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RMS Output Voltage under AC Regulator Formula

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RMS Output Voltage under AC Regulator Refers to the Effective Voltage Level that the Regulator Delivers to the Load over Time. Check FAQs

E rms = E s \cdot \sqrt{(\frac{1}{π}) \cdot \int (β - α + \frac{\sin (2 \cdot α)}{2} - \frac{\sin (2 \cdot β)}{2}, x, α, β)}

E_rms - RMS Output Voltage under AC Regulator?E_s - Supply Voltage?β - Extinction Angle of Thyristor?α - Firing Angle?π - Archimedes' constant?

RMS Output Voltage under AC Regulator Example

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Here is how the RMS Output Voltage under AC Regulator equation looks like with Values.

Here is how the RMS Output Voltage under AC Regulator equation looks like with Units.

Here is how the RMS Output Voltage under AC Regulator equation looks like.

173.7622 = 230 \cdot \sqrt{(\frac{1}{3.1416}) \cdot \int (2.568 - 1.476 + \frac{\sin (2 \cdot 1.476)}{2} - \frac{\sin (2 \cdot 2.568)}{2}, x, 1.476, 2.568)}

173.7622V = 230V \cdot \sqrt{(\frac{1}{3.1416}) \cdot \int (2.568rad - 1.476rad + \frac{\sin (2 \cdot 1.476rad)}{2} - \frac{\sin (2 \cdot 2.568rad)}{2}, x, 1.476rad, 2.568rad)}

173.7622 = 230 \cdot \sqrt{(\frac{1}{3.1416}) \cdot \int (2.568 - 1.476 + \frac{\sin (2 \cdot 1.476)}{2} - \frac{\sin (2 \cdot 2.568)}{2}, x, 1.476, 2.568)}

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RMS Output Voltage under AC Regulator Solution

Follow our step by step solution on how to calculate RMS Output Voltage under AC Regulator?

FIRST Step Consider the formula

E rms = E s \cdot \sqrt{(\frac{1}{π}) \cdot \int (β - α + \frac{\sin (2 \cdot α)}{2} - \frac{\sin (2 \cdot β)}{2}, x, α, β)}

Next Step Substitute values of Variables

∴

E rms = 230V \cdot \sqrt{(\frac{1}{π}) \cdot \int (2.568rad - 1.476rad + \frac{\sin (2 \cdot 1.476rad)}{2} - \frac{\sin (2 \cdot 2.568rad)}{2}, x, 1.476rad, 2.568rad)}

Next Step Substitute values of Constants

∴

E rms = 230V \cdot \sqrt{(\frac{1}{3.1416}) \cdot \int (2.568rad - 1.476rad + \frac{\sin (2 \cdot 1.476rad)}{2} - \frac{\sin (2 \cdot 2.568rad)}{2}, x, 1.476rad, 2.568rad)}

Next Step Prepare to Evaluate

∴

E rms = 230 \cdot \sqrt{(\frac{1}{3.1416}) \cdot \int (2.568 - 1.476 + \frac{\sin (2 \cdot 1.476)}{2} - \frac{\sin (2 \cdot 2.568)}{2}, x, 1.476, 2.568)}

Next Step Evaluate

∴

E rms = 173.762231645099V

LAST Step Rounding Answer

∴

E rms = 173.7622V

RMS Output Voltage under AC Regulator Formula Elements

Variables

Constants

Functions

RMS Output Voltage under AC Regulator

RMS Output Voltage under AC Regulator Refers to the Effective Voltage Level that the Regulator Delivers to the Load over Time.

Symbol: E_rms

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find RMS Output Voltage under AC Regulator

Supply Voltage

Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit.

Symbol: E_s

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Supply Voltage

Extinction Angle of Thyristor

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.

Symbol: β

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Extinction Angle of Thyristor

Firing Angle

Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor.

Symbol: α

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Firing Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: 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.

Syntax: int(expr, arg, from, to)

Other formulas in AC Regulator category

Go Average Thyristor Current under AC Regulator

I av = (\frac{\sqrt{2} \cdot E s}{2 \cdot π \cdot Z}) \cdot \int (\sin (x - φ) - \sin (α - φ) \cdot \exp ((\frac{R}{L}) \cdot ((\frac{α}{ω}) - t)), x, α, β)

Go RMS Thyristor Current under AC Regulator

I rms = (\frac{E s}{Z}) \cdot \sqrt{(\frac{1}{π}) \cdot \int ({(\sin (x - φ) - \sin (α - φ) \cdot \exp ((\frac{R}{L}) \cdot ((\frac{α}{ω}) - t)))}^{2}, x, α, β)}

How to Evaluate RMS Output Voltage under AC Regulator?

RMS Output Voltage under AC Regulator evaluator 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 evaluate 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 E_rms symbol.

How to evaluate RMS Output Voltage under AC Regulator using this online evaluator? To use this online evaluator for RMS Output Voltage under AC Regulator, enter Supply Voltage (E_s), Extinction Angle of Thyristor (β) & Firing Angle (α) and hit the calculate button.

FAQs on RMS Output Voltage under AC Regulator

What is the formula to find RMS Output Voltage under AC Regulator?

The formula of RMS Output Voltage under AC Regulator is expressed as 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)). Here is an example- 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)).

How to calculate RMS Output Voltage under AC Regulator?

With Supply Voltage (E_s), Extinction Angle of Thyristor (β) & Firing Angle (α) we can find RMS Output Voltage under AC Regulator using the 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)). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt), Definite Integral (int) function(s).

Can the RMS Output Voltage under AC Regulator be negative?

Yes, the RMS Output Voltage under AC Regulator, measured in Electric Potential can be negative.

Which unit is used to measure RMS Output Voltage under AC Regulator?

RMS Output Voltage under AC Regulator is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which RMS Output Voltage under AC Regulator can be measured.

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RMS Output Voltage under AC Regulator Formula

RMS Output Voltage under AC Regulator Example

RMS Output Voltage under AC Regulator Solution

RMS Output Voltage under AC Regulator Formula Elements

Other formulas in AC Regulator category

How to Evaluate RMS Output Voltage under AC Regulator?

FAQs on RMS Output Voltage under AC Regulator

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