf(thy)))) --> sqrt(((10)^2/pi)*int((sin(x))^2,x,(60+0.47996554429835),(120+0.47996554429835)))
Evaluating ... ...
Vrms(full) = 30.926495059665
STEP 3: Convert Result to Output's Unit
30.926495059665 Volt --> No Conversion Required
30.926495059665 30.9265 Volt <-- RMS Output Voltage Full Converter
(Calculation completed in 00.035 seconds)
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Created by Siddharth Raj
Heritage Institute of Technology ( HITK), Kolkata
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## <Three Phase Full Converter Calculators

RMS Output Voltage of Three-Phase Full Converter
​ Go RMS Output Voltage 3 Phase Full Converter = ((6)^0.5)*Peak Input Voltage 3 Phase Full Converter*((0.25+0.65*(cos(2*Delay Angle of 3 Phase Full Converter))/pi)^0.5)
Average Output Voltage for Three-Phase Converter
​ Go Average Voltage 3 Phase Full Converter = (2*Peak Phase Voltage Full Converter*cos(Delay Angle of 3 Phase Full Converter/2))/pi
Peak Average Output Voltage of Three-Phase Full Converters
​ Go Peak Output Voltage 3 Phase Full Converter = (5.2*Peak Input Voltage 3 Phase Full Converter)/pi
Normalized Average Output Voltage in Three-Phase Full-Converter
​ Go Normalized Output Voltage 3 Phase Full Converter = (cos(Delay Angle of 3 Phase Full Converter))

## RMS Output Voltage for Phase Controller Formula

RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter)))
Vrms(full) = sqrt(((Vm)^2/pi)*int((sin(x))^2,x,(60+αf(thy)),(120+αf(thy))))

## What is the Significance of Integral Form of RMS Output voltage of 3-phase Full Converter?

The integral form expresses the RMS output voltage as a mathematical integral, which represents the area under the curve of the output voltage waveform. This representation allows for precise mathematical analysis and facilitates the understanding of how the output voltage is affected by variations in parameters such as input voltage and firing angle.

## What is the Meaning of Root Mean Square?

The root mean square value of a quantity is the square root of the mean value of the squared values of the quantity taken over an interval. AC voltages are always given as RMS values because this allows a sensible comparison to be made with steady DC voltages.

## How to Calculate RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller calculator uses RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))) to calculate the RMS Output Voltage Full Converter, RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit. RMS Output Voltage Full Converter is denoted by Vrms(full) symbol.

How to calculate RMS Output Voltage for Phase Controller using this online calculator? To use this online calculator for RMS Output Voltage for Phase Controller, enter Peak Voltage (Vm) & Firing Angle of Thyristor Converter f(thy)) and hit the calculate button. Here is how the RMS Output Voltage for Phase Controller calculation can be explained with given input values -> 30.9265 = sqrt(((10)^2/pi)*int((sin(x))^2,x,(60+0.47996554429835),(120+0.47996554429835))).

### FAQ

What is RMS Output Voltage for Phase Controller?
RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit and is represented as Vrms(full) = sqrt(((Vm)^2/pi)*int((sin(x))^2,x,(60+αf(thy)),(120+αf(thy)))) or RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))). Peak Voltage is the peak or maximum voltage of a circuit/ rectifier & Firing Angle of Thyristor Converter refers to the Angle at which the Thyristor is triggered to start Conducting Current in an AC (alternating current) Circuit.
How to calculate RMS Output Voltage for Phase Controller?
RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit is calculated using RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))). To calculate RMS Output Voltage for Phase Controller, you need Peak Voltage (Vm) & Firing Angle of Thyristor Converter f(thy)). With our tool, you need to enter the respective value for Peak Voltage & Firing Angle of Thyristor Converter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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