IB · PHYSICS HL

Physics: Higher Level

Electromagnetic induction — HL Theme D

Name: ____________________Date: October 10, 2026

1.
A coil of 200 turns has a magnetic flux through it that changes uniformly from 0.0030 Wb to 0.0110 Wb in 0.40 s. Calculate the magnitude of the average EMF induced in the coil.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the change in flux: ΔΦ = 0.0110 − 0.0030 = 0.0080 Wb. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Uses Faraday's law EMF = N(ΔΦ/Δt). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes EMF = 200 × 0.0080/0.40. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains EMF = 4.0 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The number of turns N directly multiplies the induced EMF — a coil with more turns produces a proportionally larger EMF for the same rate of flux change.
Marking points
- Calculates the change in flux: ΔΦ = 0.0110 − 0.0030 = 0.0080 Wb.
- Uses Faraday's law EMF = N(ΔΦ/Δt).
- Substitutes EMF = 200 × 0.0080/0.40.
- Obtains EMF = 4.0 V.
Examiner tip: The number of turns N directly multiplies the induced EMF — a coil with more turns produces a proportionally larger EMF for the same rate of flux change.
2.
Marking analysis: A learner attempts the following task: “A coil of 200 turns has a magnetic flux through it that changes uniformly from 0.0030 Wb to 0.0110 Wb in 0.40 s. Calculate the magnitude of the average EMF induced in the coil.” Their response addresses only this point: “Calculates the change in flux: ΔΦ = 0.0110 − 0.0030 = 0.0080 Wb.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Calculates the change in flux: ΔΦ = 0.0110 − 0.0030 = 0.0080 Wb. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Uses Faraday's law EMF = N(ΔΦ/Δt). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes EMF = 200 × 0.0080/0.40. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains EMF = 4.0 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Calculates the change in flux: ΔΦ = 0.0110 − 0.0030 = 0.0080 Wb.
- Identifies the missing requirement: Uses Faraday's law EMF = N(ΔΦ/Δt).
- Identifies the missing requirement: Substitutes EMF = 200 × 0.0080/0.40.
- Identifies the missing requirement: Obtains EMF = 4.0 V.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
3.
State Lenz's law, and use it to explain the direction of the induced current when the north pole of a magnet is pushed toward a coil of wire.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States Lenz's law: the induced current flows in a direction that opposes the change in flux that produced it. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that as the north pole approaches, flux through the coil increases. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the induced current must flow to create a magnetic field opposing this increase, meaning the coil face nearer the magnet acts as a north pole (to repel the approaching magnet). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Lenz's law is a direct consequence of energy conservation: if the induced current aided the change instead of opposing it, energy would be created from nothing.
Marking points
- States Lenz's law: the induced current flows in a direction that opposes the change in flux that produced it.
- States that as the north pole approaches, flux through the coil increases.
- States that the induced current must flow to create a magnetic field opposing this increase, meaning the coil face nearer the magnet acts as a north pole (to repel the approaching magnet).
Examiner tip: Lenz's law is a direct consequence of energy conservation: if the induced current aided the change instead of opposing it, energy would be created from nothing.
4.
Marking analysis: A learner attempts the following task: “State Lenz's law, and use it to explain the direction of the induced current when the north pole of a magnet is pushed toward a coil of wire.” Their response addresses only this point: “States Lenz's law: the induced current flows in a direction that opposes the change in flux that produced it.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States Lenz's law: the induced current flows in a direction that opposes the change in flux that produced it. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that as the north pole approaches, flux through the coil increases. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that the induced current must flow to create a magnetic field opposing this increase, meaning the coil face nearer the magnet acts as a north pole (to repel the approaching magnet). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States Lenz's law: the induced current flows in a direction that opposes the change in flux that produced it.
- Identifies the missing requirement: States that as the north pole approaches, flux through the coil increases.
