4.5.5 The d.c. motor
Objective
Describe the operation of a d.c. motor, including the action of a split‑ring commutator and brushes, and explain how the turning effect can be increased.
Key Concepts
- A d.c. motor converts electrical energy into mechanical (rotational) energy.
- The motor consists of a coil of wire (the armature) that rotates in a magnetic field produced by permanent magnets or field coils.
- When a current flows through the armature a turning effect (torque) is produced – the motor effect:
\(\displaystyle \tau = N I A B \sin\theta\)
- \(N\) – number of turns in the coil
- \(I\) – current through the coil
- \(A\) – area of the coil (included for enrichment only; the IGCSE core does not require this term)
- \(B\) – magnetic flux density
- \(\theta\) – angle between the field direction and the normal to the coil
The torque is maximum when \(\sin\theta = 1\) (i.e. \(\theta = 90^{\circ}\)). When the coil passes through \(\theta = 0^{\circ}\) or \(180^{\circ}\) the torque would become zero or change sign; the commutator prevents this reversal.
- According to the syllabus, the turning effect increases when any of the following are increased:
- the number of turns \(N\),
- the current \(I\), or
- the magnetic field strength \(B\).
- The split‑ring commutator together with the brushes automatically reverses the direction of current in the armature each half‑turn, so the torque always acts in the same rotational direction.
- A complete closed circuit is required: the current leaves the supply, passes through one brush, the commutator, the armature, the second brush and returns to the supply.
Components of a Simple d.c. Motor
| Component | Function |
|---|
| Armature (coil) | Conducts the current; experiences magnetic forces that produce torque. |
| Permanent magnets (or field coils) | Provide a (approximately) uniform magnetic field \(B\) across the armature. |
| Split‑ring commutator | Reverses the direction of current in the armature every half‑turn, keeping the torque in the same rotational sense. |
| Brushes (usually carbon) | Maintain electrical contact with the rotating commutator while allowing free rotation; also complete the circuit back to the source. |
| Axle and bearings | Support the rotating armature and transmit the mechanical output. |
Step‑by‑Step Operation
- Connect the motor to a d.c. source. Current leaves the positive terminal, passes through one brush, enters one half of the split‑ring commutator and then flows through the armature coil.
- Apply Fleming’s left‑hand rule to determine the direction of the forces on the two sides of the coil. The forces are opposite and produce a torque that starts the coil rotating.
- As the coil turns, the commutator rotates with it. When the coil reaches the position where the torque would otherwise reverse (around \(\theta = 0^{\circ}\) or \(180^{\circ}\)):
- The split‑ring commutator swaps the contacts so that the brush which was touching the “positive” segment now touches the opposite segment.
- This reversal changes the direction of current in the armature, but the magnetic forces still act in the same rotational direction.
- This reversal occurs twice per revolution (once for each half‑turn). Continuous reversal keeps the torque acting in the same direction, giving steady rotation as long as the supply voltage is maintained.
- The second brush carries the current back to the negative terminal of the source, completing the closed circuit.
Why a Split‑Ring Commutator Is Needed
Without a commutator the torque would change sign every half‑turn because \(\sin\theta\) becomes negative when the coil passes the neutral positions. The split‑ring commutator reverses the current direction at exactly those moments, ensuring that the product \(I\,\sin\theta\) remains positive and the torque always points in the same rotational direction.
Relationship Between Torque and \(\sin\theta\)
- \(\tau \propto \sin\theta\) – torque is maximum at \(\theta = 90^{\circ}\) and zero at \(\theta = 0^{\circ}\) or \(180^{\circ}\).
- The commutator’s action makes the effective \(\sin\theta\) term always positive for the motor, so the coil never experiences a torque that would cause it to reverse direction.
Real‑World Examples
- Hand‑held electric fan – the armature drives the fan blades.
- Small kitchen blender – a higher‑power version of the same principle, with the armature turning the mixing blade.
- Toy car motor – demonstrates the same operation on a wheeled vehicle.
Safety & Practical Considerations
- Never operate a motor with the housing open; brushes can become hot and may spark.
- Carbon brushes wear gradually; ensure they are correctly aligned to minimise sparking and extend life.
- Keep the motor away from moisture to avoid short‑circuits.
Common Misconceptions
- “The magnetic field moves the coil.” – The field is static; forces on the moving charges in the coil cause the motion.
- “The commutator is a manual switch.” – It is a continuously rotating contact that automatically reverses the current direction.
- “Brushes wear out instantly.” – Modern carbon brushes have a long service life; wear is mainly due to friction and can be reduced by proper alignment.
Extension (Advanced – optional)
The approximate speed \(n\) (in revolutions per minute) of a simple d.c. motor can be expressed as:
\(\displaystyle n = \frac{V - I R}{k\,\Phi}\)
- \(V\) – applied voltage
- \(I R\) – internal voltage drop (copper loss)
- \(k\) – constant that depends on the motor construction
- \(\Phi\) – magnetic flux per pole
Increasing \(V\) or decreasing the load (reducing \(I\)) raises the speed, whereas increasing the magnetic field strength \(\Phi\) lowers the speed but increases the torque. This relationship is useful for deeper study but is not required for the core IGCSE syllabus.
Summary
A d.c. motor works by exploiting the motor effect: a current‑carrying conductor placed in a magnetic field experiences a force. The split‑ring commutator and brushes automatically reverse the current in the armature each half‑turn, ensuring that the torque always acts in the same rotational direction. This produces continuous rotary motion, which can be observed in everyday devices such as electric fans, kitchen blenders and toy‑car motors.