Energy Dissipated during Transient Operation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation)
Et = int(R*(i)^2,x,0,T)
This formula uses 1 Functions, 4 Variables
Functions Used
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
Energy Dissipated in Transient Operation - (Measured in Joule) - Energy Dissipated in Transient Operation Occurs as a Result of the Resistance of the Winding Material to the Flow of Electrical Current.
Resistance of Motor Winding - (Measured in Ohm) - Resistance of Motor Winding Refers to the Inherent Electrical Resistance of the Wire or Coil Comprising the Motor's Winding.
Electric Current - (Measured in Ampere) - Electric Current Refers to the Current Flowing through the winding During Transient Operations or any other Operating Condition. This Current is Typically Measured in Units of Amperes (A).
Time Taken for Complete Operation - (Measured in Second) - Time Taken for Complete Operation Represent the Entire Duration of Operation or a Significant Portion of it. And It is the Duration Over Which the Integral is being Calculated.
STEP 1: Convert Input(s) to Base Unit
Resistance of Motor Winding: 4.235 Ohm --> 4.235 Ohm No Conversion Required
Electric Current: 2.345 Ampere --> 2.345 Ampere No Conversion Required
Time Taken for Complete Operation: 6.88 Second --> 6.88 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Et = int(R*(i)^2,x,0,T) --> int(4.235*(2.345)^2,x,0,6.88)
Evaluating ... ...
Et = 160.22399162
STEP 3: Convert Result to Output's Unit
160.22399162 Joule --> No Conversion Required
FINAL ANSWER
160.22399162 160.224 Joule <-- Energy Dissipated in Transient Operation
(Calculation completed in 00.004 seconds)

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Heritage Institute of Technology ( HITK), Kolkata
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13 Electric Drives Calculators

Starting Time for Induction Motor under No Load
Go Starting Time For Induction motor on No Load = (-Mechanical Time Constant of Motor/2)*int((Slip/Slip at Maximum Torque+Slip at Maximum Torque/Slip)*x,x,1,0.05)
Torque of Squirrel Cage Induction Motor
Go Torque = (Constant*Voltage^2*Rotor Resistance)/((Stator Resistance+Rotor Resistance)^2+(Stator Reactance+Rotor Reactance)^2)
Torque Generated by Scherbius Drive
Go Torque = 1.35*((Back Emf*AC Line Voltage*Rectified Rotor Current*RMS Value of Rotor Side Line Voltage)/(Back Emf*Angular Frequency))
Time Taken for Drive Speed
Go Time Taken for Drive Speed = Moment of Inertia*int(1/(Torque-Load Torque),x,Initial angular Velocity,Final Angular Velocity)
Motor Terminal Voltage in Regenerative Braking
Go Motor Terminal Voltage = (1/Time Taken for Complete Operation)*int(Source Voltage*x,x,On-Period Time,Time Taken for Complete Operation)
Equivalent Current for Fluctuating and Intermittent Loads
Go Equivalent Current = sqrt((1/Time Taken for Complete Operation)*int((Electric Current)^2,x,1,Time Taken for Complete Operation))
Energy Dissipated during Transient Operation
Go Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation)
Slip of Scherbius Drive given RMS Line Voltage
Go Slip = (Back Emf/RMS Value of Rotor Side Line Voltage)*modulus(cos(Firing Angle))
DC Output Voltage of Rectifier in Scherbius Drive Given Rotor RMS Line Voltage
Go DC Voltage = (3*sqrt(2))*(RMS Value of Rotor Side Line Voltage/pi)
Gear Tooth Ratio
Go Gear Tooth Ratio = Number 1 of Teeth of Driving Gear/Number 2 of Teeth of Driven Gear
Average Back Emf with Negligible Commutation Overlap
Go Back Emf = 1.35*AC Line Voltage*cos(Firing Angle)
DC Output Voltage of Rectifier in Scherbius Drive Given Rotor RMS Line Voltage at Slip
Go DC Voltage = 1.35*RMS Value of Rotor Side Line Voltage with Slip
DC Output Voltage of Rectifier in Scherbius Drive Given Maximum Rotor Voltage
Go DC Voltage = 3*(Peak Voltage/pi)

Energy Dissipated during Transient Operation Formula

Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation)
Et = int(R*(i)^2,x,0,T)

How Does the Energy Dissipated Affect the Overall Efficiency of the Motor?

The energy dissipated in a motor winding during transient operations primarily manifests as heat, which can increase the temperature of the winding. Elevated temperatures can lead to increased resistance in the winding material, thereby reducing the overall efficiency of the motor. Additionally, excessive heat can degrade insulation materials, leading to insulation breakdown and potential motor failure. Therefore, minimizing energy dissipation during transient operations is essential for maintaining motor efficiency and reliability.

How to Calculate Energy Dissipated during Transient Operation?

Energy Dissipated during Transient Operation calculator uses Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation) to calculate the Energy Dissipated in Transient Operation, The Energy Dissipated during Transient Operation refers to the heat generated within the winding of an electric motor when subjected to sudden changes or fluctuations in voltage, current, or load. Energy Dissipated in Transient Operation is denoted by Et symbol.

How to calculate Energy Dissipated during Transient Operation using this online calculator? To use this online calculator for Energy Dissipated during Transient Operation, enter Resistance of Motor Winding (R), Electric Current (i) & Time Taken for Complete Operation (T) and hit the calculate button. Here is how the Energy Dissipated during Transient Operation calculation can be explained with given input values -> 160.224 = int(4.235*(2.345)^2,x,0,6.88).

FAQ

What is Energy Dissipated during Transient Operation?
The Energy Dissipated during Transient Operation refers to the heat generated within the winding of an electric motor when subjected to sudden changes or fluctuations in voltage, current, or load and is represented as Et = int(R*(i)^2,x,0,T) or Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation). Resistance of Motor Winding Refers to the Inherent Electrical Resistance of the Wire or Coil Comprising the Motor's Winding, Electric Current Refers to the Current Flowing through the winding During Transient Operations or any other Operating Condition. This Current is Typically Measured in Units of Amperes (A) & Time Taken for Complete Operation Represent the Entire Duration of Operation or a Significant Portion of it. And It is the Duration Over Which the Integral is being Calculated.
How to calculate Energy Dissipated during Transient Operation?
The Energy Dissipated during Transient Operation refers to the heat generated within the winding of an electric motor when subjected to sudden changes or fluctuations in voltage, current, or load is calculated using Energy Dissipated in Transient Operation = int(Resistance of Motor Winding*(Electric Current)^2,x,0,Time Taken for Complete Operation). To calculate Energy Dissipated during Transient Operation, you need Resistance of Motor Winding (R), Electric Current (i) & Time Taken for Complete Operation (T). With our tool, you need to enter the respective value for Resistance of Motor Winding, Electric Current & Time Taken for Complete Operation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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