- Identifies the missing requirement: States that the induced current must flow to create a magnetic field opposing this increase, meaning the coil face nearer the magnet acts as a north pole (to repel the approaching magnet).
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
5.
A rectangular coil of area 0.050 m² and 100 turns rotates at a constant angular frequency of 50 rad s⁻¹ in a uniform magnetic field of flux density 0.30 T. Calculate the peak EMF generated.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States the peak EMF formula for a rotating coil: EMF₀ = NBAω. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Identifies each value: N = 100, B = 0.30 T, A = 0.050 m², ω = 50 rad s⁻¹. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes EMF₀ = 100 × 0.30 × 0.050 × 50. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains EMF₀ = 75 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Peak EMF occurs when the coil plane is parallel to the field (rate of flux change is maximum), not when flux itself is maximum — these occur at different points in the rotation.
Marking points
- States the peak EMF formula for a rotating coil: EMF₀ = NBAω.
- Identifies each value: N = 100, B = 0.30 T, A = 0.050 m², ω = 50 rad s⁻¹.
- Substitutes EMF₀ = 100 × 0.30 × 0.050 × 50.
- Obtains EMF₀ = 75 V.
Examiner tip: Peak EMF occurs when the coil plane is parallel to the field (rate of flux change is maximum), not when flux itself is maximum — these occur at different points in the rotation.
6.
Marking analysis: A learner attempts the following task: “A rectangular coil of area 0.050 m² and 100 turns rotates at a constant angular frequency of 50 rad s⁻¹ in a uniform magnetic field of flux density 0.30 T. Calculate the peak EMF generated.” Their response addresses only this point: “States the peak EMF formula for a rotating coil: EMF₀ = NBAω.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States the peak EMF formula for a rotating coil: EMF₀ = NBAω. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Identifies each value: N = 100, B = 0.30 T, A = 0.050 m², ω = 50 rad s⁻¹. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes EMF₀ = 100 × 0.30 × 0.050 × 50. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains EMF₀ = 75 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States the peak EMF formula for a rotating coil: EMF₀ = NBAω.
- Identifies the missing requirement: Identifies each value: N = 100, B = 0.30 T, A = 0.050 m², ω = 50 rad s⁻¹.
- Identifies the missing requirement: Substitutes EMF₀ = 100 × 0.30 × 0.050 × 50.
- Identifies the missing requirement: Obtains EMF₀ = 75 V.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
7.
A step-up transformer has 400 turns on the primary coil and 2000 turns on the secondary coil. The primary current is 8.0 A. Assuming an ideal (100% efficient) transformer, calculate the secondary current.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States that for an ideal transformer, input power equals output power: VpIp = VsIs. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Combines this with the turns-ratio relationship to obtain NpIp = NsIs. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes 400 × 8.0 = 2000 × Is. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains Is = 1.6 A. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A step-up transformer increases voltage but always decreases current proportionally (for an ideal transformer), since power must be conserved.
Marking points
- States that for an ideal transformer, input power equals output power: VpIp = VsIs.
- Combines this with the turns-ratio relationship to obtain NpIp = NsIs.
- Substitutes 400 × 8.0 = 2000 × Is.
- Obtains Is = 1.6 A.
Examiner tip: A step-up transformer increases voltage but always decreases current proportionally (for an ideal transformer), since power must be conserved.
8.
Marking analysis: A learner attempts the following task: “A step-up transformer has 400 turns on the primary coil and 2000 turns on the secondary coil. The primary current is 8.0 A. Assuming an ideal (100% efficient) transformer, calculate the secondary current.” Their response addresses only this point: “States that for an ideal transformer, input power equals output power: VpIp = VsIs.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that for an ideal transformer, input power equals output power: VpIp = VsIs. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Combines this with the turns-ratio relationship to obtain NpIp = NsIs. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes 400 × 8.0 = 2000 × Is. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains Is = 1.6 A. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that for an ideal transformer, input power equals output power: VpIp = VsIs.
