Single Phase Motor Starting MCQ Quiz - Objective Question with Answer for Single Phase Motor Starting - Download Free PDF

Torque in the 3-phase induction motor

The torque of a 3-phase induction motor is given by:

\(T={3\over ω_s}{V^2\over ({R_2\over s}^2)+X_2^2}{R_2\over s}\)

where, V = Supply voltage

ωs = Synchronous speed in rad/sec

R2 = Rotor resistance

X2 = Rotor reactance

s = Slip

Among the following options, the starting torque does not depend on Field excitation during startup.

Concept

For maximum starting torque in a capacitor-start motor, the currents in the main winding and starting (auxiliary) winding must be 90° out of phase. This happens when the impedance of the starting winding (including the capacitor) is purely resistive.

Calculation

The given problem states that the current has a phase angle of 45°, which means the inductive reactance and resistance are equal in the auxiliary winding.

Since the current lags by 45°:

\( tan45={X_L\over R}\)

\(X_L=R\)

Thus, the resistance (R) of the auxiliary winding is also 6Ω.

To achieve a 90° phase shift, the total reactance of the auxiliary winding must be zero, which means:

\(X_L-X_C=-R\)

6 - X_C = -6

XC = 12 Ω 

Explanation:

Single-Phase Induction Motor

Definition: A single-phase induction motor is an AC motor that operates on single-phase power supply. It has two main parts: the stator and the rotor. The stator carries the alternating current and produces a rotating magnetic field, which induces current in the rotor and causes it to turn, producing mechanical motion.

Working Principle: In a single-phase induction motor, the stator winding is connected to a single-phase AC supply. When the current flows through the stator winding, it creates a pulsating magnetic field. This pulsating field can be thought of as two rotating magnetic fields of equal magnitude but rotating in opposite directions. The interaction of these fields with the rotor induces a current in the rotor, which produces torque and causes the rotor to rotate.

However, at the start, a single-phase induction motor does not produce a rotating magnetic field; it produces a pulsating magnetic field. This pulsating field is not sufficient to start the motor. Therefore, an auxiliary winding (or starting winding) is used to create a phase difference and produce a rotating magnetic field that can start the motor.

Correct Option Analysis:

The correct option is:

Option 1: zero

This option is correct because if the auxiliary winding is open at the start, the motor does not have the necessary phase difference to create a rotating magnetic field. Without a rotating magnetic field, the motor cannot produce any starting torque. Therefore, the resultant torque on the rotor is zero.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: maximum

This option is incorrect because, without the auxiliary winding, the motor cannot produce a rotating magnetic field at the start. Therefore, it cannot produce maximum torque. The motor requires the auxiliary winding to create the phase difference and start the rotation.

Option 3: 0.5 N-m

This option is also incorrect. As explained, without the auxiliary winding, the motor cannot produce any starting torque, so it is not possible for the torque to be 0.5 N-m. The torque would be zero.

Option 4: 2.0 N-m

This option is incorrect as well. Similar to option 3, the motor cannot produce any starting torque without the auxiliary winding. Therefore, the torque cannot be 2.0 N-m; it would be zero.

Conclusion:

Understanding the role of the auxiliary winding in a single-phase induction motor is crucial. The auxiliary winding is essential for creating a phase difference and producing a rotating magnetic field, which is necessary to start the motor. Without the auxiliary winding, the motor cannot produce any starting torque, resulting in zero torque on the rotor. This makes option 1 the correct answer.

In a capacitor-start capacitor-run motor, the start capacitor is connected in series with the auxiliary winding to provide the necessary starting torque.

Explanation:

Capacitor start capacitor run motor:

The capacitor start capacitor run motor has a cage rotor and its stator has two windings known as main and auxiliary windings and these windings are displaced by 90°. Therefore, this motor act as a two-phase motor.

Important Points:

• There are two capacitors in this motor represented by C_S and C_R.
• At the start, the two capacitors are connected in parallel.
• Capacitor C_S is the starting capacitor and is short time rated. It is electrolytic having large value.
• Run capacitor C_R has small value with long-time rated and is made of oil-filled paper.
• This type of motor is quiet and smooth running.
• They have higher efficiency than the motors that run only on the main windings.
• They are used for loads of higher inertia requiring frequent starts where the maximum pull-out torque and efficiency required are higher.

Split Phase Induction Motor:

• The Split Phase Motor is also known as a Resistance Start Motor.
• It has a single cage rotor, and its stator has two windings known as main winding and starting winding.
• Both the windings are displaced 90 degrees in space.
• The main winding has very low resistance and a high inductive reactance whereas the starting winding has high resistance and low inductive reactance. 

