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ElectricalMachine
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The angle between the main winding and auxiliary winding is around ____________ in Capacitor split-phase motor.

A

10тБ╗┬▓тБ░ degrees

B

30-40 degrees

C

70-90 degrees

D

20 degrees

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleElectricalMachine
Option C

70-90 degrees

Quick Summary:

In a capacitor split-phase induction motor, the angle between the main winding current and auxiliary winding current is around 70 to 90 degrees. The addition of a series capacitor in the auxiliary winding creates a large phase displacement (approaching 90┬░) between the currents flowing in the two windings. This phase shift produces a rotating magnetic field, which develops the necessary starting torque.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

In a capacitor split-phase induction motor, the angle between the main winding current and auxiliary winding current is around 70 to 90 degrees. The addition of a series capacitor in the auxiliary winding creates a large phase displacement (approaching 90┬░) between the currents flowing in the two windings. This phase shift produces a rotating magnetic field, which develops the necessary starting torque.

ЁЯФв Key Formulas

╬▒=╬╕a+╬╕mтЙИ90┬░\alpha = \theta_a + \theta_m \approx 90┬░╬▒=╬╕aтАЛ+╬╕mтАЛтЙИ90┬░ тАФ Phase angle difference between auxiliary (IaI_aIaтАЛ) and main (ImI_mImтАЛ) winding currents

TsтИЭImIasinтБб╬▒T_s \propto I_m I_a \sin\alphaTsтАЛтИЭImтАЛIaтАЛsin╬▒ тАФ Starting torque proportional to the sine of the phase angle ╬▒\alpha╬▒

тЪЩя╕П Working Principle

A single-phase supply creates an alternating magnetic field that cannot produce a starting torque on its own. By connecting an auxiliary winding in series with a capacitor parallel to the main winding, the current in the auxiliary winding leads the supply voltage while the main winding current lags it. This results in two spatial and temporal phase-displaced currents (ImI_mImтАЛ and IaI_aIaтАЛ), creating a forward-rotating magnetic field according to double-revolving field theory.

ЁЯУМ Key Points
  • тЦ╕

    The capacitor causes the auxiliary winding current IaI_aIaтАЛ to lead the supply voltage VVV.

  • тЦ╕

    The main winding is highly inductive, causing its current ImI_mImтАЛ to lag the supply voltage VVV.

  • тЦ╕

    Because sinтБб90┬░=1\sin 90┬░= 1sin90┬░=1, a phase difference near 90┬░90┬░90┬░ maximizes the starting torque per unit current.

тЬЕ Advantages
  • тЦ╕

    Higher starting torque compared to resistance split-phase motors

  • тЦ╕

    Higher power factor during starting phase

  • тЦ╕

    Lower starting current for the same developed torque

тЭМ Disadvantages / Limitations
  • тЦ╕

    Higher initial cost due to the requirement of a capacitor

  • тЦ╕

    Requires a centrifugal switch to disconnect the auxiliary winding after reaching ~75% speed (in capacitor-start motors)

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Compressors and Refrigerators

  • тЦ╕

    Pumps and Conveyors

  • тЦ╕

    Air conditioners and heavy-duty blowers

ЁЯФД Comparison Table
FeatureResistance Split-PhaseCapacitor Split-Phase

Phase Shift Angle (╬▒)

30┬░ to 40┬░

70┬░ to 90┬░

Starting Torque

Moderate (1.5 to 2 times rated)

High (3 to 4.5 times rated)

Auxiliary Circuit Component

High Resistance Winding

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ЁЯУД Additional Information
  • тЦ╕

    Option A (10тБ╗┬▓тБ░ degrees) is too low for effective starting torque in split-phase motors.

  • тЦ╕

    Option B (30-40 degrees) corresponds to a standard resistance split-phase induction motor.

  • тЦ╕

    Option D (20 degrees) is insufficient to create a near-circular rotating magnetic field.

ЁЯУК Diagram / Illustration
Capacitor Motor Phasor DiagramV (SupplyVoltage)Im (Main WindingCurrent)Ia (Auxiliary Winding Current)╬╕m╬╕a╬▒ тЙИ 70┬░ - 90┬░
тЬЕ

C is correct тАФ A capacitor-start/split-phase motor uses a capacitor in the auxiliary winding to create a phase displacement of nearly 90 degrees (typically 70-90 degrees) relative to the main winding current.

Core Concepts Used
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Single-Phase Induction Motor Phase Split Principle Rotating Magnetic Field
ЁЯТб EXAM TIP

Remember: TsтИЭsinтБб╬▒T_s \propto \sin\alphaTsтАЛтИЭsin╬▒. Resistance split-phase gives ╬▒тЙИ30┬░тИТ40┬░\alpha \approx 30┬░- 40┬░╬▒тЙИ30┬░тИТ40┬░, whereas capacitor split-phase increases ╬▒\alpha╬▒ up to 90┬░90┬░90┬░, producing maximum starting torque.

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