- Identifies the missing requirement: Combines this with the turns-ratio relationship to obtain NpIp = NsIs.
- Identifies the missing requirement: Substitutes 400 × 8.0 = 2000 × Is.
- Identifies the missing requirement: Obtains Is = 1.6 A.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
9.
Explain why transmitting electrical power over long distances at high voltage and low current, rather than low voltage and high current, reduces power losses in the transmission cables.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Work through this mathematical step: States that power loss in a cable is given by P = I²R, depending on current squared, not on voltage. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: States that for a fixed power to be delivered (P = VI), a higher transmission voltage allows a proportionally lower current. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States that halving the current, for example, would quarter the I²R power loss, since the loss depends on the square of the current. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: Concludes that lowering the current (by raising voltage) reduces I²R losses by the square of the current reduction factor, a much bigger effect than the linear change in current alone. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The squared relationship between current and power loss is the key reason high-voltage transmission is so much more efficient, not just a minor optimisation.
Marking points
- States that power loss in a cable is given by P = I²R, depending on current squared, not on voltage.
- States that for a fixed power to be delivered (P = VI), a higher transmission voltage allows a proportionally lower current.
- States that halving the current, for example, would quarter the I²R power loss, since the loss depends on the square of the current.
- Concludes that lowering the current (by raising voltage) reduces I²R losses by the square of the current reduction factor, a much bigger effect than the linear change in current alone.
Examiner tip: The squared relationship between current and power loss is the key reason high-voltage transmission is so much more efficient, not just a minor optimisation.
10.
Marking analysis: A learner attempts the following task: “Explain why transmitting electrical power over long distances at high voltage and low current, rather than low voltage and high current, reduces power losses in the transmission cables.” Their response addresses only this point: “States that power loss in a cable is given by P = I²R, depending on current squared, not on voltage.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that power loss in a cable is given by P = I²R, depending on current squared, not on voltage. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that for a fixed power to be delivered (P = VI), a higher transmission voltage allows a proportionally lower current. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that halving the current, for example, would quarter the I²R power loss, since the loss depends on the square of the current. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Concludes that lowering the current (by raising voltage) reduces I²R losses by the square of the current reduction factor, a much bigger effect than the linear change in current alone. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that power loss in a cable is given by P = I²R, depending on current squared, not on voltage.
- Identifies the missing requirement: States that for a fixed power to be delivered (P = VI), a higher transmission voltage allows a proportionally lower current.
- Identifies the missing requirement: States that halving the current, for example, would quarter the I²R power loss, since the loss depends on the square of the current.
- Identifies the missing requirement: Concludes that lowering the current (by raising voltage) reduces I²R losses by the square of the current reduction factor, a much bigger effect than the linear change in current alone.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
11.
A metal plate moves through a region of uniform magnetic field and experiences eddy currents that oppose its motion. Explain the origin of these eddy currents and why they cause a braking (retarding) force on the plate.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that as the plate moves through the field, the magnetic flux through parts of the conducting plate changes. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this changing flux induces circulating (eddy) currents within the plate, by Faraday's law. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that by Lenz's law, these induced currents create magnetic effects that oppose the plate's motion (the change that caused them). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: States that this opposition manifests as a retarding force on the plate, converting kinetic energy into thermal energy (resistive heating) in the plate. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Eddy current braking is a direct real-world application of Lenz's law and is used deliberately in some braking systems (e.g. some train and roller-coaster brakes) precisely because it requires no physical contact.
Marking points
- States that as the plate moves through the field, the magnetic flux through parts of the conducting plate changes.
- States that this changing flux induces circulating (eddy) currents within the plate, by Faraday's law.
- States that by Lenz's law, these induced currents create magnetic effects that oppose the plate's motion (the change that caused them).
- States that this opposition manifests as a retarding force on the plate, converting kinetic energy into thermal energy (resistive heating) in the plate.