• A resistor is connected in series with the auxiliary winding.
• The current in the two windings is not equal as a result the rotating field is not uniform.
• Hence, the starting torque is small, of the order of 1.5 to 2 times of the start, running torque.
• At the starting of the motor both the windings are connected in parallel.

The phasor diagram of the Split Phase Induction Motor is shown below.

• The current in the main winding (IM) lag behind the supply voltage V almost by the 90∘  
• The current in the auxiliary winding IA is approximately in phase with the line voltage.
• Thus, there exists a time difference between the currents of the two windings.
• The time phase difference ϕ is not 90 degrees, but of the order of 30 degrees.
• This phase difference is enough to produce a rotating magnetic field.

Single-phase capacitor run induction motor

• The direction of rotation of a single-phase capacitor run induction motor is reversed by changing the direction of the rotating magnetic field produced by the main and starter winding or auxiliary winding.
• This can be accomplished by reversing the polarity of the starter or auxiliary winding.
• Basically, it is done by interchanging the connections on either end of the starter or auxiliary winding.
• Sometimes this reversal is only done by the auxiliary winding & sometimes reversal is accomplished by winding, switch, and capacitor. While the order of the switch and the capacitor does not affect the reversal, as long as they are in series connection.

Important Points

Advantages of capacitor run induction motor:

• A Centrifugal switch is not required.
• It has high efficiency
• It has a high power factor because of a permanently connected capacitor.
• It has a higher pull-out torque

Limitations:

• Electrolytic capacitors cannot be used for continuous running. Therefore, paper-spaced oil-filled capacitors are used.
• It has relatively low starting torque compared to the capacitor start induction motor.

Two-value Capacitor single-phase Induction Motor:

This motor has a cage rotor, and its stator has two windings namely the main winding and the auxiliary winding. The two windings are displaced 90° in space. The motor uses two capacitors C_S and C_R. In the initial stage, the two capacitors are connected in parallel. 

R_M, X_M = Main winding resistance and reactance.

R_A, X_A = Auxiliary winding resistance and reactance.

I_A = Current through the auxiliary winding 

IM = Current through the main winding

V = 1-ϕ supply voltage

C_S = Starting capacitor

C_R = Running capacitor

ϕ = Angle between main winding current and auxiliary winding current.

During starting of motor CS, CR both working so, ϕ is greater than 90° 

During the running of motor only CR is working so, ϕ equals 90° 

Due to this, it has a high power factor and efficiency under running conditions.

Additional Information

Applications:

1. Two-value capacitor motors are used for loads of higher inertia that require frequent start.
2. These are used in pumping equipment.
3.These are used in refrigeration, air compressors, etc.

Concept:

• A capacitor-start motor is a single-phase induction motor that employs a capacitor in the auxiliary winding circuit to produce a greater phase difference between the current in the main and the auxiliary windings.
• The figure below shows the connection diagram of a capacitor start motor.

• The capacitor start motor has a cage rotor and has two windings on the stator. They are known as the main winding and the auxiliary or the starting winding. The two windings are placed 90 degrees apart.
• A capacitor CS is connected in series with the starting winding. A centrifugal switch SC is also connected in the circuit.
• The phasor diagram of capacitor start motor is shown below:

• IM is the current in the main winding which is lagging the auxiliary current IA by 90 degrees as shown in the phasor diagram above. The auxiliary current IA leads the voltage.
• As the motor approaches its rated speed, the auxiliary winding and the starting capacitor is disconnected automatically by the centrifugal switch provided on the shaft of the motor.

Calculation:

Given that ∅a + ∅m = 90°

\(\begin{array}{l} {\tan ^{ - 1}}\left( {\frac{{{X_c} - {X_a}}}{{{R_a}}}} \right) + {\tan ^ - }\left( {\frac{{{X_m}}}{{{R_m}}}} \right) = 90^\circ \\ {\tan ^{ - 1}}\left( {\frac{{X_c - {3}}}{{7}}} \right) + {\tan ^ - }\left( {\frac{3}{{{3}}}} \right) = 90^\circ \\ \Rightarrow {\tan ^{ - 1}}\left( {\frac{{{X_c}-3}}{{7}}} \right) = 45\\ \Rightarrow \frac{{{X_c}-3}}{{7}} = 1 \end{array}\)

⇒ Xc = 10

\(\Rightarrow \frac{1}{{2{\rm{\pi fC}}}} = 10 \Rightarrow {\rm{C}} =318 {\rm{\;\mu F}}\)

