The d.c. motor

1. Overview

The d.c. motor is a device that converts electrical energy into kinetic energy (rotational motion) using the motor effect. This principle is fundamental to modern technology, powering everything from small cooling fans in computers to the powerful engines in electric vehicles.

Key Definitions

• Motor Effect: The force experienced by a current-carrying conductor when placed inside a magnetic field.
• Turning Effect (Torque): The rotational force that causes the coil in a motor to spin around its axis.
• Split-ring Commutator: A metal ring split into two halves that rotates with the coil to reverse the direction of the current every half-turn.
• Brushes: Stationary graphite or metal contacts that rub against the commutator to pass electrical current from the battery into the rotating coil.

Core Content

When a rectangular coil of wire is placed in a magnetic field and a current flows through it, the magnetic field of the wire interacts with the magnetic field of the magnets. This creates a force on each side of the coil (in opposite directions), resulting in a turning effect.

Increasing the Turning Effect

To make a motor spin faster or provide more power (torque), you can increase the turning effect. This is achieved in three ways:

1. Increase the number of turns on the coil: More loops of wire mean more current-carrying conductors are interacting with the magnetic field.
2. Increase the current: Using a higher voltage battery or a lower resistance wire increases the flow of charge.
3. Increase the strength of the magnetic field: Using stronger permanent magnets or moving the magnets closer to the coil.

Worked Example: Question: Motor A has 50 turns and a 2A current. Motor B has 100 turns and a 2A current. Which motor provides a stronger turning effect? Answer: Motor B. Because the number of turns is doubled while the current remains the same, the total magnetic force acting on the coil sides increases, resulting in a larger turning effect.

Extended Content (Extended Curriculum Only)

How the Motor Rotates

For a motor to keep spinning in the same direction, the forces acting on the sides of the coil must switch every half-turn ($180^\circ$). If they didn't, the coil would just oscillate back and forth.

1. Fleming’s Left-Hand Rule: Use this to determine the direction of the force. (Thumb = Force, Index = Magnetic Field N→S, Middle = Current + to -).
2. The Split-ring Commutator: This is the "switch." As the coil reaches the vertical position, the gaps in the split-ring lose contact with the brushes for a tiny fraction of a second. Momentum carries the coil forward. When the rings reconnect with the brushes, the current flows into the opposite side of the coil.
3. Continuous Rotation: By reversing the current every half-turn, the commutator ensures that the force on the left side of the motor is always "up" and the force on the right side is always "down," maintaining clockwise or anticlockwise rotation.

Variation in Turning Effect

Even if the magnetic force ($F=BIL$) is constant, the turning effect changes as the coil rotates:

• Maximum Torque: When the coil is horizontal (parallel to the field). The perpendicular distance from the pivot is greatest.
• Zero Torque: When the coil is vertical. The forces act directly up and down through the center of the coil, providing no "leverage."

Key Equations

While specific torque calculations are often not required, the relationship is defined by: $F = B \times I \times L$

• $F$: Force (Newtons, N)
• $B$: Magnetic Field Strength (Tesla, T)
• $I$: Current (Amperes, A)
• $L$: Length of wire in the field (Metres, m)

Note: The total turning effect is also proportional to the number of turns ($N$) and the width of the coil.

Common Mistakes to Avoid

• ❌ Wrong: Thinking fewer turns of wire helps the motor by reducing electrical resistance.
  • ✓ Right: More turns always increase the motor effect because each turn experiences its own force, which adds up.
• ❌ Wrong: Thinking that the magnetic force on the wire changes as it spins.
  • ✓ Right: The force remains constant, but the turning effect (moment) changes because the distance from the pivot changes with the angle.
• ❌ Wrong: Confusing the brushes and the commutator.
  • ✓ Right: The Brushes stay still; the Commutator spins.
• ❌ Wrong: Thinking that reversing both the battery and the magnets will change the motor's direction.
  • ✓ Right: Reversing both variables cancels the change out, and the motor will spin in the same direction as it did originally.