Examiner tip: Eddy current braking is a direct real-world application of Lenz's law and is used deliberately in some braking systems (e.g. some train and roller-coaster brakes) precisely because it requires no physical contact.
12.
Marking analysis: A learner attempts the following task: “A metal plate moves through a region of uniform magnetic field and experiences eddy currents that oppose its motion. Explain the origin of these eddy currents and why they cause a braking (retarding) force on the plate.” Their response addresses only this point: “States that as the plate moves through the field, the magnetic flux through parts of the conducting plate changes.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that as the plate moves through the field, the magnetic flux through parts of the conducting plate changes. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this changing flux induces circulating (eddy) currents within the plate, by Faraday's law. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that by Lenz's law, these induced currents create magnetic effects that oppose the plate's motion (the change that caused them). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: States that this opposition manifests as a retarding force on the plate, converting kinetic energy into thermal energy (resistive heating) in the plate. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that as the plate moves through the field, the magnetic flux through parts of the conducting plate changes.
- Identifies the missing requirement: States that this changing flux induces circulating (eddy) currents within the plate, by Faraday's law.
- Identifies the missing requirement: States that by Lenz's law, these induced currents create magnetic effects that oppose the plate's motion (the change that caused them).
- Identifies the missing requirement: States that this opposition manifests as a retarding force on the plate, converting kinetic energy into thermal energy (resistive heating) in the plate.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
13.
A straight conducting rod of length 0.60 m moves at 4.0 m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.25 T, with its length also perpendicular to its velocity. Calculate the EMF induced between the ends of the rod.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses the motional EMF equation EMF = BLv for mutually perpendicular B, L and v. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes EMF = 0.25 × 0.60 × 4.0. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains EMF = 0.60 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: EMF = BLv applies only when the field, rod length and velocity are all mutually perpendicular; other orientations require a component (angle) adjustment.
Marking points
- Uses the motional EMF equation EMF = BLv for mutually perpendicular B, L and v.
- Substitutes EMF = 0.25 × 0.60 × 4.0.
- Obtains EMF = 0.60 V.
Examiner tip: EMF = BLv applies only when the field, rod length and velocity are all mutually perpendicular; other orientations require a component (angle) adjustment.
14.
Marking analysis: A learner attempts the following task: “A straight conducting rod of length 0.60 m moves at 4.0 m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.25 T, with its length also perpendicular to its velocity. Calculate the EMF induced between the ends of the rod.” Their response addresses only this point: “Uses the motional EMF equation EMF = BLv for mutually perpendicular B, L and v.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses the motional EMF equation EMF = BLv for mutually perpendicular B, L and v. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes EMF = 0.25 × 0.60 × 4.0. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains EMF = 0.60 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses the motional EMF equation EMF = BLv for mutually perpendicular B, L and v.
- Identifies the missing requirement: Substitutes EMF = 0.25 × 0.60 × 4.0.
- Identifies the missing requirement: Obtains EMF = 0.60 V.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
15.
A generator produces an alternating EMF with peak value 340 V. Calculate the root-mean-square (rms) voltage, and explain what this rms value physically represents.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses Vrms = V₀/√2. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains Vrms = 340/√2 ≈ 240 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Explains that the rms voltage is the value of a direct (constant) voltage that would deliver the same average power to a resistive load as the actual alternating voltage. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The rms value, not the peak value, is what's used for power calculations (P = Vrms²/R) and is the value normally quoted for mains electricity.
Marking points
- Uses Vrms = V₀/√2.
- Obtains Vrms = 340/√2 ≈ 240 V.
- Explains that the rms voltage is the value of a direct (constant) voltage that would deliver the same average power to a resistive load as the actual alternating voltage.
Examiner tip: The rms value, not the peak value, is what's used for power calculations (P = Vrms²/R) and is the value normally quoted for mains electricity.
16.
