Physics • Year 12 • Module 6 • Lesson 17
DC Motors in Depth
Lock in the key vocabulary, formulas, and conceptual relationships for back emf, motor current, and starting resistors before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: back emf, stall current, starting resistor, no-load speed, net voltage, mechanical power output, coil resistance, efficiency, angular speed, Lenz’s Law. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The voltage induced in a motor’s rotating coil that opposes the applied voltage. It is proportional to the angular speed of the motor. | |
| 1.2 | The maximum current drawn by a motor when it is stationary (omega = 0) and no back emf is present. Equal to V/R. | |
| 1.3 | A resistor placed in series with a DC motor at startup to limit the dangerous surge current before back emf builds up. | |
| 1.4 | The maximum speed reached by a motor running with no external load, at which back emf nearly equals the applied voltage. | |
| 1.5 | The applied voltage minus the back emf; drives the current through the coil. Equal to IR. | |
| 1.6 | The rate at which the motor converts electrical energy into mechanical energy. Equal to the back emf multiplied by the current. | |
| 1.7 | The intrinsic resistance of the motor’s wire windings, which determines heat losses as I²R. | |
| 1.8 | The ratio of mechanical power output to electrical power input, expressed as a percentage. | |
| 1.9 | The rate of rotation of the motor coil, measured in radians per second (rad s−1). Symbol: ω. | |
| 1.10 | The principle that an induced emf always acts in a direction that opposes the change producing it; the physical basis for back emf in a motor. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 At startup (omega = 0), the back emf in a DC motor is equal to the applied voltage, so the initial current is zero. T / F
2.2 As a DC motor speeds up, the back emf increases, reducing the net voltage and therefore reducing the current drawn from the supply. T / F
2.3 The mechanical power output of a DC motor equals the electrical power input (P = VI) minus the heat losses (P = I²R). T / F
2.4 If a DC motor is suddenly loaded (slows down), the back emf increases and the current drops. T / F
2.5 A starting resistor is gradually removed from the circuit (bypassed) as the motor speeds up. T / F
2.6 The back emf is not required by any conservation law; it is simply a side-effect of motor rotation. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
back emf · conservation of energy · decreases · heat · increases · Lenz’s Law · mechanical · stall current
When a DC motor rotates, the coil cuts through magnetic field lines, inducing a voltage known as ___________. By ___________, this induced voltage opposes the applied voltage. As the motor speeds up, the back emf ___________, reducing the current drawn from the supply. The maximum current occurs when the motor is stationary; this is called the ___________. The electrical power delivered to the motor is split between two forms: some is wasted as ___________ in the coil resistance, and the remainder becomes ___________ power output. Back emf is required by the law of ___________ — without it, the motor would do unlimited work for free. When the motor is loaded and slows, the back emf ___________, automatically increasing the current to meet the greater torque demand.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What is the function of the back emf in a DC motor, and which physical law requires it to exist?
4.2 Why does a DC motor draw a large surge current at startup, and what is the danger this poses?
4.3 What is the function of a starting resistor, and why is it bypassed once the motor is running at speed?
4.4 How does the mechanical power output of a DC motor relate to the back emf and the current?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “increases”, “limits”, “converts to”, “is required by”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: back emf · motor speed · current · mechanical power · heat losses · Lenz’s Law.
6. Formula matching — DC motor relationships
Match each physical quantity (left column) to its correct formula or expression (right column) by writing the letter in the blank. 6 marks (1 each)
| Physical quantity | Letter | Formula / expression |
|---|---|---|
| Motor current at any speed | A. Pin − Pheat | |
| Stall current (omega = 0) | B. (V − εback) / R | |
| Electrical power input | C. V / R | |
| Heat dissipated in coil | D. VI | |
| Mechanical power output | E. I²R | |
| Motor efficiency (η) | F. (Pmech / Pin) × 100 % |
Q1 — Term–definition match
1.1 back emf • 1.2 stall current • 1.3 starting resistor • 1.4 no-load speed • 1.5 net voltage • 1.6 mechanical power output • 1.7 coil resistance • 1.8 efficiency • 1.9 angular speed • 1.10 Lenz’s Law.
Q2 — True / false with correction
2.1 False. At startup (omega = 0), the back emf is zero (not equal to V). The initial current is maximum, equal to V/R — called the stall current.
2.2 True.
2.3 True. Pmech = Pin − Pheat = VI − I²R. Equivalently, Pmech = εback × I.
2.4 False. If the motor slows, the back emf decreases, so the net voltage and current both increase — the motor automatically draws more current to generate more torque.
2.5 True. As back emf builds, the net voltage falls; the starting resistor is no longer needed to protect the coil, so it is bypassed (short-circuited by a relay or switch).
2.6 False. Back emf is required by the law of conservation of energy. It ensures that electrical energy in = mechanical energy out + heat losses; without it, the motor would extract unlimited mechanical energy from a finite electrical supply, violating energy conservation.
Q3 — Cloze paragraph
In order: back emf / Lenz’s Law / increases / stall current / heat / mechanical / conservation of energy / decreases.
Q4.1 — Function of back emf
Back emf is the voltage induced in the rotating coil that opposes the applied voltage, thereby limiting the current and ensuring energy conservation. It is required by Lenz’s Law, which states that an induced emf always opposes the change producing it — in this case, the rotation driven by the applied voltage.
Q4.2 — Startup surge current
At startup, the motor coil is stationary (omega = 0), so back emf = 0 and the full applied voltage drives current through the coil resistance: I = V/R. This stall current can be 5–10 times the running current, which can overheat the coil, damage the commutator and brushes, or cause voltage dips in the supply.
Q4.3 — Function of starting resistor
A starting resistor is placed in series at startup to limit the surge current to a safe value (I = V / (R + Rstart)). Once the motor speeds up and back emf builds, the effective current drops; the starting resistor is then bypassed because it would waste energy and reduce the running voltage unnecessarily.
Q4.4 — Mechanical power output
The mechanical power output equals the back emf multiplied by the current: Pmech = εback × I. This is the portion of electrical input power that has been converted to mechanical energy, equal to the total input power VI minus the coil heat loss I²R.
Q5 — Sample concept map
Correct maps should include arrows such as:
- motor speed — determines → back emf
- back emf — reduces → current
- current — produces → heat losses (via I²R)
- back emf × current — equals → mechanical power
- Lenz’s Law — requires existence of → back emf
- current — drives → mechanical power (together with back emf)
Award 1 mark per valid labelled arrow. Accept any physically correct linking phrase.
Q6 — Formula matching
Motor current: B • Stall current: C • Electrical power input: D • Heat dissipated: E • Mechanical power output: A • Efficiency: F.