DC motor is an electrical machine that converts electrical energy into mechanical energy. The working of DC motor is based on the principle, “When a current-carrying conductor is placed in a rotating magnetic field, the conductor experiences a force which tends to the conductor”.

Construction-wise, there is no difference between DC Generator and DC motor. In fact, a DC machine can be interchangeably used as a generator or as a motor. Learn the construction of DC machines.

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## How a DC Motor Work?

Let us consider the following figure to understand the working principle of DC motor. The figure shows a part of multipolar DC motor. It has two field poles: North(N) pole and South(S) pole. The rotor is drawn as a semi-circle, which carries the armature conductor(shown as small circles).

When the motor is connected to the DC supply, the direct current flows through the brushes and commutator to the armature winding. Once the current passes through the commutator, it becomes alternating.

The armature conductors under the North pole carry the current in an inward direction(shown as plus). Similarly, the conductors under the south pole carry current in an outward direction(shown as minus). Hence the group of conductors under the successive filed poles carry current in opposite direction.

Now each conductor under the respective poles experiences a force in a direction given by Fleming’s left hand rule. When a current-carrying conductor is placed perpendicularly in a magnetic field, it experiences a force in a direction that is mutually perpendicular to both the field and the current-carrying conductor.

The arrow shown above each conductor denotes the direction of force experienced by it. These forces collectively produce a rotating torque, which will rotate the motor.

The magnitude of the mechanical force is given by *F = BIl* Newton. In this equation, *B* represents the magnetic flux density, *I* is the current flowing through the armature winding and *l* is the length of the conductor within the magnetic field.

## Back Emf

As soon as the armature conductors start rotating, it cuts the magnetic flux and so dynamically induced emf is induced in the armature conductors. The emf thus produced is said to be back emf or counter emf.

The direction of this induced emf is such that it opposes the armature current, which is given by Lenz’s law. The value of this induced back emf is equal to the emf induced in a dc generator, which is given by

where is the magnetic flux produced,

N is the speed of rotor in revolutions per minute,

Z is the total number of conductors,

P is the total number of poles and

A is the number of parallel paths.

The applied voltage must force the current through the armature conductors against the back emf E_{b}. Thus the mechanical energy produced is the result of armature current overcoming the dynamically induced emf.

### Importance of Back Emf

The equivalent circuit of a DC motor is shown below. The armature circuit consists of back emf E_{b} in series with the armature resistance R_{a} and brush contact drop V_{br}. It is connected across a DC supply of V volts.

From the circuit, it can be observed that the applied voltage should be large enough to overcome the drops in armature resistance, brush contact and the back emf at all times. It is given by,

Where V is the applied voltage, E_{b} is the developed back emf, I_{a} is the armature current, R_{a} is the armature resistance, V_{br} is the brush contact drop.

As the brush contact drop is very small, it can be neglected. Hence, the above equation can be re-written as,

From equation(1), it can be observed that the induced back emf(E_{b}) depends on the armature speed(N). Similarly from equation(2), it is observed that the armature current(Ia) depends on the back emf(Eb) for a constant applied voltage and armature resistance.

Considering both equations, we can say that when the armature speed is high, the back emf will be large and therefore the armature current is small. If the speed is low, then the back emf is less, which results in high value of armature current. Hence, high torque is produced.

Thus the presence of back emf makes the DC motor to act like a governor or a self-regulating machine.

## FAQs

**What is Flemings’ Left hand rule?**

Stretch out the index finger, middle finger and thumb of your left hand in such a way that they are mutually perpendicular to each other. If the index finger represents the direction of the magnetic field(B) and the middle finger represents that of the current(I), then the thumb gives the direction of the mechanical force(F).

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