Back EMF MCQ Quiz - Objective Question with Answer for Back EMF - Download Free PDF

Explanation:

Back EMF in a DC Motor

Definition: Back EMF (Electromotive Force), also known as counter EMF, is the voltage that is induced in the armature windings of a DC motor when it rotates. This induced voltage opposes the applied voltage (supply voltage) and is a result of the motor's operation as a generator while it is running. The back EMF is a fundamental characteristic of DC motors and plays a critical role in their operation.

Working Principle:

When a DC motor operates, electrical energy is supplied to the armature windings, creating a magnetic field. This magnetic field interacts with the field produced by the permanent magnets or field windings, resulting in a torque that causes the armature to rotate. As the armature rotates, the conductors within it cut through the magnetic field, inducing an electromotive force (EMF) in accordance with Faraday's Law of Electromagnetic Induction. This induced EMF is known as back EMF because it opposes the current flow that is driving the motor.

The back EMF is given by the formula:

E_b = (P × Φ × Z × N) / (60 × A)

Where:

• E_b = Back EMF (volts)
• P = Number of poles
• Φ = Flux per pole (webers)
• Z = Total number of armature conductors
• N = Speed of the armature (RPM)
• A = Number of parallel paths in the armature winding

Significance of Back EMF:

• Opposition to Current: Back EMF opposes the applied voltage and regulates the current flowing through the armature. This self-regulating mechanism ensures that the motor draws only the necessary current, preventing excessive current flow that could damage the motor.
• Energy Conversion: Back EMF is a direct consequence of energy conversion in the motor. As electrical energy is converted into mechanical energy, the motor also acts as a generator, producing the back EMF.
• Speed Control: The magnitude of the back EMF is proportional to the speed of the armature. As the motor speed increases, the back EMF increases, reducing the net voltage and current in the armature. This relationship helps maintain a stable operating speed under varying load conditions.
• Efficiency: The presence of back EMF minimizes energy losses by limiting the current flow in the armature, improving the efficiency of the motor.

Importance in DC Motors:

Back EMF is an essential feature of DC motors. Without back EMF, the motor would draw an excessive amount of current from the power supply, leading to overheating and potential damage. It provides a natural feedback mechanism that ensures the motor operates safely and efficiently. Additionally, back EMF is used in speed control and monitoring systems to assess the motor's operating conditions.

Correct Option Analysis:

The correct option is:

Option 2: Back EMF

This option correctly identifies the induced EMF in a DC motor that opposes the current flow in the armature conductors as back EMF. The term "back EMF" precisely describes this phenomenon, which is a fundamental characteristic of DC motors and is responsible for regulating current, maintaining efficiency, and ensuring safe operation.

Additional Information

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

Option 1: Field EMF

This option is incorrect. Field EMF refers to the electromotive force associated with the field windings of a motor or generator. It is not the induced EMF in the armature conductors that opposes the current flow. Field EMF is related to the creation of the magnetic field, not the regulation of armature current.

Option 3: Induced Voltage

While it is true that back EMF is an induced voltage, this term is too generic and does not specifically describe the opposing EMF in a DC motor. Induced voltage can refer to any voltage generated by electromagnetic induction, including those in transformers, generators, or other electrical devices. Back EMF is a more precise term for the phenomenon in question.

Option 4: Supply EMF

This option is incorrect. Supply EMF refers to the voltage provided by the power source to the motor. It is the applied voltage that drives the current through the armature windings. Back EMF, on the other hand, is the voltage induced within the motor that opposes the supply EMF.

Conclusion:

Understanding the concept of back EMF is crucial for comprehending the operation of DC motors. Back EMF is the induced voltage in the armature windings that opposes the applied voltage, regulating the current and ensuring efficient operation. It is distinct from other types of EMF, such as field EMF or supply EMF, and plays a vital role in the performance and safety of DC motors. The correct answer, option 2, accurately identifies this phenomenon as back EMF.

Concept

The circuit diagram of DC shunt generator is shown below:

The current across the field resistance is given by:

The load current is given by:

I = 100 A

The armature current is:

I_a = 102.5 A

The correct answer is option "4".

