Electrical Machines MCQ Quiz - Objective Question with Answer for Electrical Machines - Download Free PDF

Explanation:

Step 1: Understanding the parameters

• Generated Current (I_G): The total current generated by the DC shunt generator is given as 450A.
• Terminal Voltage (V_T): The terminal voltage of the generator is given as 230V.
• Shunt Field Resistance (R_sh): The resistance of the shunt field is 50 ohms.
• Armature Resistance (R_a): The resistance of the armature is 0.025 ohms.

Step 2: Calculating the shunt field current (I_sh)

The shunt field current can be calculated using Ohm's law:

I_sh = V_T / R_sh

Substituting the known values:

I_sh = 230 / 50 = 4.6 A

Step 3: Calculating the armature current (I_a)

The armature current can be determined as the difference between the total generated current (I_G) and the shunt field current (I_sh):

I_a = I_G - I_sh

Substituting the known values:

I_a = 450 - 4.6 = 445.4 A

Step 4: Calculating the armature voltage drop (V_a)

The armature voltage drop is given by Ohm's law:

V_a = I_a × R_a

Substituting the known values:

V_a = 445.4 × 0.025 = 11.36 V

Conclusion:

The armature voltage drop is 11.36V, making Option 1 the correct answer.

Explanation:

DC Series Motor Torque Calculation:

Definition: The torque (T) produced by a DC series motor is directly proportional to the square of the armature current (I_a) under normal operating conditions, where magnetic saturation is neglected. Mathematically, this relationship can be expressed as:

T ∝ I_a²

This means that any change in the armature current will result in a corresponding change in the torque, following a quadratic relationship.

Given Data:

• Initial current, I_a1 = 10 A
• Final current, I_a2 = 12 A

Objective: To calculate the percentage increase in torque when the current increases from 10 A to 12 A.

Step-by-Step Solution:

1. Expression for torque: Since torque is proportional to the square of the armature current, we can write:

T₁ ∝ I_a1² and T₂ ∝ I_a2²

2. Ratio of torques: To find the percentage increase in torque, calculate the ratio of the final torque (T₂) to the initial torque (T₁):

T₂/T₁ = (I_a2/I_a1)²

Substituting the given values of I_a1 and I_a2:

T₂/T₁ = (12/10)²

T₂/T₁ = (1.2)² = 1.44

3. Percentage increase in torque: The percentage increase in torque is given by:

Percentage Increase = [(T₂ - T₁)/T₁] × 100

Substituting T₂/T₁ = 1.44:

Percentage Increase = [(1.44 - 1) × 100] = 0.44 × 100 = 44%

Thus, the percentage increase in torque is 44%.

Hence the current Option 1 is (0.44 or 44%)

Concept

The synchronous speed of an induction motor is given by:

where, N_s = Synchronous speed

f = Frequency

P = No. of poles

Calculation

Given, P = 6

f = 60 Hz

Ns = 1200 rpm

Function of the commutator in the DC machine:

• A commutator consists of a set of copper segments, fixed around the part of the circumference of the rotating machine, or the rotor, and a set of spring-loaded brushes fixed to the stationary frame of the machine.
• The main function of the commutator in the DC machine is to collect the current from the armature conductor as well as supply the current to the load using brushes. And also provides uni-directional torque for the DC motor. 
• The commutator can be built with a huge number of segments in the edge form of hard-drawn copper.
• The segments in the commutator are protected by the thin mica layer.

Rotor emf injection method:

For below-rated speeds: In this method, injected emf has the same frequency of rotor slip frequency and that emf is 180° out of phase with rotor emf.

E_2R is resultant emf in the rotor

E_2R = E₂ – E₁

R₂ is rotor resistance

T is the torque

s is the slip

Here, the value of rotor emf becomes less. To maintain constant torque, the value of slip will increase. Therefore, the speed will be decreased.

At this condition, effective rotor resistance increases.

For above-rated speeds: In this method, injected emf has the same frequency of rotor slip frequency and that emf is in phase with rotor emf.

E_2R is resultant emf in the rotor

E_2R = E₂ + E₁

R₂ is rotor resistance

T is the torque

s is the slip

Here, the value of rotor emf becomes more. To maintain constant torque, the value of slip will decrease. Therefore, the speed will be increased.