Exam Tips

1. Check the symmetry: Remember that the turning effect at $45^\circ$ is exactly the same as at $135^\circ$ (positions 2 and 4 in many diagrams) because they are mirror images relative to the magnetic field.
2. Explain the "Why": If asked how to reverse the motor, state: "Reverse the direction of the current OR reverse the direction of the magnetic field." Do not say "both" unless you want it to keep spinning the same way!
3. Left-Hand Rule: Always use your Left Hand for motors (where current creates motion). Many students accidentally use their right hand and get the direction backwards.

---

Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

A simple d.c. motor is constructed using a coil of wire placed between the poles of a permanent magnet.

(a) State three ways in which the turning effect on the coil can be increased. [3]

(b) The direction of the current in the coil is reversed every half-turn. State the name of the component in the motor that achieves this. [1]

(c) State one other function of the brushes in the motor. [1]

Worked Solution:

(a)

1. Increasing the number of turns on the coil. More turns mean more force acting on the coil.
2. Increasing the current in the coil. A larger current creates a stronger magnetic field around the coil.
3. Using a stronger magnet. A stronger magnetic field exerts a greater force on the current-carrying coil.

How to earn full marks:

• Stating each correct factor earns 1 mark.
• Accept equivalent answers, e.g., "increasing the magnetic field strength" or "using a more powerful magnet".

(b)

1. Split-ring commutator. This component reverses the current direction.

How to earn full marks:

• "Split-ring commutator" is the only acceptable answer. Do not accept "commutator" or "slip rings".

(c)

1. To provide electrical contact to the rotating coil. The brushes allow current to flow to the coil as it rotates.

How to earn full marks:

• Any reasonable description of electrical contact is acceptable. Do not accept "to make the motor work" or similar vague answers.

Common Pitfall: Many students focus only on the magnetic field and current when thinking about improving motor performance. Remember that increasing the number of turns on the coil also directly increases the turning effect. Don't forget that the brushes are essential for maintaining electrical contact as the coil rotates.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A student builds a simple d.c. motor for a science project. It consists of a single loop of wire, a battery, a magnet, and some electrical contacts. The motor initially fails to turn.

(a) Suggest two reasons why the motor might not turn, even though the circuit is complete. [2]

(b) The student modifies the motor, and it now rotates slowly. Describe one change the student could make to increase the speed of rotation. Explain why this change would increase the speed. [4]

Worked Solution:

(a)

1. The initial starting position of the coil is perpendicular to the magnetic field. At this position, the force on the coil is zero, so no initial turning effect is present.
2. The friction in the bearings is too high. High friction opposes the rotation of the coil.

How to earn full marks:

• 1 mark for each valid reason.
• Accept other reasonable suggestions, such as "The battery is not providing enough current" or "The magnetic field is too weak."

(b)

1. Change: Increase the current flowing through the coil. This can be achieved by using a higher voltage battery or reducing the resistance in the circuit.
2. Explanation: Increasing the current increases the force acting on the coil due to the magnetic field. $F = BIL$, where $F$ is the force, $B$ is the magnetic field strength, $I$ is the current, and $L$ is the length of the wire in the magnetic field. A larger force results in a greater torque and a faster rotation speed.

How to earn full marks:

• 1 mark for suggesting a valid change.
• 3 marks for a clear and correct explanation of how the change affects the speed of rotation, including reference to the increased force.

Common Pitfall: Students often forget about the importance of the coil's initial position. If the coil starts perpendicular to the magnetic field, there's no initial turning force. Also, remember to link the increase in current directly to an increase in force and then to an increase in torque for a complete explanation.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A small d.c. motor is used to power a toy car. The motor contains a coil with 50 turns and operates in a magnetic field of 0.2 T. The coil has an effective length of 4 cm within the magnetic field.

(a) When a current of 0.5 A flows through the coil, calculate the force acting on the coil. [3]

(b) Explain how the split-ring commutator ensures continuous rotation of the motor. [3]

(c) The motor's efficiency is 60%. If the input power to the motor is 3.0 W, calculate the output power of the motor. [2]

Worked Solution:

(a)

1. Calculate the force on one length of wire: $F = BIL = 0.2 \text{ T} \times 0.5 \text{ A} \times 0.04 \text{ m} = 0.004 \text{ N}$ Using the formula for the force on a current-carrying wire in a magnetic field, converting cm to m.
2. The coil has 50 turns, so the total force is $50 \times 0.004 \text{ N} = 0.2 \text{ N}$. Multiplying the force on one length of wire by the number of turns.
3. The force acting on the coil is $\boxed{0.2 \text{ N}}$.