Marking analysis: A learner attempts the following task: “A generator produces an alternating EMF with peak value 340 V. Calculate the root-mean-square (rms) voltage, and explain what this rms value physically represents.” Their response addresses only this point: “Uses Vrms = V₀/√2.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses Vrms = V₀/√2. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Obtains Vrms = 340/√2 ≈ 240 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Explains that the rms voltage is the value of a direct (constant) voltage that would deliver the same average power to a resistive load as the actual alternating voltage. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses Vrms = V₀/√2.
- Identifies the missing requirement: Obtains Vrms = 340/√2 ≈ 240 V.
- Identifies the missing requirement: Explains that the rms voltage is the value of a direct (constant) voltage that would deliver the same average power to a resistive load as the actual alternating voltage.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
17.
A generator's coil rotates at constant angular speed in a magnetic field. State how the induced EMF varies with time, and explain why the EMF is zero when the coil plane is perpendicular to the field.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the induced EMF varies sinusoidally with time. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that when the coil plane is perpendicular to the field, the magnetic flux through the coil is at a maximum. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that at maximum flux, the rate of change of flux (and hence EMF, by Faraday's law) is momentarily zero, since the flux is turning around from increasing to decreasing. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: EMF depends on the rate of change of flux, not flux itself — EMF is zero exactly when flux is at a turning point (maximum or minimum), not when flux is zero.
Marking points
- States that the induced EMF varies sinusoidally with time.
- States that when the coil plane is perpendicular to the field, the magnetic flux through the coil is at a maximum.
- States that at maximum flux, the rate of change of flux (and hence EMF, by Faraday's law) is momentarily zero, since the flux is turning around from increasing to decreasing.
Examiner tip: EMF depends on the rate of change of flux, not flux itself — EMF is zero exactly when flux is at a turning point (maximum or minimum), not when flux is zero.
18.
Marking analysis: A learner attempts the following task: “A generator's coil rotates at constant angular speed in a magnetic field. State how the induced EMF varies with time, and explain why the EMF is zero when the coil plane is perpendicular to the field.” Their response addresses only this point: “States that the induced EMF varies sinusoidally with time.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that the induced EMF varies sinusoidally with time. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that when the coil plane is perpendicular to the field, the magnetic flux through the coil is at a maximum. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that at maximum flux, the rate of change of flux (and hence EMF, by Faraday's law) is momentarily zero, since the flux is turning around from increasing to decreasing. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that the induced EMF varies sinusoidally with time.
- Identifies the missing requirement: States that when the coil plane is perpendicular to the field, the magnetic flux through the coil is at a maximum.
- Identifies the missing requirement: States that at maximum flux, the rate of change of flux (and hence EMF, by Faraday's law) is momentarily zero, since the flux is turning around from increasing to decreasing.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
19.
A transformer with 100% efficiency has a primary voltage of 230 V and a secondary voltage of 11.5 V. Calculate the turns ratio (primary:secondary), and state whether this is a step-up or step-down transformer.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses Np/Ns = Vp/Vs. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Calculates the ratio 230/11.5 = 20. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States the turns ratio as 20:1. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: States that this is a step-down transformer, since the secondary voltage is lower than the primary voltage. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The turns ratio equals the voltage ratio directly for an ideal transformer; a larger primary-to-secondary ratio always corresponds to a step-down transformer.
Marking points
- Uses Np/Ns = Vp/Vs.
- Calculates the ratio 230/11.5 = 20.
- States the turns ratio as 20:1.
- States that this is a step-down transformer, since the secondary voltage is lower than the primary voltage.
Examiner tip: The turns ratio equals the voltage ratio directly for an ideal transformer; a larger primary-to-secondary ratio always corresponds to a step-down transformer.
20.
Marking analysis: A learner attempts the following task: “A transformer with 100% efficiency has a primary voltage of 230 V and a secondary voltage of 11.5 V. Calculate the turns ratio (primary:secondary), and state whether this is a step-up or step-down transformer.” Their response addresses only this point: “Uses Np/Ns = Vp/Vs.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses Np/Ns = Vp/Vs. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Calculates the ratio 230/11.5 = 20. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States the turns ratio as 20:1. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: States that this is a step-down transformer, since the secondary voltage is lower than the primary voltage. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses Np/Ns = Vp/Vs.
