RMS Output Voltage under AC Regulator Solution

STEP 0: Pre-Calculation Summary
Formula Used
RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor))
Erms = Es*sqrt((1/pi)*int(β-α+sin(2*α)/2-sin(2*β)/2,x,α,β))
This formula uses 1 Constants, 3 Functions, 4 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 under AC Regulator - (Measured in Volt) - RMS Output Voltage under AC Regulator Refers to the Effective Voltage Level that the Regulator Delivers to the Load over Time.
Supply Voltage - (Measured in Volt) - Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit.
Extinction Angle of Thyristor - (Measured in Radian) - Extinction Angle of Thyristor is the angle of Delay between the Zero crossing of the AC Current Waveform and the point where the Thyristor naturally turns off due to the reversal of Voltage across it.
Firing Angle - (Measured in Radian) - Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor.
STEP 1: Convert Input(s) to Base Unit
Supply Voltage: 230 Volt --> 230 Volt No Conversion Required
Extinction Angle of Thyristor: 2.568 Radian --> 2.568 Radian No Conversion Required
Firing Angle: 1.476 Radian --> 1.476 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Erms = Es*sqrt((1/pi)*int(β-α+sin(2*α)/2-sin(2*β)/2,x,α,β)) --> 230*sqrt((1/pi)*int(2.568-1.476+sin(2*1.476)/2-sin(2*2.568)/2,x,1.476,2.568))
Evaluating ... ...
Erms = 173.762231645099
STEP 3: Convert Result to Output's Unit
173.762231645099 Volt --> No Conversion Required
FINAL ANSWER
173.762231645099 173.7622 Volt <-- RMS Output Voltage under AC Regulator
(Calculation completed in 00.004 seconds)

Credits

Created by Siddharth Raj
Heritage Institute of Technology ( HITK), Kolkata
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Dayananda Sagar College of Engineering (DSCE), Bangalore
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3 AC Regulator Calculators

Average Thyristor Current under AC Regulator
Go Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor)
RMS Thyristor Current under AC Regulator
Go RMS Thyristor Current Under AC Regulator = (Supply Voltage/Impedance)*sqrt((1/pi)*int((sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)))^2,x,Firing Angle,Extinction Angle of Thyristor))
RMS Output Voltage under AC Regulator
Go RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor))

RMS Output Voltage under AC Regulator Formula

RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor))
Erms = Es*sqrt((1/pi)*int(β-α+sin(2*α)/2-sin(2*β)/2,x,α,β))

How is the RMS Output Voltage Different from the Peak Output Voltage in an AC Regulator Circuit?

The RMS (Root Mean Square) output voltage in an AC regulator circuit represents the effective voltage level delivered to the load over time, taking into account the fluctuations of the AC waveform. On the other hand, the peak output voltage refers to the maximum instantaneous voltage reached by the waveform during each cycle. It represents the highest voltage amplitude achieved by the waveform.

How to Calculate RMS Output Voltage under AC Regulator?

RMS Output Voltage under AC Regulator calculator uses RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor)) to calculate the RMS Output Voltage under AC Regulator, The RMS Output Voltage under AC Regulator formula is defined as the effective voltage level that the regulator delivers to the load over time. It is calculated by taking the square root of the mean of the squares of the instantaneous voltage values over one complete cycle of the waveform. RMS Output Voltage under AC Regulator is denoted by Erms symbol.

How to calculate RMS Output Voltage under AC Regulator using this online calculator? To use this online calculator for RMS Output Voltage under AC Regulator, enter Supply Voltage (Es), Extinction Angle of Thyristor (β) & Firing Angle (α) and hit the calculate button. Here is how the RMS Output Voltage under AC Regulator calculation can be explained with given input values -> 173.7622 = 230*sqrt((1/pi)*int(2.568-1.476+sin(2*1.476)/2-sin(2*2.568)/2,x,1.476,2.568)).

FAQ

What is RMS Output Voltage under AC Regulator?
The RMS Output Voltage under AC Regulator formula is defined as the effective voltage level that the regulator delivers to the load over time. It is calculated by taking the square root of the mean of the squares of the instantaneous voltage values over one complete cycle of the waveform and is represented as Erms = Es*sqrt((1/pi)*int(β-α+sin(2*α)/2-sin(2*β)/2,x,α,β)) or RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor)). Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit, Extinction Angle of Thyristor is the angle of Delay between the Zero crossing of the AC Current Waveform and the point where the Thyristor naturally turns off due to the reversal of Voltage across it & Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor.
How to calculate RMS Output Voltage under AC Regulator?
The RMS Output Voltage under AC Regulator formula is defined as the effective voltage level that the regulator delivers to the load over time. It is calculated by taking the square root of the mean of the squares of the instantaneous voltage values over one complete cycle of the waveform is calculated using RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor)). To calculate RMS Output Voltage under AC Regulator, you need Supply Voltage (Es), Extinction Angle of Thyristor (β) & Firing Angle (α). With our tool, you need to enter the respective value for Supply Voltage, Extinction Angle of Thyristor & Firing Angle 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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