DC Motor Efficiency MCQ Quiz - Objective Question with Answer for DC Motor Efficiency - Download Free PDF

Explanation:

Direct Testing of DC Machines

Definition: Direct testing of a DC machine involves operating the machine under actual working conditions and measuring its performance directly. This method provides accurate results as the machine is tested in real-time under actual load conditions. Among the various testing methods available for DC machines, the Brake Test is one of the most common direct testing methods.

Correct Option Analysis:

The correct option is:

Option 4: Brake Test

The Brake Test is a direct testing method where the DC machine is tested under load conditions, and its performance is evaluated. In this method, the machine is loaded mechanically using a brake drum, and the torque produced by the machine is measured. The output power is calculated based on the torque and speed. The input power is measured using electrical instruments to evaluate the efficiency of the machine.

Working Principle of Brake Test:

• A belt or rope is wound around the brake drum, which is mounted on the shaft of the DC machine.
• The ends of the belt or rope are connected to a spring balance and a fixed weight. The tension in the rope creates a braking torque on the drum.
• The torque produced by the machine is measured by the difference in readings of the spring balance on either side of the drum.
• The rotational speed of the shaft is measured using a tachometer.
• Electrical instruments are used to measure the input power supplied to the machine.
• The output power is calculated using the formula:

Output Power, P_out = 2 × π × N × T

• Where:
• N = Rotational speed of the shaft in revolutions per second (rps)
• T = Torque produced by the machine (measured using the spring balance)
• The efficiency of the DC machine can be calculated using the formula:

Efficiency, η = (P_out / P_in) × 100%

Advantages of Brake Test:

• Provides accurate results as the machine is tested under actual working conditions.
• Simple and straightforward method for performance evaluation.

Disadvantages of Brake Test:

• Cannot be used for large machines due to the difficulty in dissipating the heat generated during testing.
• Requires a mechanical setup, which may involve additional costs and effort.

Applications:

• Commonly used for small and medium-sized DC machines to evaluate their performance.
• Widely used in laboratories for educational and research purposes.

Additional Information

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

Option 1: Swinburne's Test

Swinburne's Test is an indirect testing method used for DC machines. It involves measuring the no-load losses of the machine and estimating its performance under load conditions. This method is not a direct test as the machine is not tested under actual working conditions. It is suitable for machines where loading is difficult or impractical, such as large DC machines.

Option 2: Field Test

The Field Test is a specific method used for testing two identical DC machines connected back-to-back, where one machine acts as a motor and the other as a generator. This method is not a direct testing method, as it involves testing two machines simultaneously under controlled conditions.

Option 3: Hopkinson’s Test

Hopkinson’s Test, also known as the Regenerative Test, is another indirect testing method. It involves connecting two identical DC machines back-to-back, with one operating as a motor and the other as a generator. The power circulating between the machines reduces the external power requirement. This method is suitable for large machines but is not considered a direct testing method.

Conclusion:

The Brake Test is the correct answer as it is a direct testing method where the DC machine is tested under actual load conditions. While other methods like Swinburne's Test, Field Test, and Hopkinson’s Test are valuable for specific applications, they are not direct testing methods. The Brake Test provides accurate results and is widely used for evaluating the performance of small and medium-sized DC machines.

Concept

The efficiency of the motor is given by:

% η \(={P_{out}\over P_{in}}× 100\)

Calculation

Given, P_out = 10 × 735.5 = 7355 W

P_in = 500 × 18 = 9000 W

% η \(={P_{out}\over P_{in}}× 100\)

% η \(={7355\over 9000}× 100\)

% η = 81.7%

Concept

The circuit diagram of the DC shunt motor is:

The back emf (E_b) is given by:

\(E_b={V_t-I_aR_a}\)

where, V_t = Terminal voltage

I_a = Armature current

R_a = Armature Resistance

Calculation

Given, P_out = 23 HP = 23 × 746 = 17158 W

It is given that the input to the motor is 20.2 kW. Hence, P_in = 20.2 kW = 20200 W.