At this condition, effective rotor resistance decreases.

• 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.

• When two generators are operating in parallel, the load may be shifted from one shunt generator to another merely by adjusting the field excitation
• If generator 1 is to be shut down, the whole load can be shifted onto generator 2 provided it has the capacity to supply that load
• In that case, the field current of generator 1 gradually reduces to zero

 

Important Points:

For stable parallel operation, the most suitable type of DC generator is a shunt generator as it has slightly drooping characteristics. If there is any tendency for a generator to supply more or less than its proper share of load it changes system voltage which certainly opposes this tendency. This restores the original division of load. Thus the shunt generators automatically remain in parallel, once they are paralleled.

The characteristics of dc shunt generator are shown below

Fleming right-hand thumb rule:

When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. 

Fleming's right-hand rule (for generators) shows the direction of induced current when a conductor attached to a circuit moves in a magnetic field.

• The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.
• The first finger is pointed in the direction of the magnetic field. (north to south)
• Then the second finger represents the direction of the induced or generated current within the conductor (from the terminal with lower electric potential to the terminal with higher electric potential, as in a voltage source)

Conclusion:

The direction of induced emf is known by Flemings right-hand thumb rule

Induction generator always works with leading power factor since it will take large amount of reactive power to produce sufficient amount of working flux so that armature reaction is always magnetizing hence it will work always with leading pf.

Important Point

• induction generator is basically an induction motor, which runs above the synchronous speed
• when it acts as a generator it will supply the active power back to source, but for this supply of active power it needs reactive power as input to keep its winding excited
• in case if the induction motor is connected to the grid, it will draw the required reactive power for the excitation of windings, but if it is standalone system (ie. not connected to grid) then a capacitor bank will be always connected, and this will provide leading reactive power to keep the winding excited for the process of mechanical to electrical energy conversion
• since the reactive power is supplied by the capacitor, the induction generator is operating in leading power factor

In a DC motor, T ∝ ϕI_a

In series motor, ϕ ∝ I_a

⇒ T ∝ (I_a)²

In shunt motor, ϕ is constant

⇒ T ∝ I_a

The characteristic of DC series and shunt motor are shown below.

Characteristics of DC series motor:

Characteristics of DC shunt motor:

Based on the connection of armature and field windings DC generators can be classified as:

Therefore, the machine shown in the question represents a DC long shunt compound generator.

The correct answer is option "3'.

Concept :- For differential compound generator it is positive (Poorest positive regulation among all)

• The voltage regulation of a generator is defined as the change in the voltage drop from no load to full load to full load voltage.
• Voltage regulation = (no-load voltage - full load voltage)/full load voltage
• In the case of a series generator, the field is connected in series with the armature. Any increase in load current causes an increase in the field and hence the terminal voltage rises.
• Hence it has negative voltage regulation and it has the poorest voltage regulation.

During on-load conditions, the differentially compounded DC generator has the poorest voltage regulation as shown.

During the no-load condition, the DC series generator has the poorest voltage regulation.

Key Points

•  Voltage regulation of shunt generator is positive
• For series generator, it  is negative (Poorest negative voltage regulation among all)
• For over compound generator it is negative
• For under compound it is positive
• For, flat compound generator it is zero (lowest Voltage regulation among all)
• For differential compound generator it is positive (Poorest positive regulation among all)

Regenerative braking: In this type braking back emf Eb is greater than the supply voltage V, which reverses the direction of the motor armature current. The motor begins to operate as an electric generator.

Overhauling motor: A motoring motor is converting electrical energy into mechanical energy. An overhauling motor is being driven by the load and is converting mechanical energy into electricity, acting as a generator.

In case of regenerative braking, dc shunt motor acts a generator and hence regenerative braking is employed when the load has an overhauling characteristic.

Concept:

Pitch factor for nth harmonic is given by,

Where α is short pitch angle in degrees

Calculation:

Given-

Total slots = 36,

Number of poles = 4

Coil span = 1 to 8 = 8 - 1 = 7 slots

Now, Slots per pole = 36 / 4 = 9

Number of empty slots = 9 – 7 = 2 slots

Hence pitch factor can be calculated as

K_c = cos 20°