Single Phase Motor and Special Machines MCQ Quiz - Objective Question with Answer for Single Phase Motor and Special Machines - Download Free PDF

Concept:

Split-phase motors and shaded-pole motors are both single-phase induction motors, but they differ significantly in terms of starting torque. Split-phase motors use an auxiliary winding to create a phase difference, resulting in higher starting torque.

Calculation

Split-phase motors provide moderate to high starting torque because of the phase shift introduced by the auxiliary winding. Shaded-pole motors, on the other hand, have very low starting torque due to the weak rotating magnetic field generated by the shaded portion of the pole.

Therefore, split-phase motors are better suited for applications requiring higher starting torque, such as fans, pumps, and small tools, whereas shaded-pole motors are used in low-torque applications like small fans and clocks.

Shaded pole induction motor

• Shaded-pole motors are used to drive devices that require low starting torque; hence are ideal for low-power, continuous-duty applications.
• These motors are very suitable for small devices like relays, fans of all kinds, etc., because of their low initial cost and easy starting.
• The power factor of a shaded pole induction motor is generally quite low.  They often have a power factor of around 0.5 to 0.6, which is considered low. The low power factor is due to their design, which includes a small and non-optimized core and winding arrangement, leading to poor efficiency and a lagging power factor.

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.

Calculation of Active Power Absorbed by the Motor

Problem Statement: A single-phase motor draws a current of 5 A from a 120 V, 60 Hz line. The power factor of the motor is 65%. Calculate the active power absorbed by the motor.

Solution:

To calculate the active power absorbed by the motor, we use the formula:

Active Power (P) = Voltage (V) × Current (I) × Power Factor (PF)

Here, the given values are:

• Voltage (V) = 120 V
• Current (I) = 5 A
• Power Factor (PF) = 65% = 0.65 (in decimal form)

Substitute the values into the formula:

P = 120 × 5 × 0.65

Perform the calculation:

P = 600 W

Therefore, the active power absorbed by the motor is 600 W.

Correct Option Analysis:

The correct option is:

Option 1: 600 W

This is the correct answer as it is derived by correctly applying the formula for active power and substituting the given values. The calculation matches the problem statement accurately.

Additional Information

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

Option 2: 390 W

This option is incorrect because it results from an incorrect calculation, likely due to a miscalculation of the product of voltage, current, and power factor. For example, if a lower power factor (e.g., 0.52) or an incorrect current value was used, this incorrect result could be derived.

Option 3: 456 W

This option is also incorrect. It may result from using an incorrect value for the power factor, such as 0.76 instead of 0.65, or possibly an incorrect current value. The correct calculation does not lead to this result.

Option 4: 650 W

This option is incorrect because it represents an overestimation of the active power. This could occur if a higher power factor (e.g., 0.72) was mistakenly used in the calculation, or if the power factor was ignored altogether and only voltage and current were multiplied (P = 120 × 5 = 600 W). However, neglecting the power factor would not yield a value higher than 600 W in this case.

Option 5: Not given

This option is invalid as the correct answer is explicitly provided in the problem statement and matches the calculated value of 600 W.

Conclusion:

Understanding the relationship between voltage, current, and power factor is crucial for accurately calculating the active power absorbed by electrical devices. In this case, the correct calculation yielded an active power of 600 W, which aligns with Option 1. The other options were derived from incorrect assumptions or miscalculations, demonstrating the importance of using precise values and the correct formula.

Explanation:

The Direction of Rotation of a Hysteresis Motor

Definition: A hysteresis motor is a type of synchronous motor that operates on the principle of hysteresis loss in the rotor material. It is primarily used in applications requiring smooth and noiseless operation, such as in clocks, record players, and other precision devices. The unique feature of a hysteresis motor is its ability to achieve synchronous speed without requiring an auxiliary winding or external synchronization device.

Working Principle: The hysteresis motor relies on the magnetic properties of its rotor material. When the stator produces a rotating magnetic field, the rotor material undergoes hysteresis due to its ability to retain magnetism. This hysteresis effect leads to the generation of torque in the rotor, which brings it into synchronism with the rotating magnetic field. The rotor’s material plays a crucial role in determining the performance and efficiency of the motor.

