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Average Thyristor Current under AC Regulator Formula

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Average Thyristor Current Under AC Regulator refers to the Mean Value of the Current flowing through the Thyristor over a Complete Cycle of the Alternating Current (AC) Waveform. Check FAQs

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)

I_av - Average Thyristor Current Under AC Regulator?E_s - Supply Voltage?Z - Impedance?φ - Phase Angle?α - Firing Angle?R - Resistance?L - Inductance?ω - Angular Frequency?t - Time?β - Extinction Angle of Thyristor?π - Archimedes' constant?

Average Thyristor Current under AC Regulator Example

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Here is how the Average Thyristor Current under AC Regulator equation looks like with Values.

Here is how the Average Thyristor Current under AC Regulator equation looks like with Units.

Here is how the Average Thyristor Current under AC Regulator equation looks like.

11.4927 = (\frac{\sqrt{2} \cdot 230}{2 \cdot 3.1416 \cdot 3.37}) \cdot \int (\sin (x - 1.213) - \sin (1.476 - 1.213) \cdot \exp ((\frac{10.1}{1.258}) \cdot ((\frac{1.476}{314}) - 0.558)), x, 1.476, 2.568)

11.4927A = (\frac{\sqrt{2} \cdot 230V}{2 \cdot 3.1416 \cdot 3.37Ω}) \cdot \int (\sin (x - 1.213rad) - \sin (1.476rad - 1.213rad) \cdot \exp ((\frac{10.1Ω}{1.258H}) \cdot ((\frac{1.476rad}{314rad/s}) - 0.558s)), x, 1.476rad, 2.568rad)

11.4927 = (\frac{\sqrt{2} \cdot 230}{2 \cdot 3.1416 \cdot 3.37}) \cdot \int (\sin (x - 1.213) - \sin (1.476 - 1.213) \cdot \exp ((\frac{10.1}{1.258}) \cdot ((\frac{1.476}{314}) - 0.558)), x, 1.476, 2.568)

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Average Thyristor Current under AC Regulator Solution

Follow our step by step solution on how to calculate Average Thyristor Current under AC Regulator?

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

I av = (\frac{\sqrt{2} \cdot 230V}{2 \cdot π \cdot 3.37Ω}) \cdot \int (\sin (x - 1.213rad) - \sin (1.476rad - 1.213rad) \cdot \exp ((\frac{10.1Ω}{1.258H}) \cdot ((\frac{1.476rad}{314rad/s}) - 0.558s)), x, 1.476rad, 2.568rad)

Next Step Substitute values of Constants

∴

I av = (\frac{\sqrt{2} \cdot 230V}{2 \cdot 3.1416 \cdot 3.37Ω}) \cdot \int (\sin (x - 1.213rad) - \sin (1.476rad - 1.213rad) \cdot \exp ((\frac{10.1Ω}{1.258H}) \cdot ((\frac{1.476rad}{314rad/s}) - 0.558s)), x, 1.476rad, 2.568rad)

Next Step Prepare to Evaluate

∴

I av = (\frac{\sqrt{2} \cdot 230}{2 \cdot 3.1416 \cdot 3.37}) \cdot \int (\sin (x - 1.213) - \sin (1.476 - 1.213) \cdot \exp ((\frac{10.1}{1.258}) \cdot ((\frac{1.476}{314}) - 0.558)), x, 1.476, 2.568)

Next Step Evaluate

∴

I av = 11.4926511298528A

LAST Step Rounding Answer

∴

I av = 11.4927A

Average Thyristor Current under AC Regulator Formula Elements

Variables

Constants

Functions

Average Thyristor Current Under AC Regulator

Average Thyristor Current Under AC Regulator refers to the Mean Value of the Current flowing through the Thyristor over a Complete Cycle of the Alternating Current (AC) Waveform.

Symbol: I_av

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Average Thyristor Current 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

Impedance

Impedance is a Measure of the Total Opposition that an Electrical Circuit presents to the flow of Alternating Current (AC).

Symbol: Z

Measurement: Electric ResistanceUnit: Ω

Note: Value can be positive or negative.

Formulas to find Impedance

Phase Angle

Phase Angle typically refers to the Angular Displacement of the Waveform from its Zero crossing point.

Symbol: φ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Phase Angle

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

Resistance

Resistance is a measure of the opposition to current flow in any voltage regulator circuit. Its S.I unit is ohm.

Symbol: R

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Resistance

Inductance

Inductance refers to the Property of a Circuit Element, typically an Inductor, that Opposes changes in the Current flowing through it by Inducing a Voltage in the Circuit.

Symbol: L

Measurement: InductanceUnit: H

Note: Value can be positive or negative.

Formulas to find Inductance

Angular Frequency

Angular Frequency is Defined as the Rate of Change of the Phase Angle of the Voltage or Current with Respect to Time.

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Frequency

Time

Time is a fundamental parameter that measures the progression of events or changes in a system. It represents the elapsed time since the start of the waveform's cycle.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time

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

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)

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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 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)}

Go RMS Output Voltage under AC Regulator

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)}

How to Evaluate Average Thyristor Current under AC Regulator?

Average Thyristor Current under AC Regulator evaluator uses 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) to evaluate the Average Thyristor Current Under AC Regulator, The Average Thyristor Current under AC Regulator formula is defined as the mean value of the current flowing through the thyristor over a complete cycle of the alternating current (AC) waveform. Average Thyristor Current Under AC Regulator is denoted by I_av symbol.

How to evaluate Average Thyristor Current under AC Regulator using this online evaluator? To use this online evaluator for Average Thyristor Current under AC Regulator, enter Supply Voltage (E_s), Impedance (Z), Phase Angle (φ), Firing Angle (α), Resistance (R), Inductance (L), Angular Frequency (ω), Time (t) & Extinction Angle of Thyristor (β) and hit the calculate button.

FAQs on Average Thyristor Current under AC Regulator

What is the formula to find Average Thyristor Current under AC Regulator?

The formula of Average Thyristor Current under AC Regulator is expressed as 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). Here is an example- 11.49265 = ((sqrt(2)*230)/(2*pi*3.37))*int(sin(x-1.213)-sin(1.476-1.213)*exp((10.1/1.258)*((1.476/314)-0.558)),x,1.476,2.568).

How to calculate Average Thyristor Current under AC Regulator?

With Supply Voltage (E_s), Impedance (Z), Phase Angle (φ), Firing Angle (α), Resistance (R), Inductance (L), Angular Frequency (ω), Time (t) & Extinction Angle of Thyristor (β) we can find Average Thyristor Current under AC Regulator using the formula - 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). This formula also uses Archimedes' constant and , Sine (sin), Exponential Growth (exp), Square Root (sqrt), Definite Integral (int) function(s).

Can the Average Thyristor Current under AC Regulator be negative?

Yes, the Average Thyristor Current under AC Regulator, measured in Electric Current can be negative.

Which unit is used to measure Average Thyristor Current under AC Regulator?

Average Thyristor Current under AC Regulator is usually measured using the Ampere[A] for Electric Current. Milliampere[A], Microampere[A], Centiampere[A] are the few other units in which Average Thyristor Current under AC Regulator can be measured.

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Average Thyristor Current under AC Regulator Formula

Average Thyristor Current under AC Regulator Example

Average Thyristor Current under AC Regulator Solution

Average Thyristor Current under AC Regulator Formula Elements

Other formulas in AC Regulator category

How to Evaluate Average Thyristor Current under AC Regulator?

FAQs on Average Thyristor Current under AC Regulator

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