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RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Formula

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RMS Voltage in Half Wave is defined as the root mean square value of the voltage in a thyristor rectifier. Check FAQs

V rms(half) = \frac{V o(max) \cdot \sqrt{π - α r + (0.5 \cdot \sin (2 \cdot α d))}}{2 \cdot \sqrt{π}}

V_rms(half) - RMS Voltage in Half Wave?V_o(max) - Maximum Output Voltage?α_r - Trigger Angle in Radians?α_d - Trigger Angle in Degree?π - Archimedes' constant?

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Example

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Here is how the RMS Output Voltage of Half Wave Thyristor Rectifier with R Load equation looks like with Values.

Here is how the RMS Output Voltage of Half Wave Thyristor Rectifier with R Load equation looks like with Units.

Here is how the RMS Output Voltage of Half Wave Thyristor Rectifier with R Load equation looks like.

9.9156 = \frac{21 \cdot \sqrt{3.1416 - 0.84 + (0.5 \cdot \sin (2 \cdot 45))}}{2 \cdot \sqrt{3.1416}}

9.9156V = \frac{21V \cdot \sqrt{3.1416 - 0.84rad + (0.5 \cdot \sin (2 \cdot 45°))}}{2 \cdot \sqrt{3.1416}}

9.9156 = \frac{21 \cdot \sqrt{3.1416 - 0.84 + (0.5 \cdot \sin (2 \cdot 45))}}{2 \cdot \sqrt{3.1416}}

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RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Solution

Follow our step by step solution on how to calculate RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

FIRST Step Consider the formula

V rms(half) = \frac{V o(max) \cdot \sqrt{π - α r + (0.5 \cdot \sin (2 \cdot α d))}}{2 \cdot \sqrt{π}}

Next Step Substitute values of Variables

∴

V rms(half) = \frac{21V \cdot \sqrt{π - 0.84rad + (0.5 \cdot \sin (2 \cdot 45°))}}{2 \cdot \sqrt{π}}

Next Step Substitute values of Constants

∴

V rms(half) = \frac{21V \cdot \sqrt{3.1416 - 0.84rad + (0.5 \cdot \sin (2 \cdot 45°))}}{2 \cdot \sqrt{3.1416}}

Next Step Convert Units

∴

V rms(half) = \frac{21V \cdot \sqrt{3.1416 - 0.84rad + (0.5 \cdot \sin (2 \cdot 0.7854rad))}}{2 \cdot \sqrt{3.1416}}

Next Step Prepare to Evaluate

∴

V rms(half) = \frac{21 \cdot \sqrt{3.1416 - 0.84 + (0.5 \cdot \sin (2 \cdot 0.7854))}}{2 \cdot \sqrt{3.1416}}

Next Step Evaluate

∴

V rms(half) = 9.91555111511209V

LAST Step Rounding Answer

∴

V rms(half) = 9.9156V

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Formula Elements

Variables

Constants

Functions

RMS Voltage in Half Wave

RMS Voltage in Half Wave is defined as the root mean square value of the voltage in a thyristor rectifier.

Symbol: V_rms(half)

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find RMS Voltage in Half Wave

Maximum Output Voltage

Maximum Output Voltage is the Maximum voltage that can be produced at the output of the converter of any controlled rectifier.

Symbol: V_o(max)

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Maximum Output Voltage

Trigger Angle in Radians

Trigger Angle in Radians is defined as the firing angle of a thyristor in radians.

Symbol: α_r

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Trigger Angle in Radians

Trigger Angle in Degree

Trigger Angle in Degree it gives the firing angle of thyristor in degree.

Symbol: α_d

Measurement: AngleUnit: °

Note: Value should be less than 181.

Formulas to find Trigger Angle in Degree

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)

Other formulas in Half Wave Controlled Rectifiers category

Go Average Voltage of Half Wave Thyristor Rectifier with RL Load

V avg(half) = (\frac{V o(max)}{2 \cdot π}) \cdot (\cos (α d) - \cos (β d))

Go Voltage Ripple Factor of Half Wave Thyristor Rectifier with R Load

RF = \sqrt{{FF}^{2} - 1}

Go Average Load Voltage of Half Wave Thyristor Rectifier with RLE Load

V L(half) = (\frac{V o(max)}{2 \cdot π}) \cdot (\cos (α d) + \cos (β d)) + (\frac{E b}{2}) \cdot (1 + (\frac{θ r + α r}{π}))

Go Turn On Angle of Half Wave Rectifier

θ r = a \sin (\frac{E L}{V i(max)})

How to Evaluate RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load evaluator uses RMS Voltage in Half Wave = (Maximum Output Voltage*sqrt(pi-Trigger Angle in Radians+(0.5*sin(2*Trigger Angle in Degree))))/(2*sqrt(pi)) to evaluate the RMS Voltage in Half Wave, RMS output voltage of Half Wave Thyristor Rectifier with R load formula gives the value of RMS value of output voltage of single phase fully controlled Half wave rectifier with R load. RMS Voltage in Half Wave is denoted by V_rms(half) symbol.

How to evaluate RMS Output Voltage of Half Wave Thyristor Rectifier with R Load using this online evaluator? To use this online evaluator for RMS Output Voltage of Half Wave Thyristor Rectifier with R Load, enter Maximum Output Voltage (V_o(max)), Trigger Angle in Radians (α_r) & Trigger Angle in Degree (α_d) and hit the calculate button.

FAQs on RMS Output Voltage of Half Wave Thyristor Rectifier with R Load

What is the formula to find RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

The formula of RMS Output Voltage of Half Wave Thyristor Rectifier with R Load is expressed as RMS Voltage in Half Wave = (Maximum Output Voltage*sqrt(pi-Trigger Angle in Radians+(0.5*sin(2*Trigger Angle in Degree))))/(2*sqrt(pi)). Here is an example- 9.915551 = (21*sqrt(pi-0.84+(0.5*sin(2*0.785398163397301))))/(2*sqrt(pi)).

How to calculate RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

With Maximum Output Voltage (V_o(max)), Trigger Angle in Radians (α_r) & Trigger Angle in Degree (α_d) we can find RMS Output Voltage of Half Wave Thyristor Rectifier with R Load using the formula - RMS Voltage in Half Wave = (Maximum Output Voltage*sqrt(pi-Trigger Angle in Radians+(0.5*sin(2*Trigger Angle in Degree))))/(2*sqrt(pi)). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

Can the RMS Output Voltage of Half Wave Thyristor Rectifier with R Load be negative?

No, the RMS Output Voltage of Half Wave Thyristor Rectifier with R Load, measured in Electric Potential cannot be negative.

Which unit is used to measure RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load 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 of Half Wave Thyristor Rectifier with R Load can be measured.

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RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Formula

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Example

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Solution

RMS Output Voltage of Half Wave Thyristor Rectifier with R Load Formula Elements

Other formulas in Half Wave Controlled Rectifiers category

How to Evaluate RMS Output Voltage of Half Wave Thyristor Rectifier with R Load?

FAQs on RMS Output Voltage of Half Wave Thyristor Rectifier with R Load

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