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RMS Output Voltage for Phase Controller Formula

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RMS Output Voltage Full Converter is defined as the root mean square value of the voltage at output terminal of a full converter circuit. Check FAQs

V rms(full) = \sqrt{(\frac{{(V m)}^{2}}{π}) \cdot \int ({(\sin (x))}^{2}, x, (60 + α f(thy)), (120 + α f(thy)))}

V_rms(full) - RMS Output Voltage Full Converter?V_m - Peak Voltage?α_f(thy) - Firing Angle of Thyristor Converter?π - Archimedes' constant?

RMS Output Voltage for Phase Controller Example

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Here is how the RMS Output Voltage for Phase Controller equation looks like with Values.

Here is how the RMS Output Voltage for Phase Controller equation looks like with Units.

Here is how the RMS Output Voltage for Phase Controller equation looks like.

30.9265 = \sqrt{(\frac{{(10)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 27.5), (120 + 27.5))}

30.9265V = \sqrt{(\frac{{(10V)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 27.5°), (120 + 27.5°))}

30.9265 = \sqrt{(\frac{{(10)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 27.5), (120 + 27.5))}

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RMS Output Voltage for Phase Controller Solution

Follow our step by step solution on how to calculate RMS Output Voltage for Phase Controller?

FIRST Step Consider the formula

V rms(full) = \sqrt{(\frac{{(V m)}^{2}}{π}) \cdot \int ({(\sin (x))}^{2}, x, (60 + α f(thy)), (120 + α f(thy)))}

Next Step Substitute values of Variables

∴

V rms(full) = \sqrt{(\frac{{(10V)}^{2}}{π}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 27.5°), (120 + 27.5°))}

Next Step Substitute values of Constants

∴

V rms(full) = \sqrt{(\frac{{(10V)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 27.5°), (120 + 27.5°))}

Next Step Convert Units

∴

V rms(full) = \sqrt{(\frac{{(10V)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 0.48rad), (120 + 0.48rad))}

Next Step Prepare to Evaluate

∴

V rms(full) = \sqrt{(\frac{{(10)}^{2}}{3.1416}) \cdot \int ({(\sin (x))}^{2}, x, (60 + 0.48), (120 + 0.48))}

Next Step Evaluate

∴

V rms(full) = 30.926495059665V

LAST Step Rounding Answer

∴

V rms(full) = 30.9265V

RMS Output Voltage for Phase Controller Formula Elements

Variables

Constants

Functions

RMS Output Voltage Full Converter

RMS Output Voltage Full Converter is defined as the root mean square value of the voltage at output terminal of a full converter circuit.

Symbol: V_rms(full)

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find RMS Output Voltage Full Converter

Peak Voltage

Peak Voltage is the peak or maximum voltage of a circuit/ rectifier.

Symbol: V_m

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Peak Voltage

Firing Angle of Thyristor Converter

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.

Symbol: α_f(thy)

Measurement: AngleUnit: °

Note: Value should be between 0 to 181.

Formulas to find Firing Angle of Thyristor Converter

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 Three Phase Full Converter category

Go Average Output Voltage for Three-Phase Converter

V avg(3Φ-full) = \frac{2 \cdot V m(3Φ-full) \cdot \cos (\frac{α d(3Φ-full)}{2})}{π}

Go Peak Average Output Voltage of Three-Phase Full Converters

V om(3Φ-full) = \frac{5.2 \cdot V in(3Φ-full)}{π}

Go Normalized Average Output Voltage in Three-Phase Full-Converter

V n(3Φ-full) = (\cos (α d(3Φ-full)))

Go RMS Output Voltage of Three-Phase Full Converter

V rms(3Φ-full) = ({(6)}^{0.5}) \cdot V in(3Φ-full) \cdot ({(0.25 + 0.65 \cdot \frac{\cos (2 \cdot α d(3Φ-full))}{π})}^{0.5})

How to Evaluate RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller evaluator 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 evaluate 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 V_rms(full) symbol.

How to evaluate RMS Output Voltage for Phase Controller using this online evaluator? To use this online evaluator for RMS Output Voltage for Phase Controller, enter Peak Voltage (V_m) & Firing Angle of Thyristor Converter (α_f(thy)) and hit the calculate button.

FAQs on RMS Output Voltage for Phase Controller

What is the formula to find RMS Output Voltage for Phase Controller?

The formula of RMS Output Voltage for Phase Controller is expressed as 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))). Here is an example- 30.9265 = sqrt(((10)^2/pi)*int((sin(x))^2,x,(60+0.47996554429835),(120+0.47996554429835))).

How to calculate RMS Output Voltage for Phase Controller?

With Peak Voltage (V_m) & Firing Angle of Thyristor Converter (α_f(thy)) we can find RMS Output Voltage for Phase Controller using the 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))). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt), Definite Integral (int) function(s).

Can the RMS Output Voltage for Phase Controller be negative?

No, the RMS Output Voltage for Phase Controller, measured in Electric Potential cannot be negative.

Which unit is used to measure RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller 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 for Phase Controller can be measured.

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