How to earn full marks:

• 1 mark for using the correct formula $F=BIL$.
• 1 mark for correctly substituting the values, including converting cm to meters.
• 1 mark for the correct final answer with the correct unit.

(b)

1. The split-ring commutator reverses the direction of the current in the coil every half-turn. This is the fundamental function of the commutator.
2. When the coil rotates past the vertical position, the commutator switches the current direction. This ensures the force on the coil continues to produce a torque in the same direction.
3. Without the commutator, the coil would rotate half a turn and then stop, as the force would then act in the opposite direction. The commutator prevents the motor from stopping and ensures continuous rotation.

How to earn full marks:

• 1 mark for stating that the commutator reverses the current direction.
• 1 mark for explaining that this happens every half-turn.
• 1 mark for explaining that this ensures continuous rotation by maintaining the torque in the same direction.

(c)

1. Efficiency = (Output Power / Input Power) x 100%. So, Output Power = (Efficiency / 100%) x Input Power. Using the definition of efficiency.
2. Output Power = (60 / 100) x 3.0 W = 1.8 W. Substituting the values into the equation.
3. The output power of the motor is $\boxed{1.8 \text{ W}}$.

How to earn full marks:

• 1 mark for using the correct formula.
• 1 mark for the correct final answer with the correct unit.

Common Pitfall: Remember to convert all units to SI units before performing calculations, especially centimeters to meters. When explaining the commutator's function, be specific about why reversing the current is necessary for continuous rotation – it prevents the motor from simply oscillating back and forth.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A student is investigating the factors that affect the turning effect on a coil in a d.c. motor. She constructs a simple motor and varies the current flowing through the coil while keeping other factors constant. She measures the torque produced by the motor for different current values.

(a) Describe how the student could measure the torque produced by the motor. [3]

(b) The student plots a graph of torque against current. Sketch the graph you would expect to see. Label the axes with appropriate units. [2]

(c) The student then increases the strength of the magnetic field and repeats the experiment. On the same axes as in (b), sketch the graph she would obtain. [1]

(d) Explain why increasing the strength of the magnetic field increases the torque produced by the motor for the same current. [3]

Worked Solution:

(a)

1. The student could use a spring balance attached to a lever arm connected to the motor's axle. This allows the force required to stop the motor from turning to be measured.
2. The lever arm should be of known length, $r$. The length $r$ is needed to calculate the torque.
3. The torque, $\tau$, is then calculated using the formula $\tau = rF$, where $F$ is the force measured by the spring balance. This converts the measured force into a torque value.

How to earn full marks:

• 1 mark for describing a method to measure the force needed to oppose rotation.
• 1 mark for mentioning a lever arm of known length.
• 1 mark for stating the correct formula to calculate torque from the force and lever arm length.

(b)

1. 📊A graph with "Torque (Nm)" on the y-axis and "Current (A)" on the x-axis. The graph is a straight line passing through the origin with a positive gradient.

How to earn full marks:

• 1 mark for correctly labeling the axes with appropriate units.
• 1 mark for sketching a straight line graph passing through the origin.

(c)

1. 📊Add a second straight line to the graph in part (b). This line should also pass through the origin but have a steeper gradient than the first line.

How to earn full marks:

• 1 mark for drawing a line with a steeper gradient, still passing through the origin.

(d)

1. The torque on the coil is proportional to the magnetic field strength. This is a fundamental relationship.
2. A stronger magnetic field exerts a greater force on the current-carrying wires of the coil. Based on the equation $F=BIL$
3. Since torque is proportional to the force, a greater force results in a greater torque for the same current. Torque is defined as the product of force and the distance from the axis of rotation.

How to earn full marks:

• 1 mark for stating that torque is proportional to magnetic field strength.
• 1 mark for explaining that a stronger field exerts a greater force.
• 1 mark for linking the greater force to a greater torque.

Common Pitfall: When describing the experiment to measure torque, be sure to mention how the force is converted into a torque value using the lever arm. When sketching the graph, remember that the relationship between torque and current is linear, and increasing the magnetic field strength will increase the gradient of the line.