- Identifies the missing requirement: Calculates the ratio 230/11.5 = 20.
- Identifies the missing requirement: States the turns ratio as 20:1.
- Identifies the missing requirement: States that this is a step-down transformer, since the secondary voltage is lower than the primary voltage.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
21.
Define self-inductance, and calculate the magnitude of the average EMF induced in a coil of self-inductance 0.50 H when the current through it changes from 2.0 A to 6.0 A in 0.20 s.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: Defines self-inductance as the property of a circuit (coil) whereby a changing current within it induces an EMF in itself, opposing the change. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: States EMF = −L(ΔI/Δt). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Calculates ΔI = 6.0 − 2.0 = 4.0 A, and substitutes magnitude EMF = 0.50 × 4.0/0.20. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains EMF = 10 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Self-inductance is Lenz's law applied to a single coil's own changing current — the induced EMF always opposes the current change that produced it, which is why the negative sign appears in the formula.
Marking points
- Defines self-inductance as the property of a circuit (coil) whereby a changing current within it induces an EMF in itself, opposing the change.
- States EMF = −L(ΔI/Δt).
- Calculates ΔI = 6.0 − 2.0 = 4.0 A, and substitutes magnitude EMF = 0.50 × 4.0/0.20.
- Obtains EMF = 10 V.
Examiner tip: Self-inductance is Lenz's law applied to a single coil's own changing current — the induced EMF always opposes the current change that produced it, which is why the negative sign appears in the formula.
22.
Marking analysis: A learner attempts the following task: “Define self-inductance, and calculate the magnitude of the average EMF induced in a coil of self-inductance 0.50 H when the current through it changes from 2.0 A to 6.0 A in 0.20 s.” Their response addresses only this point: “Defines self-inductance as the property of a circuit (coil) whereby a changing current within it induces an EMF in itself, opposing the change.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Defines self-inductance as the property of a circuit (coil) whereby a changing current within it induces an EMF in itself, opposing the change. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States EMF = −L(ΔI/Δt). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Calculates ΔI = 6.0 − 2.0 = 4.0 A, and substitutes magnitude EMF = 0.50 × 4.0/0.20. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains EMF = 10 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Defines self-inductance as the property of a circuit (coil) whereby a changing current within it induces an EMF in itself, opposing the change.
- Identifies the missing requirement: States EMF = −L(ΔI/Δt).
- Identifies the missing requirement: Calculates ΔI = 6.0 − 2.0 = 4.0 A, and substitutes magnitude EMF = 0.50 × 4.0/0.20.
- Identifies the missing requirement: Obtains EMF = 10 V.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
23.
State two reasons why a real transformer is not 100% efficient, and state one design feature used to reduce each.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that resistance in the windings causes I²R (resistive) heating losses. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this is reduced by using thick, low-resistance (high-conductivity) wire for the windings. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the changing magnetic flux induces eddy currents in the iron core, causing further heating losses. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: States that this is reduced by using a laminated core (thin, mutually insulated sheets) instead of a solid block of iron. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Lamination works by breaking up the core into thin, electrically insulated sheets, which greatly restricts the paths available for eddy currents to circulate, without significantly affecting the core's ability to carry magnetic flux.
Marking points
- States that resistance in the windings causes I²R (resistive) heating losses.
- States that this is reduced by using thick, low-resistance (high-conductivity) wire for the windings.
- States that the changing magnetic flux induces eddy currents in the iron core, causing further heating losses.
- States that this is reduced by using a laminated core (thin, mutually insulated sheets) instead of a solid block of iron.
Examiner tip: Lamination works by breaking up the core into thin, electrically insulated sheets, which greatly restricts the paths available for eddy currents to circulate, without significantly affecting the core's ability to carry magnetic flux.
