RMS Thyristor Current under AC Regulator Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Irms = (Es/Z)*sqrt((1/pi)*int((sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)))^2,x,α,β))
This formula uses 1 Constants, 4 Functions, 10 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
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., 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., 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., 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., int(expr, arg, from, to)
Variables Used
RMS Thyristor Current Under AC Regulator - (Measured in Ampere) - 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.
Supply Voltage - (Measured in Volt) - Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit.
Impedance - (Measured in Ohm) - Impedance is a Measure of the Total Opposition that an Electrical Circuit presents to the flow of Alternating Current (AC).
Phase Angle - (Measured in Radian) - Phase Angle typically refers to the Angular Displacement of the Waveform from its Zero crossing point.
Firing Angle - (Measured in Radian) - Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor.
Resistance - (Measured in Ohm) - Resistance is a measure of the opposition to current flow in any voltage regulator circuit. Its S.I unit is ohm.
Inductance - (Measured in Henry) - 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.
Angular Frequency - (Measured in Radian per Second) - Angular Frequency is Defined as the Rate of Change of the Phase Angle of the Voltage or Current with Respect to Time.
Time - (Measured in Second) - 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.
Extinction Angle of Thyristor - (Measured in Radian) - 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.
STEP 1: Convert Input(s) to Base Unit
Supply Voltage: 230 Volt --> 230 Volt No Conversion Required
Impedance: 3.37 Ohm --> 3.37 Ohm No Conversion Required
Phase Angle: 1.213 Radian --> 1.213 Radian No Conversion Required
Firing Angle: 1.476 Radian --> 1.476 Radian No Conversion Required
Resistance: 10.1 Ohm --> 10.1 Ohm No Conversion Required
Inductance: 1.258 Henry --> 1.258 Henry No Conversion Required
Angular Frequency: 314 Radian per Second --> 314 Radian per Second No Conversion Required
Time: 0.558 Second --> 0.558 Second No Conversion Required
Extinction Angle of Thyristor: 2.568 Radian --> 2.568 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Irms = (Es/Z)*sqrt((1/pi)*int((sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)))^2,x,α,β)) --> (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))
Evaluating ... ...
Irms = 28.87532115923
STEP 3: Convert Result to Output's Unit
28.87532115923 Ampere --> No Conversion Required
FINAL ANSWER
28.87532115923 28.87532 Ampere <-- RMS Thyristor Current Under AC Regulator
(Calculation completed in 00.022 seconds)

Credits

Created by Siddharth Raj
Heritage Institute of Technology ( HITK), Kolkata
Siddharth Raj has created this Calculator and 10+ more calculators!
Verified by banuprakash
Dayananda Sagar College of Engineering (DSCE), Bangalore
banuprakash has verified this Calculator and 25+ more calculators!

3 AC Regulator Calculators

Average Thyristor Current under AC Regulator
Go 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)
RMS Thyristor Current under AC Regulator
Go 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))
RMS Output Voltage under AC Regulator
Go 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))

RMS Thyristor Current under AC Regulator 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))
Irms = (Es/Z)*sqrt((1/pi)*int((sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)))^2,x,α,β))

What Factors Influence the RMS Thyristor Current in an AC Regulator Circuit?

The RMS thyristor current in an AC regulator circuit represents the effective current flowing through the thyristor, impacting its power dissipation and reliability. Factors influencing it include load characteristics, control strategy, AC voltage, thyristor specifications, and heat dissipation. Proper management of these factors ensures safe operation and optimal performance of the regulator circuit.












How to Calculate RMS Thyristor Current under AC Regulator?

RMS Thyristor Current under AC Regulator calculator 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 calculate 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 Irms symbol.

How to calculate RMS Thyristor Current under AC Regulator using this online calculator? To use this online calculator for RMS Thyristor Current under AC Regulator, enter Supply Voltage (Es), 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. Here is how the RMS Thyristor Current under AC Regulator calculation can be explained with given input values -> 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)).

FAQ

What is 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 and is represented as Irms = (Es/Z)*sqrt((1/pi)*int((sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)))^2,x,α,β)) or 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)). Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit, Impedance is a Measure of the Total Opposition that an Electrical Circuit presents to the flow of Alternating Current (AC), Phase Angle typically refers to the Angular Displacement of the Waveform from its Zero crossing point, Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor, Resistance is a measure of the opposition to current flow in any voltage regulator circuit. Its S.I unit is ohm, 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, Angular Frequency is Defined as the Rate of Change of the Phase Angle of the Voltage or Current with Respect to 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 & 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.
How to calculate 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 is calculated using 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 calculate RMS Thyristor Current under AC Regulator, you need Supply Voltage (Es), Impedance (Z), Phase Angle (φ), Firing Angle (α), Resistance (R), Inductance (L), Angular Frequency (ω), Time (t) & Extinction Angle of Thyristor (β). With our tool, you need to enter the respective value for Supply Voltage, Impedance, Phase Angle, Firing Angle, Resistance, Inductance, Angular Frequency, Time & Extinction Angle of Thyristor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!