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ElectricalMachine
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The voltage equation of the synchronous motor is?

A

V=Eb+IaRa+jXsV = E_{b} + I_{a} R_{a} + j X_{s}V=EbтАЛ+IaтАЛRaтАЛ+jXsтАЛ

B

V=EbтИТIaRa+jXsV = E_{b} - I_{a} R_{a} + j X_{s}V=EbтАЛтИТIaтАЛRaтАЛ+jXsтАЛ

C

V=Eb+IaRaтИТjXsV = E_{b} + I_{a} R_{a} - j X_{s}V=EbтАЛ+IaтАЛRaтАЛтИТjXsтАЛ

D

V=EbтИТIaRaтИТjXsV = E_{b} - I_{a} R_{a} - j X_{s}V=EbтАЛтИТIaтАЛRaтАЛтИТjXsтАЛ

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleElectricalMachine
Option A

V=Eb+IaRa+jXsV = E_{b} + I_{a} R_{a} + j X_{s}V=EbтАЛ+IaтАЛRaтАЛ+jXsтАЛ

Quick Summary:

The correct voltage equation for a synchronous motor is given by V=Eb+Ia(Ra+jXs)V = E_b + I_a (R_a + jX_s)V=EbтАЛ+IaтАЛ(RaтАЛ+jXsтАЛ), where VVV is the terminal voltage, EbE_bEbтАЛ is the back electromotive force (EMF), IaI_aIaтАЛ is the armature current, RaR_aRaтАЛ is the armature resistance, and XsX_sXsтАЛ is the synchronous reactance.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

The correct voltage equation for a synchronous motor is given by V=Eb+Ia(Ra+jXs)V = E_b + I_a (R_a + jX_s)V=EbтАЛ+IaтАЛ(RaтАЛ+jXsтАЛ), where VVV is the terminal voltage, EbE_bEbтАЛ is the back electromotive force (EMF), IaI_aIaтАЛ is the armature current, RaR_aRaтАЛ is the armature resistance, and XsX_sXsтАЛ is the synchronous reactance.

ЁЯФв Key Formulas

V=Eb+Ia(Ra+jXs)V = E_b + I_a (R_a + jX_s)V=EbтАЛ+IaтАЛ(RaтАЛ+jXsтАЛ) тАФ Terminal voltage equation of the synchronous motor

тЪЩя╕П Working Principle

This equation describes the relationship between voltage, current, and the impedance faced by the current in the armature winding of the synchronous motor. The synchronous reactance represents the total opposition to current flow due to both resistance and inductive reactance at synchronous speed.

ЁЯУМ Key Points
  • тЦ╕

    The synchronous motor operates at constant speed irrespective of load conditions.

  • тЦ╕

    The concept of synchronous reactance is crucial in determining the motor's performance characteristics.

тЬЕ Advantages
  • тЦ╕

    High efficiency

  • тЦ╕

    Good power factor characteristics

тЭМ Disadvantages / Limitations
  • тЦ╕

    Requires additional starting mechanisms

  • тЦ╕

    Sensitive to load changes

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Used in power plants for synchronous generation

  • тЦ╕

    Drives in industrial applications requiring constant speed

ЁЯУД Additional Information
  • тЦ╕

    Standard value or specification for synchronous reactance varies based on motor design and application.

  • тЦ╕

    Option B is incorrect because it uses a minus sign instead of a plus sign in the equation.

ЁЯУК Diagram / Illustration
Voltage EquationE_b + IтВР (RтВР +jXтВЫ)
тЬЕ

A is correct тАФ it accurately represents the terminal voltage relationship in a synchronous motor.

Core Concepts Used
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Synchronous Motor Back EMF Synchronous Reactance
ЁЯТб EXAM TIP

Understanding the impedance in AC circuits is crucial when analyzing synchronous motors and their performance.

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