R_f = 50 Ω and R_a = 0.06 Ω

\(I_f={V\over R_f}={200\over 50}=4A\)

\(P_{in}=V_t\times I_L\)

\(I_L={20200\over 200}=101A\)

\(I_a=I_L-I_f\)

\(I_a=101-4=97A\)

The field copper loss is given by:

\(P_{fc}=I_f^2\times R_f=4^2\times 50=800W\)

The armature copper loss is given by:

\(P_{ac}=I_a^2\times R_a=97^2\times 0.06=941.94W\)

Total losses are given by:

\(P_{losses}=P_{input}-P_{output}\)

\(P_{losses}=20200-17158\)

\(P_{losses}=3042\space W\)

The correct answer is option 3):(1 - True, 2 - True)

Concept:

Swinburne's test:

• It is an indirect method of testing a DC shunt machine.
• We can run the machine as a motor or as a generator.
• In this method of testing, no-load or constant losses are measured separately.
• eventually, we can determine the efficiency.
• This test is very convenient and economical as it requires very little power from the supply to perform it.
• Since constant losses are known, the efficiency of Swinburne's test can be pre-determined at any load.
• This method is applicable to constant flux motors. Swinburne's is not suitable for DC series motor as it cannot run on no load

The correct answer is option 3):(1 - True, 2 - True)

Concept:

Swinburne's test:

• It is an indirect method of testing a DC shunt machine.
• We can run the machine as a motor or as a generator.
• In this method of testing, no-load or constant losses are measured separately.
• eventually, we can determine the efficiency.
• This test is very convenient and economical as it requires very little power from the supply to perform it.
• Since constant losses are known, the efficiency of Swinburne's test can be pre-determined at any load.
• This method is applicable to constant flux motors. Swinburne's is not suitable for DC series motor as it cannot run on no load

Concept:

Consider a separately excited DC motor as,

Eb is back EMF developed in the motor at speed N rpm

V = Eb + Ia Ra .....(1)

V is the supply voltage

Ra is armature resistance

Ia is armature current

Vf is field supply

Rf is field winding resistance

If is field winding current

Let T is the torque developed by the armature of a motor running at N rpm.

Power developed in the armature of motor can be written as,

P = V Ia = Eb Ia+ I2a Ra

Thus the gross mechanical power output provided by the motor is

Pm = Eb Ia = V Ia -  I2a Ra(losses)

The efficiency of the motor is = Output Power(Pm) / Input power(P)

Calculation

P_m = 10 HP

= 10 × 746 = 7460 W

V = 400

η = 0.7355

η = 7460 / (400 × I) 

⇒ 0.7355 = 7460 / (400 × I) 

⇒ I = 25.35 ≈ 25 A

Additional Information

Maximum power condition:

If the value of \(\frac{dP_m}{dI_a}=0,\) the motor will deliver maximum power

\(\frac{dP_m}{dI_a}= V - 2I_aR_a = 0\)

Ia Ra = V / 2 ....(2)

From equation (1) & (2)

Eb = V / 2

The efficiency of the motor is = Output Power(Pm) / Input power(P)

\(η= \frac{E_b I_a }{VI_a }× 100=\frac{E_b }{V}× 100=50\)%

Hopkinson’s test:

• It is a full load test, used to test the efficiency of a DC machine.
• Temperature rise and commutation can be observed and maintained in the limit because this test is done under full load condition.
• It requires two identical machines that are coupled to each other. One of these two machines is operated as a generator to supply the mechanical power to the motor and the other is operated as a motor to drive the generator.
• It is also called a regenerative test or back to back test or heat run test.

Swinburne’s test:

• It is an indirect method of testing a DC machine. We can run the machine as a motor or as a generator.
• In this method of testing, no-load or constant losses are measured separately and eventually, we can determine the efficiency.
• This test is very convenient and economical as it is required very less power from supply to perform the test.
• Since constant losses are known, the efficiency of Swinburne's test can be pre-determined at any load.

Retardation test:

This test is used to determine the moment of inertia and the frictional losses of the machine but is not specifically designed for measuring constant losses of DC motors.

Voltage drop test:

It is often carried out for checking the condition of the armature winding by using open and short circuit conditions of armature coil.

The correct answer is option 2.

The DC motor is 30% more efficient than AC motors due to the magnetic field generated from the permanent magnets rather than copper windings.