Circuit Diagram of DC motor:

Applying KVL across armature:

Eb = V - IaRa

where, Eb = Back EMF

V = Terminal voltage

Ia = Armature currentt

Ra = Armature resistance

When the motor is at rest, the back EMF is zero.

• It is zero at the standstill condition because the back emf opposes the supply voltage and limits the armature current to a safe value.
• The supply voltage induces the current in the coil which rotates the armature. The electrical work required by the motor for causing the current against the back emf is converted into mechanical energy.

The correct answer is option 1):(210 V )

Concept:

In a DC generator, generated emf is given by

E_g = V_t + I_aR_a

In a DC motor, back emf is given by

E_b = V – I_aR_a

Where,

I_a is the armature current

R_a is armature resistance

Calculation:

Armature resistance (Ra) = 0.8 ohm

Voltage (V) = 230 V

Armature current (I_a) = 25 A

E_b = V – I_aR_a = 230 – 25(0.8) = 230 - 20 = 210 V

The correct answer is option 1):  475 V

Concept:

 In a dc generator, induced emf is Eg = V + IaRa

In a dc motor, the back emf is Eb = V – IaRa

Where,

N is the speed in rpm

V is the terminal voltage

I_a is the armature current

R_a is the armature resistance

I_a = I_L -  I_sh

E_m = V_L -  I_a R_a

Calculation:

Given

I_L = 52 A

V = 500 V

Ra = 0.5 Ω 

= 

= 2

Ia = IL - Ish

= 50 A

E_b = VL - Ia Ra

= 500 - ( 50 × 0.5)

=  475  V

Concept

The induced EMF of the DC machine is given by:

where, E = EMF

ϕ = Flux

ω = Speed

For constant speed, the EMF is directly proportional to the speed.

As the armature speed increases, the back emf E_b also increases and causes the armature current I_a to decrease. 

The motor will stop accelerating when the armature current is just sufficient to produce the reduced torque required by the load.

The correct answer is option 1):  475 V

Concept:

 In a dc generator, induced emf is Eg = V + IaRa

In a dc motor, the back emf is Eb = V – IaRa

Where,

N is the speed in rpm

V is the terminal voltage

I_a is the armature current

R_a is the armature resistance

I_a = I_L -  I_sh

E_m = V_L -  I_a R_a

Calculation:

Given

I_L = 52 A

V = 500 V

Ra = 0.5 Ω 

= 

= 2

Ia = IL - Ish

= 50 A

E_b = VL - Ia Ra

= 500 - ( 50 × 0.5)

=  475  V

The correct answer is option 1):(210 V )

Concept:

In a DC generator, generated emf is given by

E_g = V_t + I_aR_a

In a DC motor, back emf is given by

E_b = V – I_aR_a

Where,

I_a is the armature current

R_a is armature resistance

Calculation:

Armature resistance (Ra) = 0.8 ohm

Voltage (V) = 230 V

Armature current (I_a) = 25 A

E_b = V – I_aR_a = 230 – 25(0.8) = 230 - 20 = 210 V

The correct answer is (option 2) i.e. V > E

Explanation:

The equivalent circuit of the DC motor is given below

Figure: equivalent circuit of DC motor

Apply KVL in the supply loop of the equivalent circuit we will get

V - Ia Ra - E = 0

⇒ V - E = I_a R_a

Here Ia R_a is positive.

So, V > E

Where

E is back emf, V is the supply voltage, Ia is armature current, Ra is armature resistance.

Back emf:

• In dc motor also generator action takes place. 
• Because of this generator action the rotating conductor's cuts the flux and emf induced in the conductors.
• This induced emf is called back emf. It always opposes the supply voltage.

The back emf induced in the dc motor can be given by,

E_b = (ϕZNP) / (60 A)

Where

ϕ = flux/pole

Z = total number of conductors

A = number of parallel paths

N = speed in RPM

P = number of poles

In the back emf expression Z, P, and A are constant once machine design is completed

⇒ E_b ∝ Nϕ 

⇒ E_b ∝ N

∴ The back emf in the dc motor is directly proportional to the speed.