Correct Option Analysis:

The correct option is:

Option 1: The direction of rotation of the hysteresis motor is determined by the resistivity of the rotor material.

This option correctly identifies the factor influencing the direction of rotation. In hysteresis motors, the rotor material’s resistivity directly impacts the hysteresis loss, which in turn governs the motor's behavior. Specifically, the resistivity affects the torque production and synchronization process, ultimately determining the direction in which the rotor aligns with the rotating magnetic field.

In practical terms, the resistivity of the rotor material influences the hysteresis loop, which is a graphical representation of the material's magnetic properties. The shape and area of the hysteresis loop are critical for determining the motor's operational characteristics, including its direction of rotation.

Advantages of Using Resistivity in Rotor Material:

• Precise control over the motor's direction of rotation.
• Enhanced efficiency and performance due to optimized hysteresis loss.
• Smooth and noiseless operation, ideal for sensitive applications.

Important Information

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

Option 2: The direction of rotation is determined by the amount of hysteresis loss.

This option is incorrect because while hysteresis loss is a crucial factor for the operation of the motor, it does not directly determine the direction of rotation. Instead, hysteresis loss affects the torque and efficiency of the motor. The direction of rotation is influenced by the resistivity of the rotor material, as explained in the correct option.

Option 3: The direction of rotation is determined by the permeability of the rotor material.

This option is also incorrect. Permeability of the rotor material is related to its ability to support the formation of magnetic flux, but it does not directly affect the direction of rotation. Resistivity is the key factor that governs the hysteresis loop and, consequently, the direction of rotation.

Option 4: The direction of rotation is determined by the position of the shaded pole with respect to the main pole.

While the position of shaded poles is a significant design parameter in shaded pole motors, it is not relevant to hysteresis motors. Hysteresis motors do not rely on shaded poles for determining direction of rotation; instead, they depend on the rotor material's resistivity and magnetic properties.

Option 5: This option is not listed in the original question, so it cannot be evaluated in this context.

Conclusion:

In summary, the direction of rotation in a hysteresis motor is determined by the resistivity of the rotor material. This factor influences the hysteresis loop characteristics, which are central to the motor's operation. While other options describe aspects of motor design and operation, they do not directly impact the direction of rotation in hysteresis motors. Understanding these principles is essential for designing and optimizing hysteresis motors for various applications.

• The single-phase induction motor is not self-starting. Hence, it requires an auxiliary means or equipment to start the motor.
• Mechanical methods are impractical and, therefore the motor is started temporarily converting it into the two-phase motor.
• Commonly used starting methods for a ceiling fan is a permanent capacitor or single value capacitor motor.
• The permanent capacitor motor also has a cage rotor and the two windings named as main and auxiliary windings.
• The capacitor C is permanently connected in the circuit both at the starting and the running conditions.
• It is also called as a single value capacitor motor as the capacitor is always connected in the circuit.
• A paper capacitor is used in the permanent capacitor motor as an electrolytic capacitor cannot be used for the continuous running operation of the ceiling fan.
• The cost of the paper capacitor is higher, and the size is also large as compared to the electrolytic capacitor of the same ratings.

Unexcited single phase synchronous motor runs at constant speed equal to synchronous speed of revolving flux. They do not need a dc excitation for their rotors.

Capacitor start capacitor run 1-phase Induction motor:

• Capacitor ‘A’ is Running  Capacitor made up of oil type of low capacity. Manufactured for continuous duty cycle.
• Capacitor ‘B’ is Starting Capacitor made up of electrolytic type of high capacity. Manufactured for short duty cycle.
• Rating of starting capacitor is 10 to 15 times the running capacitor.
• Running winding also known as Main winding and starting winding as Auxilary winding.
• Initially, both capacitors are connected in parallel, the motor starts with high starting torque due to the phase difference created by starting winding and running winding.
• The starting torque is proportional to the sine of the angle between the two currents produced by the starting winding as well as running winding. Angle maintained at θ = 90° 

• In running condition After the motor has reached 75% full-load speed, the switch opens and only capacitor A (running capacitor) remains in the starting winding circuit.

Advatnages:

• High starting torque .
• High efficiency and power factor.
• Noise free operation.