Difference between DC and AC machine

The correct answer is option 3):(1 - True, 2 - True)

Concept:

Swinburne's test:

• It is an indirect method of testing a DC shunt machine.
• We can run the machine as a motor or as a generator.
• In this method of testing, no-load or constant losses are measured separately.
• eventually, we can determine the efficiency.
• This test is very convenient and economical as it requires very little power from the supply to perform it.
• Since constant losses are known, the efficiency of Swinburne's test can be pre-determined at any load.
• This method is applicable to constant flux motors. Swinburne's is not suitable for DC series motor as it cannot run on no load

Power flow in DC Motor:

Electrical input is given by:

I = V_T × I_a

where I = electrical input

V_T = supply voltage

I_a = armature current

Developed power is given by:

P_d = E_b × I_a

where P_d = developed power

E_b = back emf

Back EMF in DC series motor is given by:

Eb = V_T - I_a (R_a + R_se)

Calculation:

Given, V_T = 220 V

R_a = 0.2 Ω 

R_se = 0.3 Ω 

Eb = 220 - 30(0.2 + 0.3)

Eb = 205 V

Pd = 205 × 30

Pd = 6150 W = 6.15 kW

P_o = P_d - iron and friction loss

Po = 6.15 - 0.3

Po = 5.85 kW

Power Equation of DC Motor:

For a DC Motor,

V = E_b + IR     ---(1)

Where V is the terminal voltage

E_b is back-EMF

I is current through armature in Shunt motor and current through both armature and field in series motor

R is armature resistance in Shunt motor and both armature and field resistance in series motor

Since back EMF E_b acts in opposition to the applied voltage V, the net voltage across the armature circuit is (V - E_b).

If Equation (1) above is multiplied by 'l' throughout, we get,

VI = IE_b + I²R

Where,

VI is electric power supplied to the armature (armature input)

IE_b (= P_m) power developed by armature (armature output) 

I²R is copper loss

P_m = VI - I2R

Since V and R are fixed, the power developed by the motor depends upon armature current.

For maximum power, \(\frac{dP_m}{dI}=0\)

or, \(\frac{dP_m}{dI}=V-2IR=0\)

or, V = 2IR

or, IR = V/2     ---(2)

From equation (1) & (2),

V = E_b + V/2

or, \(E_b =\frac{V}{2}\)

Hence, The gross mechanical power developed by the motor is maximum when the back EMF is equal to 50% (1/2) of the supply voltage.

Explanation:

Direct Testing of DC Machines

Definition: Direct testing of a DC machine involves operating the machine under actual working conditions and measuring its performance directly. This method provides accurate results as the machine is tested in real-time under actual load conditions. Among the various testing methods available for DC machines, the Brake Test is one of the most common direct testing methods.

Correct Option Analysis:

The correct option is:

Option 4: Brake Test

The Brake Test is a direct testing method where the DC machine is tested under load conditions, and its performance is evaluated. In this method, the machine is loaded mechanically using a brake drum, and the torque produced by the machine is measured. The output power is calculated based on the torque and speed. The input power is measured using electrical instruments to evaluate the efficiency of the machine.

Working Principle of Brake Test:

• A belt or rope is wound around the brake drum, which is mounted on the shaft of the DC machine.
• The ends of the belt or rope are connected to a spring balance and a fixed weight. The tension in the rope creates a braking torque on the drum.
• The torque produced by the machine is measured by the difference in readings of the spring balance on either side of the drum.
• The rotational speed of the shaft is measured using a tachometer.
• Electrical instruments are used to measure the input power supplied to the machine.
• The output power is calculated using the formula:

Output Power, P_out = 2 × π × N × T

• Where:
• N = Rotational speed of the shaft in revolutions per second (rps)
• T = Torque produced by the machine (measured using the spring balance)
• The efficiency of the DC machine can be calculated using the formula:

Efficiency, η = (P_out / P_in) × 100%

Advantages of Brake Test:

• Provides accurate results as the machine is tested under actual working conditions.
• Simple and straightforward method for performance evaluation.

Disadvantages of Brake Test:

• Cannot be used for large machines due to the difficulty in dissipating the heat generated during testing.
• Requires a mechanical setup, which may involve additional costs and effort.