Concept:

In a single-phase resistor split induction motor, the condition to get the maximum starting torque is

θm = 2θa

\( \Rightarrow {\tan ^{ - 1}}\left( {\frac{{{X_m}}}{{{R_m}}}} \right) = 2{\tan ^{ - 1}}\left( {\frac{{{X_a}}}{{{R_a}}}} \right)\)

In a capacitor start induction motor,

The condition to get the maximum starting torque is

θm + 2θa = 90°

\( \Rightarrow {\tan ^{ - 1}}\left( {\frac{{{X_m}}}{{{R_m}}}} \right) + 2{\tan ^{ - 1}}\left( {\frac{{{X_a}}}{{{R_a}}}} \right) = 90^\circ \)

Where θm is the power factor angle of the main winding

θa is the power factor angle of the auxiliary winding

Calculation:

Given that, Rm = √3 Ω, Xm = 1 Ω

Power factor angle of main winding, \({\theta _m} = {\tan ^{ - 1}}\left( {\frac{{{X_m}}}{{{R_m}}}} \right)\)

\( = {\tan ^{ - 1}}\left( {\frac{{1}}{\sqrt 3 }} \right) = 30^\circ \)

The condition to get the maximum starting torque is

θm + 2θa = 90°

⇒ 30° + 2θa = 90°

Capacitor start capacitor run motor:

• It has a cage rotor, and its stator has two windings named as Main and Auxillary windings.
• The two windings are displaced 90° in space.
• There are two capacitors used in this motor, one is used at the time of starting and thus brown as a starting capacitor.
• The other is used for continuous running of the motor and this known as RUN Capacitor.
• This motor is also called two value capacitor motor.

• The two capacitors in this motor are C_S and C_R
• At starting, the two capacitors are connected in parallel.
• The capacitor C_S is starting capacitor is short time rated. It is almost electrolytic.
• Since a large amount of current is required to obtain the starting torque, therefore the value of the capacitor reactance X should be low in the starting winding.
• Since \({X_s} = \frac{1}{{2\pi f{C_S}}}\) therefore for low X_S, C_S should be high i.e. the value of the starting capacitor should be large.
• Now, the rated current is smaller than the starting current at the normal operating condition of the motor. Hence the value of capacitive reactance should be large.
• Since \({X_r} = = \frac{1}{{2\pi f{C_R}}}\), thus the value of running capacitor (C_R) should be small.
• The run capacitor is long time rated and is made of oil-filled paper.

• This type of motor is quiet and smooth running.
• They have higher efficiency than the motors that run the main winding only
• They are used for leads for higher inertia requiring frequent starts where the maximum pull-out torque and efficiently required are higher.
• These two value capacitor motors are used in pumping equipment, refrigeration, air compressor, etc.

Note:

• The main aim of using a capacitor is to split the single phase supply into 2 phases, having time displacement of 90 degrees.
• It gives an RMF which produces a starting torque & makes it a self-starting motor.
• When the capacitor is replaced by a resistance motor will continue to run in the same direction.

Capacitor Start Capacitor Run Motor:

• Capacitor Start Capacitor Run Motor has a cage rotor, and its stator has two windings known as Main and Auxiliary Windings.
• The two windings are displaced 90° in space.
• Two capacitors are used in these types of motors.
• One is used at the time of the starting and is known as the starting capacitor.
• The other one is used for continuous running of the motor and is known as the run capacitor.
• So this motor is named as Capacitor Start Capacitor Run Motor or also known as Two Value Capacitor Motor.
•  It has the ability to start heavy loads.
   

• There are two capacitors in this motor represented by C_S and C_R.
• In the starting, the two capacitors are connected in parallel.
• Capacitor C_S is the starting capacitor and is short time rated. It is electrolytic in nature having a large (high) value.
• Run capacitor C_R has a small (low) value with long-time rated and is made of oil-filled paper.
• This type of motor is quiet and smooth running.
• They have higher efficiency than the motors that run only on the main windings.
• They are used for loads of higher inertia requiring frequent starts where the maximum pull-out torque and efficiency required are higher.
• They are used in pumping equipment, refrigeration, air compressors, etc.
   

Conclusion:

A two-value capacitor-run motor starts with a High capacitor and runs with a Low capacitor.

The correct answer is option 1):

Concept:

Permanent-split Capacitor motor( single value capacitor motor):

• These motors have a cage rotor, and its rotor consists of two windings namely, the main winding and the auxiliary winding.
• The single-phase induction motor has only one capacitor C which is connected in series with the starting winding.
• The capacitor C is permanently connected in series with the starting winding.
• The capacitor C is permanently connected to the circuit at starting and running conditions.