Back emf :

• In the DC motor also generator action (mechanical energy converted into electrical energy) takes place. Due to generator action the rotating conductor's cuts the flux and emf induced, this induced emf is called back emf.
• It always opposes the supply voltage.
• The induced back emf is A.C in the armature winding. But with respect to brushes, the back emf is D.C.
• The induced back emf (E_b) = 

Where 

ϕ is flux/pole, Z is the number of conductors, N is the speed of the motor in rpm, P is the number of poles, and A is the number of parallel paths.

The relation between Back emf (E_b) and armature current (I_a) :

The equivalent circuit of the DC motor is given below

Figure: equivalent circuit of DC motor

Apply KVL in the supply loop of the equivalent circuit we will get

V_t - I_a R_a - E_b = 0

⇒ E_b = V_t - I_a R_a

Where

E_b is back emf, V_t is the supply voltage, I_a is armature current, R_a is armature resistance.

Note:

From the above expression, we can observe that if the armature current is more, the back emf will be less and vice versa.

Significance of Back EMF & Speed:

In the DC motor also generator action (mechanical energy converted into electrical energy) takes place. Due to generator action, the rotating conductor cuts the flux and emf induced, this induced emf is called back EMF.

It always opposes the supply voltage.

The induced back emf is A.C in the armature winding. But with respect to brushes, the back emf is D.C.

In a DC shunt motor, Back EMF is given by

Eb = V – IaRa

Where, Ia is armature current

Ra is armature resistance

Also,

The back emf of a dc motor is directly proportional to speed.

Eb ∝ Nϕ

If the speed of a DC motor increases, there will be increase in back emf also.

Current drawn in the DC motor is given by,

Concept:

Circuit diagram for DC shunt motor is given below.

Back emf (Eb) = V – IaRa

Vt = terminal voltage DC

IL = line current

IF = field current

Calculation:

Given that, voltage (V) = 250 V

Armature resistance (Ra) = 2 Ω

Shunt current is neglected.

Armature current (Ia) = (IL) = 10 A

Back emf (Eb) = V – IaRa = 250 – 10 × 2 = 230 V

Circuit Diagram of DC motor:

Applying KVL across armature:

E_b = V - I_aR_a

where, E_b = Back EMF

V = Terminal voltage

I_a = Armature currentt

R_a = Armature resistance

When the motor is at rest, the back EMF is zero.

It is zero at the standstill condition because the back emf opposes the supply voltage and limits the armature current to a safe value. The supply voltage induces the current in the coil which rotates the armature. The electrical work required by the motor for causing the current against the back emf is converted into mechanical energy.

Relation between Mechanical power (P_m), Supply Voltage (V_t), and Back emf (E_b):

The back emf in the dc motor is expressed as:

E_b = V – I_aR_a .......(1)

E_b = back emf

I_a = armature current

V_t = terminal voltage

R_a = resistance of amature

The Power developed on the motor is expressed by

P_m = E_bI_a = VI_a – I_a²Ra ......(2)

On differentiating of the given equation

For maximum power develop

V = 2 I_aR_a ⇒ I_aR_a = V / 2

From the back emf equation 

E_b = V – I_aR_a = V – V / 2

 .......(3)

The maximum power is developed in the motor when the back emf is equal to half of the supply voltage.

and the maximum power is

(P_m)_max = VI_a – I­_a²R_a = I_a (V – I­_aR_a)

(P_m)_max = E_bI_a

Key Points

Back EMF in DC Motor:

• When the current-carrying conductor placed in a magnetic field, the torque induces on the conductor, the torque rotates the conductor which cuts the flux of the magnetic field.
• According to the Electromagnetic Induction Phenomenon “when the conductor cuts the magnetic field, EMF induces in the conductor”.
• It is seen that the direction(Right hand rule) of the induced emf is opposite to the applied voltage. Thereby the emf is known as the counter emf or back emf.