Applications:

• Commonly used for small and medium-sized DC machines to evaluate their performance.
• Widely used in laboratories for educational and research purposes.

Additional Information

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

Option 1: Swinburne's Test

Swinburne's Test is an indirect testing method used for DC machines. It involves measuring the no-load losses of the machine and estimating its performance under load conditions. This method is not a direct test as the machine is not tested under actual working conditions. It is suitable for machines where loading is difficult or impractical, such as large DC machines.

Option 2: Field Test

The Field Test is a specific method used for testing two identical DC machines connected back-to-back, where one machine acts as a motor and the other as a generator. This method is not a direct testing method, as it involves testing two machines simultaneously under controlled conditions.

Option 3: Hopkinson’s Test

Hopkinson’s Test, also known as the Regenerative Test, is another indirect testing method. It involves connecting two identical DC machines back-to-back, with one operating as a motor and the other as a generator. The power circulating between the machines reduces the external power requirement. This method is suitable for large machines but is not considered a direct testing method.

Conclusion:

The Brake Test is the correct answer as it is a direct testing method where the DC machine is tested under actual load conditions. While other methods like Swinburne's Test, Field Test, and Hopkinson’s Test are valuable for specific applications, they are not direct testing methods. The Brake Test provides accurate results and is widely used for evaluating the performance of small and medium-sized DC machines.

Concept

The efficiency of the motor is given by:

% η \(={P_{out}\over P_{in}}× 100\)

Calculation

Given, P_out = 10 × 735.5 = 7355 W

P_in = 500 × 18 = 9000 W

% η \(={P_{out}\over P_{in}}× 100\)

% η \(={7355\over 9000}× 100\)

% η = 81.7%

Concept:

Consider a separately excited DC motor as,

Eb is back EMF developed in the motor at speed N rpm

V = Eb + Ia Ra .....(1)

V is the supply voltage

Ra is armature resistance

Ia is armature current

Vf is field supply

Rf is field winding resistance

If is field winding current

Let T is the torque developed by the armature of a motor running at N rpm.

Power developed in the armature of motor can be written as,

P = V Ia = Eb Ia+ I2a Ra

Thus the gross mechanical power output provided by the motor is

Pm = Eb Ia = V Ia -  I2a Ra(losses)

The efficiency of the motor is = Output Power(Pm) / Input power(P)

Calculation

P_m = 10 HP

= 10 × 746 = 7460 W

V = 400

η = 0.7355

η = 7460 / (400 × I) 

⇒ 0.7355 = 7460 / (400 × I) 

⇒ I = 25.35 ≈ 25 A

Additional Information

Maximum power condition:

If the value of \(\frac{dP_m}{dI_a}=0,\) the motor will deliver maximum power

\(\frac{dP_m}{dI_a}= V - 2I_aR_a = 0\)

Ia Ra = V / 2 ....(2)

From equation (1) & (2)

Eb = V / 2

The efficiency of the motor is = Output Power(Pm) / Input power(P)

\(η= \frac{E_b I_a }{VI_a }× 100=\frac{E_b }{V}× 100=50\)%

Hopkinson’s test:

• It is a full load test, used to test the efficiency of a DC machine.
• Temperature rise and commutation can be observed and maintained in the limit because this test is done under full load condition.
• It requires two identical machines that are coupled to each other. One of these two machines is operated as a generator to supply the mechanical power to the motor and the other is operated as a motor to drive the generator.
• It is also called a regenerative test or back to back test or heat run test.

Swinburne’s test:

• It is an indirect method of testing a DC machine. We can run the machine as a motor or as a generator.
• In this method of testing, no-load or constant losses are measured separately and eventually, we can determine the efficiency.
• This test is very convenient and economical as it is required very less power from supply to perform the test.
• Since constant losses are known, the efficiency of Swinburne's test can be pre-determined at any load.

Retardation test:

This test is used to determine the moment of inertia and the frictional losses of the machine but is not specifically designed for measuring constant losses of DC motors.

Voltage drop test:

It is often carried out for checking the condition of the armature winding by using open and short circuit conditions of armature coil.