A single-value capacitor motor has the following advantages:

• In this type of motor, no centrifugal switch is required.
• This motor has higher efficiency.
• It has a higher power-factor because of a permanently-connected capacitor.
• It has higher pull-out torque.

Limitations of permanent-split capacitor motor:

• Electrolytic capacitors cannot be used for continuous running. Therefore, paper-spaced oil-filled type capacitors are to be used.
• A single-value capacitor has a low starting torque usually less than full-load torque.
• Paper capacitors of the same rating are larger in size and more costly. The paper capacitor is not used hence option 1 is wrong.
• Paper capacitors require a larger physical volume to achieve the same capacitance rating due to the lower dielectric constant of paper. This means that for the same electrical performance, paper capacitors tend to be bulkier than their modern counterparts.
• The manufacturing process for paper capacitors involves more complex or older technologies, often requiring more materials and insulation to ensure the required performance. Additionally, their inefficiency in terms of size and performance makes them less economical in comparison to newer, more advanced capacitors. This results in higher costs.
  
  Additional Information 

Paper capacitors are not suitable for use in single-value capacitor motors for the following reasons:

1. Lower Dielectric Strength: Paper capacitors have a lower dielectric strength compared to modern capacitors (like electrolytic or polypropylene capacitors), making them less capable of handling the high voltage and stress that occur during motor operation.
2. High Losses: Paper capacitors have relatively high dielectric losses, which lead to energy dissipation as heat. This inefficiency would reduce the overall performance and efficiency of the motor.
3. Moisture Sensitivity: Paper is hygroscopic, meaning it can absorb moisture from the environment. Moisture absorption significantly reduces the insulation properties of paper capacitors, which can lead to failure or short circuits in the motor over time.
4. Limited Durability: Compared to modern capacitors (such as plastic-film or electrolytic capacitors), paper capacitors have a shorter lifespan and are more prone to degradation, especially in high-temperature and high-stress environments like motor applications.
5. Size and Bulkiness: Paper capacitors are typically larger and bulkier than modern alternatives for the same capacitance value. This makes them less practical for use in compact motor designs.

Conclusion:
Paper capacitors are outdated and inefficient for use in single-value capacitor motors due to their lower dielectric strength, higher losses, moisture sensitivity, and shorter lifespan. Modern motors prefer more reliable and efficient capacitors like polypropylene or electrolytic capacitors.

Split Phase Induction Motor:

• The Split Phase Motor is also known as a Resistance Start Motor.
• It has a single cage rotor, and its stator has two windings known as main winding and starting winding.
• Both the windings are displaced 90 degrees in space.
• The main winding has very low resistance and a high inductive reactance whereas the starting winding has high resistance and low inductive reactance. 

• A resistor is connected in series with the auxiliary winding.
• The current in the two windings is not equal as a result the rotating field is not uniform.
• Hence, the starting torque is small, of the order of 1.5 to 2 times of the start, running torque.
• At the starting of the motor both the windings are connected in parallel.

The phasor diagram of the Split Phase Induction Motor is shown below.

• The current in the main winding (IM) lag behind the supply voltage V almost by the 90∘  
• The current in the auxiliary winding IA is approximately in phase with the line voltage.
• Thus, there exists a time difference between the currents of the two windings.
• The time phase difference ϕ is not 90 degrees, but of the order of 30 degrees.
• This phase difference is enough to produce a rotating magnetic field.

The correct answer is option 4):(single value capacitor run motor)

Concept:

Induction heating

• This heating process makes use of the currents induced by the electromagnetic action in the charge to be heated.
• It is based on the principle of transformer working. The primary winding which is supplied from an AC source is magnetically coupled to the charge which acts as a short-circuited secondary of a single turn.
• When an AC voltage is applied to the primary, it induces a voltage in the secondary i.e. charge.
• The secondary current heats up the charge in the same way as any electric current does while passing through a resistance.
• If V is the voltage induced in the charge and R is the charge resistance, then heat produced = V2/R.
• The value of current induced in the charge depends on the magnitude of the primary current, the turn ratio of the transformer, and the coefficient of magnetic coupling.

Induction furnace:

• An induction furnace is an electrical furnace in which the heat is applied by induction heating of meta
• The capacity of the induction furnace used from kilogram to one hundred tonnes, and are used to melt iron and steel, copper, aluminium, and precious metals.
• For applications such as induction furnace control single value capacitor run motor is used.