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RMS Thyristor Current under AC Regulator Formula

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The RMS Thyristor Current Under AC regulator refers to the root mean square (RMS) value of the current flowing through the thyristor in an alternating current (AC) power regulator circuit. Check FAQs

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)}

I_rms - RMS 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?

RMS Thyristor Current under AC Regulator Example

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

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

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

28.8753 = (\frac{230}{3.37}) \cdot \sqrt{(\frac{1}{3.1416}) \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)))}^{2}, x, 1.476, 2.568)}

28.8753A = (\frac{230V}{3.37Ω}) \cdot \sqrt{(\frac{1}{3.1416}) \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)))}^{2}, x, 1.476rad, 2.568rad)}

28.8753 = (\frac{230}{3.37}) \cdot \sqrt{(\frac{1}{3.1416}) \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)))}^{2}, x, 1.476, 2.568)}

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RMS Thyristor Current under AC Regulator Solution

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

FIRST Step Consider the formula

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)}

Next Step Substitute values of Variables

∴

I rms = (\frac{230V}{3.37Ω}) \cdot \sqrt{(\frac{1}{π}) \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)))}^{2}, x, 1.476rad, 2.568rad)}

Next Step Substitute values of Constants

∴

I rms = (\frac{230V}{3.37Ω}) \cdot \sqrt{(\frac{1}{3.1416}) \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)))}^{2}, x, 1.476rad, 2.568rad)}

Next Step Prepare to Evaluate

∴

I rms = (\frac{230}{3.37}) \cdot \sqrt{(\frac{1}{3.1416}) \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)))}^{2}, x, 1.476, 2.568)}

Next Step Evaluate

∴

I rms = 28.87532115923A

LAST Step Rounding Answer

∴

I rms = 28.8753A

RMS Thyristor Current under AC Regulator Formula Elements

Variables

Constants

Functions

RMS Thyristor Current Under AC Regulator

The RMS Thyristor Current Under AC regulator refers to the root mean square (RMS) value of the current flowing through the thyristor in an alternating current (AC) power regulator circuit.

Symbol: I_rms

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find RMS 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 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 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 RMS Thyristor Current under AC Regulator?

RMS Thyristor Current under AC Regulator evaluator uses 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)) to evaluate the RMS Thyristor Current Under AC Regulator, The RMS Thyristor Current under AC Regulator refers to the root mean square (RMS) value of the current flowing through the thyristor (a semiconductor device) in an alternating current (AC) power regulator circuit. RMS Thyristor Current Under AC Regulator is denoted by I_rms symbol.

How to evaluate RMS Thyristor Current under AC Regulator using this online evaluator? To use this online evaluator for RMS 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 RMS Thyristor Current under AC Regulator

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

The formula of RMS Thyristor Current under AC Regulator is expressed as 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)). Here is an example- 28.87532 = (230/3.37)*sqrt((1/pi)*int((sin(x-1.213)-sin(1.476-1.213)*exp((10.1/1.258)*((1.476/314)-0.558)))^2,x,1.476,2.568)).

How to calculate RMS 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 RMS Thyristor Current under AC Regulator using the formula - 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)). This formula also uses Archimedes' constant and , Sine (sin), Exponential Growth (exp), Square Root (sqrt), Definite Integral (int) function(s).

Can the RMS Thyristor Current under AC Regulator be negative?

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

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

RMS 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 RMS Thyristor Current under AC Regulator can be measured.

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RMS Thyristor Current under AC Regulator Formula

RMS Thyristor Current under AC Regulator Example

RMS Thyristor Current under AC Regulator Solution

RMS Thyristor Current under AC Regulator Formula Elements

Other formulas in AC Regulator category

How to Evaluate RMS Thyristor Current under AC Regulator?

FAQs on RMS Thyristor Current under AC Regulator

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