Disadvantages:

High cost

Applications:

• Motors are used to start heavy loads where frequent starting is required.
• Pumps, compressors, refrigerator, conveyors and machine tools.

Important Points

Types of Single Phase Induction Motors:

• Split-phase motor
• Capacitor start motor
• Capacitor start capacitor run motor
• Shaded pole motor

Concept:

Step angle of the hybrid stepper motor is given by

\(β = {{(N_s -N_r)× 360°} \over (N_s× N_r)}\)

Where N_s = Number of stator teeth

N_r = Number of rotor teeth

Calculation:

Given that, N_r = 60

N_s = 8 × 6 = 48

∴ stepping angle can be calculated as 

\(β = {{(60 -48)× 360°} \over (60× 48)}\)

β = 1.5°

• Single phase induction motor is used in household refrigerator.

Brushless DC motor (BLDC) motor

• A brushless DC motor is an electronically commuted DC motor that does not have brushes like conventional DC motors.
• The controller provides pulses of current to the motor windings which control the speed and torque of this motor.
• The working principle of a BLDC motor is based on Lorentz force law.
• The Lorentz force law states that whenever a current-carrying conductor is placed in a magnetic field it experiences a force. As a consequence of reaction force, the magnet will experience an equal and opposite force.
• With the brushed motor, rotation is achieved by controlling the magnetic fields generated by the coils on the rotor, while the magnetic field generated by the stationary magnets remains fixed.
• To change the rotation speed, you change the voltage for the coils.
• With a BLDC motor, it is the permanent magnet that rotates ( N and S ); rotation is achieved by changing the direction of the magnetic fields generated by the surrounding stationary coils. To control the rotation, you adjust the magnitude and direction of the current into these coils.

Concept:

A hybrid stepper motor is a combination of variable reluctance and permanent magnet-type motors. The rotor of a hybrid stepper motor is axially magnetized like a permanent magnet stepper motor, and the stator is electromagnetically energized like a variable reluctance stepper motor

The step angle of the stepper motor is defined as the angle traversed by the motor in one step.

Step angle of the hybrid stepper motor is given by
\(\beta =\frac{{N_r -N_s}}{{N_s\times N_r}}\times 360^\circ \)

Where N_s = Number of stator teeth 

N_r = Number of rotor teeth

Calculation:

Given that, N_r = 50

N_s =  8 x 5 = 40

∴ stepping angle can be calculated as 

\(\beta =\frac{{50 -40}}{{50\times 40}}\times 360^\circ \)

β = 1.8°

Universal motor: It is used in high-speed vacuum cleaners, vacuum cleaners, drink and food mixers, domestic sewing machine, mixer-grinder.

D.C. shunt motor: It is a constant speed motor and is used in centrifugal pumps, fans, blowers

3-phase synchronous motor: It is used for constant speed applications where speed is independent of the load over the operating range of the motor

Concept:

The synchronous speed is given by

\({N_s} = \frac{{120f}}{P}\)

Where,

f is the supply frequency in Hz or C/s

P is the number of poles

The induction motor rotates at a speed (Nr) close but less than the synchronous speed.

Slip of an induction motor is given by,

\(s = \frac{{{N_s} - {N_r}}}{{{N_s}}}\)

Where,

Ns is the synchronous speed

and Nr is the rotor speed

Rotor current frequency for forward slip (fr) = sf

Rotor current frequency for backward slip (f_r') = (2 - s) f

The slip is negative when the rotor speed is more than the synchronous speed of the rotor field and is in the same direction.

Calculation:

Given - 

Number of poles (P) = 6

Frequency (f) = 50 Hz

Speed of the induction motor, N_r = 900 rpm

Speed of the rotating magnetic field is, 

\({N_s} = \frac{{120f}}{P} = \frac{{120 \times 50}}{{6}} = 1000\;rpm\)

Slip, \(s = \frac{{1000 - 900}}{{1000}} = 0.1 = 10\%\)

The two rotor current frequencies are

\(\begin{array}{l} sf = 0.1 \times 50 = 5\;Hz\\ \left( {2 - s} \right)f = 1.9 \times 50 = 95\;Hz \end{array}\)

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.