Operation of a DC Motor – Learn

A DC motor is a device that transforms electrical potential energy into rotational kinetic energy through the application of a direct current (DC). Electric motors produce rotational motion by passing a current through a coil in a magnetic field.

Structure of a DC Motor

DC motors consist of several components:

  • A magnetic field (stator). This may be a permanent magnet or an electromagnet.
  • A coil (rotor)
  • Split ring commutator
  • Carbon brushes
  • Source of an emf

The magnets provide an external magnetic field in which the coil rotates. The magnets are known as the stator because they are fixed to the casing of the motor and are stationary, . The stator sometimes consists of a pair of electromagnets. The coil is connected to a source of an emf through the split ring commutator and carbon brushes. The coil is wound onto a frame known as an armature and the coil will consist of many turns. The armature and coil together are known as the rotor. The armature axle extends from the motor casing and connects to the split ring commutator. The split-ring commutator and the brushes form a mechanism which enables the current to change direction through the coil every half turn so that the coil continues rotating in the same direction. The source of the emf (electromotive force) may be a battery or mains electricity, in which case the supply AC current would need to be converted to DC.

Operation of a DC Motor

Power, or an emf may be supplied from a battery or external source and is directed to the carbon brushes. Whilst electron current flows from the negative to the positive terminal, keep in mind that for the purposes of determining the direction of a force on a conductor due to the motor effect, conventional current is used – conventional current assumes the current flows from the positive to the negative terminal. The carbon brushes are spring loaded graphite blocks mounted on either side of the commutator and are points of electrical contact between the rotor and circuit. They allow free rotation of the coils without tangling the circuit. Carbon brushes are used as they are good conductors and they do not wear down the commutator component. The split ring commutator is two metal half rings connecting either end of the rotor coils to the brushes. They provide points of electrical contact between coils and external circuit. The purpose of the split ring commutator is to reverse the current every 180o. This ensures that the torque continues in the same direction. The split ring commutator makes connection with the rotor coil (armature). The armature usually consists of several coils of insulated wire wound around an iron core and each end is attached to one half of the commutator. It conducts the current which interacts with the magnetic field to provide torque. The magnets form the stator as either permanent magnets or electromagnets. They are on opposing sides of the rotor and are usually curved (radial) to provide a uniform magnetic field to the coil. There will usually be an axle that connects to the rotor coil and this may have components connected to it (drill bits, fan, blender).

Understanding Force and Torque

Force: A force is applied to the side of the coil as a result of the magnetic field interacting with the current in the coil. This force is always perpendicular to the field and is always a constant. 

Torque: Torque is the rotational effect of the force and is what keeps the coil rotating. The torque is always perpendicular to the plane of the coil and varies as the coil rotates. It is a maximum when the plane of the coil is parallel with the magnetic field and decreases as the coil rotates. When the plane of the coil is perpendicular to the magnetic field, the torque becomes 0. Inertia of the coil allows the coil to rotate pass the perpendicular, allowing the current to change direction and the coil to continue rotating.

The diagram below illustrates how the force (blue) and torque (pink) vary as the coil rotates and the different directions of the current through the coil. Note how the current changes direction between image b) and c).

The animation below shows a rotating coil and the variations in current and torque on a graph:


Calculating Torque

The torque that a coil experiences varies as the coil rotates as outlined above. The magnitude of the torque in any position can be calculated using the following formula:

\tau =nBIA\cos { \theta }


\tau is the torque (in Nm)

n is the number of turns on the coil

B is the magnetic field (in T)

I is the current (in A)

A is the area of the coil (in m2)

 \theta is the angle between the plane of the coil and the magnetic field

From the equation above it can be seen that the torque can be increased by:

  • increasing the number of turns on the coil
  • increasing the magnetic field
  • increasing the current
  • increasing the area of the coil

Also note that the torque is:

  • maximum when the plane of the coil is parallel to the magnetic field
  • 0 when the plane of the coil is perpendicular to the magnetic field

Effects of Back emf

There is an input voltage or external emf applied to produce a current in a coil to make the coil rotate in the external magnetic field. As the coil rotates in the external magnetic field, another emf is induced in the coil that is rotating in the field – this follows Lenz’s Law. The emf induced in the motor’s coil, as it rotates in the external magnetic field, is opposite in direction to the input voltage or supply emf and is known as the back emf

The net voltage across the coil equals the input voltage (or supply emf) minus the back emf:

{ \varepsilon }_{ net }\: =\: V\: -\: { \varepsilon }_{ back }

If there is nothing attached to an electric motor to slow it down, the speed of the armature coil increases until the back emf is equal to the external emf. When this occurs, there is no voltage (net emf = 0) across the coil and therefore no current flowing through the coil. With no current through the coil there is no net torque acting on it and the armature rotates at a constant rate.

When there is a load on the motor, the coil rotates at a slower rate and the back emf is reduced. This allows a small voltage across the armature coil and a current flows through it. This current allows for the force that is required to do the work.

The smaller the back emf is, the greater the current flowing through the coil. This becomes a problem if the motor is overloaded. It may rotate too slowly and the back emf will reduce. The voltage across the coil will then remain high and this will result in a large current through the coil that could burn out the motor.

A series resistor is usually used to protect motors from the initially high currents produced when they are switched on. At higher speeds this resistor is switched out of the circuit because as the speed increases, the increasing back emf results in a lower current in the coil.


A DC motor consists of a coil that contains 50 loops and its plane is at an angle of 20° to the direction of a magnetic field. The magnetic field has a strength of 0.05T. The coil has dimensions of 6cm by 10cm and a 10 mA current passes through the coil.

a) Determine the magnitude of the torque acting on the coil

b) What is the maximum torque this coil could produce


a) using: \tau =nBIA\cos { \theta }

\tau =50\times 0.05\times 0.01\times (0.06\times 0.1)\cos { 20 }

\tau =0.00014\:Nm

b) maximum torque occurs when the plane of the coil is parallel to the magnetic field ie: θ=0°

\tau =50\times 0.05\times 0.01\times (0.06\times 0.1)\cos { 0 }

\tau =0.00015\:Nm

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