IGCSE · 4 · extended response
A motor coil that must keep turning
Electricity and magnetism · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Coil torque calibration
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Torque / N m
Horizontal axis (x): sin θ
Read the exact data as a table
| sin θ | Torque / N m |
|---|---|
| 0 | 0 |
| 0.5 | 0.04 |
| 1 | 0.08 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A rectangular coil has 20 turns and area 0.010 m² in a uniform 0.20 T field. It carries 2.0 A. The supplied graph gives torque versus sinθ, where θ is the angle between the coil's area normal and the magnetic field. Use τ = NBIA sinθ. Supplied data (sin θ; Torque / N m): (0, 0), (0.5, 0.04), (1, 0.08).
- (a)
Find the maximum torque, torque at θ = 30°, and mechanical power when the instantaneous torque is 0.060 N m at 50 rad s⁻¹.
3 marks - (b)
Explain why a DC motor needs current reversal and assess one energy-loss mechanism and one useful application trade-off.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Find the maximum torque, torque at θ = 30°, and mechanical power when the instantaneous torque is 0.060 N m at 50 rad s⁻¹.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
The torque factor is NBIA = 20(0.20)(2.0)(0.010) = 0.080 N m.
- 2
At θ = 30°, multiply by sin30° = 0.50 to obtain 0.040 N m. Torque is greatest when the normal is perpendicular to the field.
- 3
Instantaneous mechanical power is τω = 0.060(50) = 3.0 W. Opposite forces on opposite sides form a couple, even if the net force on the whole coil is zero.
(b)
Explain why a DC motor needs current reversal and assess one energy-loss mechanism and one useful application trade-off.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Without reversal, the magnetic couple would reverse after half a turn and oppose continued rotation. Inertia carries the coil through positions of zero torque.
- 2
Electrical input is divided between mechanical output and losses such as I²R heating, bearing friction and magnetic losses; power output cannot exceed input.
- 3
Increasing current increases torque but raises resistive heating quadratically. A lifting motor needs sufficient torque while meeting temperature and efficiency constraints.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- The torque factor is NBIA = 20(0.20)(2.0)(0.010) = 0.080 N m.
- At θ = 30°, multiply by sin30° = 0.50 to obtain 0.040 N m. Torque is greatest when the normal is perpendicular to the field.
- Instantaneous mechanical power is τω = 0.060(50) = 3.0 W. Opposite forces on opposite sides form a couple, even if the net force on the whole coil is zero.
- Without reversal, the magnetic couple would reverse after half a turn and oppose continued rotation. Inertia carries the coil through positions of zero torque.
- Electrical input is divided between mechanical output and losses such as I²R heating, bearing friction and magnetic losses; power output cannot exceed input.
- Increasing current increases torque but raises resistive heating quadratically. A lifting motor needs sufficient torque while meeting temperature and efficiency constraints.
Private on this device