22.7 BACK emf IN DC MOTOR
22.7.1 Back emf in a Simple DC Motor
1. A simple motor has a coil placed inside a magnetic field. An external dc voltage is applied across the coil so that current flows through the coil. Since the current is inside the magnetic field, a torque is produced which acts on the coil, thus rotating the coil.
2. When the coil rotates, it ‘cuts’ the magnetic field lines. Hence electromagnetic induction occurs within the coil. According to Faraday’s law of electromagnetic induction, an induced emf is produced in the coil.
3. This induced emf, which opposes the voltage across the armature in accordance with Lenz’s law, is the back emf. Hence, a back emf is produced when the armature of the motor rotates in the magnetic field.
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| Figure 22.73 The figure shows the production of back emf in a rotating armature, which opposes the applied voltage according to Lenz’s law. |
22.7.2 Armature Current
Refer to the circuit shown in Figure 22.73.
Let E = applied voltage
V = voltage across the armature
Eb = back emf in the coil
Ra = resistance of the armature
R = resistance of external circuit
At any instant, the effective p.d. across the coil is
p.d. = V − Eb
The current I flowing through the armature is given by
I = p.d. / Ra
or,
I = (V − Eb) / Ra
22.7.3 Starting Resistance
When the motor coil is not rotating, electromagnetic induction cannot occur in the motor coil and no back emf is produced. Hence, when a voltage V exists across the armature, the current through the armature becomes
I = (V − Eb) / Ra
= V / Ra
where Ra is the resistance of the armature. The initial current can be very large and may produce a large quantity of heat in the armature. For example, let V = 220 V, R = 0.50 ohm. Then we have
I = 220 / 0.5 = 440 A
In order to prevent the armature current from becoming too large when we start the motor, we can connect a large external resistance R in series to the motor circuit, as shown in Figure 22.74. As the motor picks up speed, the back emf produced in the coil increases, thus greatly reducing the armature current. Then the resistance of R can be reduced to zero.
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| Figure 22.74 The figure shows a large external resistance connected in series to limit the armature current during motor start-up, which is reduced as the motor gains speed and back emf increases. |
EXAMPLE 22.42
The armature coil of a dc motor has a resistance of 0.25 ohm. A p.d. of 220 V is produced across the armature. When the armature current becomes 40 A, determine the back emf in the coil.
Answer
The armature current is given by
I = (V − Eb) / Ra
40 = (220 − Eb) / 0.25
Eb = 210 V
22.7.4 Relationship between Back emf and Mechanical Power of Motor
A voltage V across the armature of dc motor produces a current I through the motor. The motor rotates at a constant speed, producing back emf Eb in the motor coil.
Refer to the motor circuit shown in Figure 22.73. Taking into account the complete circuit, we have
E = IR + V
But,
V = IRa + Eb
Hence,
E = IR + IRa + Eb
= I(R + Ra) + Eb
The electrical power delivered by the electrical supply to the external circuit is given by
IE = I2(R + Ra) + IEb
Hence, we have
electrical power supplied = power lost as heat + power used by motor
This means that part of the electrical energy supplied is converted to mechanical energy (rotational kinetic energy). We have
mechanical power of motor = IEb
EXAMPLE 22.43
Explain what is meant by the back emf of a motor. State some factors which determine its magnitude.
Answer
When the coils of the armature of a motor rotate in the magnetic field found within the motor, an emf is induced in the coils. This emf, which opposes the voltage existing across the armature and provided by an external electrical power supply, is known as the back emf of the motor.
Factors:
(a) the angular velocity of the coils
(b) the magnetic field strength of the magnetic field
(c) the size of each coil
(d) the number of turns of the coils
EXAMPLE 22.44
A toy car has a small electric motor whose armature has a resistance of 0.50 ohm. A battery of 9.0 V is connected across the motor. A current of 2.5 A flows through the motor when the car runs at a constant speed of 0.60 m s−1 on the floor. The car then runs up a slope at a constant speed of 0.20 m s−1. Determine the current flowing through the motor when the car runs up the slope.
Answer
The current I flowing through the armature is given by
I = (V − Eb) / Ra
At speed v1 = 0.60 m s−1, the current is I1 = 2.5 A. Hence, we have
2.5 = (9.0 − Eb1) / 0.50
where Eb1 is the back emf of the motor at speed v1.
Eb1 = 9.0 − (2.5)(0.50) = 7.75 V
At speed v2 = 0.20 m s−1, the current is I2. Hence, we have
I2 = (9.0 − Eb2) / 0.50
where Eb2 is the back emf of the motor at speed v2.
Eb2 = 9.0 − 0.5 I2
Assume that back emf ∝ angular velocity of armature ∝ linear velocity of car
Eb1 = k v1
Eb2 = k v2
Eb1 / Eb2 = v1 / v2
7.75 / (9.0 − 0.5 I2) = 0.60 / 0.20
9.0 − 0.5 I2 = 2.58
I2 = 12.8 A
Applications of Back EMF in DC Motor
⚙️ Speed Control in Motors
Back EMF helps regulate motor speed automatically. As speed increases, back EMF increases, reducing current and stabilizing the motor.
🔌 Current Limitation
Back EMF reduces excessive current in the armature, preventing overheating and protecting the motor from damage.
🚗 Electric Vehicles
In electric vehicles, back EMF plays a role in controlling motor performance and efficiency during acceleration and motion.
🏭 Industrial Machines
DC motors in industries rely on back EMF to maintain stable operation under varying loads.
🔋 Energy Efficiency
Back EMF improves energy efficiency by reducing unnecessary current flow when the motor reaches operating speed.
🌀 Motor Protection System
It acts as a natural protection mechanism by opposing applied voltage, reducing the risk of electrical damage.
⚡ Starting Mechanism
Since back EMF is zero at start, external resistance is used to control high starting current in DC motors.
🔊 Robotics and Automation
Back EMF is used in feedback systems to monitor motor speed in robotics and automated systems.
Conclusion: Back EMF in DC Motor
Back EMF (Electromotive Force) is a key concept in the operation of DC motors. It is an induced voltage that opposes the applied voltage and plays an important role in controlling motor performance and efficiency.
- Back EMF is produced due to electromagnetic induction when the motor rotates.
- It opposes the applied voltage according to Lenz’s Law.
- Back EMF helps regulate current and prevents excessive heating.
- At starting, back EMF is zero, causing a large initial current.
- It improves efficiency and stability of DC motors in real applications.
In conclusion, back EMF is essential for safe and efficient motor operation, making it a fundamental principle in electrical engineering and everyday applications such as electric vehicles, industrial machines, and automation systems.
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