24.
Marking analysis: A learner attempts the following task: “State two reasons why a real transformer is not 100% efficient, and state one design feature used to reduce each.” Their response addresses only this point: “States that resistance in the windings causes I²R (resistive) heating losses.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that resistance in the windings causes I²R (resistive) heating losses. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this is reduced by using thick, low-resistance (high-conductivity) wire for the windings. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that the changing magnetic flux induces eddy currents in the iron core, causing further heating losses. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: States that this is reduced by using a laminated core (thin, mutually insulated sheets) instead of a solid block of iron. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that resistance in the windings causes I²R (resistive) heating losses.
- Identifies the missing requirement: States that this is reduced by using thick, low-resistance (high-conductivity) wire for the windings.
- Identifies the missing requirement: States that the changing magnetic flux induces eddy currents in the iron core, causing further heating losses.
- Identifies the missing requirement: States that this is reduced by using a laminated core (thin, mutually insulated sheets) instead of a solid block of iron.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
25.
Explain, in terms of mutual inductance, how a transformer transfers electrical energy from its primary coil to its secondary coil without any direct electrical (wired) connection between them.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that an alternating current in the primary coil produces a continuously changing magnetic flux. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this changing flux, linked through the iron core, also passes through the secondary coil. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that, by Faraday's law, this changing flux induces an EMF (and a current, if the circuit is closed) in the secondary coil — this linking of two coils via a shared changing flux is called mutual inductance. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A transformer works entirely through the shared, changing magnetic flux linking its two coils — no electrons ever travel from the primary circuit to the secondary circuit.
Marking points
- States that an alternating current in the primary coil produces a continuously changing magnetic flux.
- States that this changing flux, linked through the iron core, also passes through the secondary coil.
- States that, by Faraday's law, this changing flux induces an EMF (and a current, if the circuit is closed) in the secondary coil — this linking of two coils via a shared changing flux is called mutual inductance.
Examiner tip: A transformer works entirely through the shared, changing magnetic flux linking its two coils — no electrons ever travel from the primary circuit to the secondary circuit.
26.
Marking analysis: A learner attempts the following task: “Explain, in terms of mutual inductance, how a transformer transfers electrical energy from its primary coil to its secondary coil without any direct electrical (wired) connection between them.” Their response addresses only this point: “States that an alternating current in the primary coil produces a continuously changing magnetic flux.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that an alternating current in the primary coil produces a continuously changing magnetic flux. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this changing flux, linked through the iron core, also passes through the secondary coil. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that, by Faraday's law, this changing flux induces an EMF (and a current, if the circuit is closed) in the secondary coil — this linking of two coils via a shared changing flux is called mutual inductance. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that an alternating current in the primary coil produces a continuously changing magnetic flux.
- Identifies the missing requirement: States that this changing flux, linked through the iron core, also passes through the secondary coil.
- Identifies the missing requirement: States that, by Faraday's law, this changing flux induces an EMF (and a current, if the circuit is closed) in the secondary coil — this linking of two coils via a shared changing flux is called mutual inductance.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
27.
Explain, using Lenz's law, why a spinning electric motor generates a 'back EMF' that opposes the supply voltage driving it, and state what happens to the current drawn by the motor as its speed increases.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that as the motor's coil rotates within the magnetic field, it is itself acting like a generator, so by Faraday's law it induces an EMF. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that, by Lenz's law, this induced EMF (back EMF) opposes the applied (supply) voltage that is driving the current in the first place. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the net driving voltage across the coil's resistance is therefore (supply voltage − back EMF), which decreases as back EMF increases. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: States that since back EMF increases with the motor's rotational speed, the current drawn by the motor decreases as its speed increases. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: This is why a motor draws its largest current the instant it starts (back EMF is zero at zero speed) and a much smaller current once running freely at full speed — a stalled (jammed) motor can draw dangerously large currents for exactly this reason.
Marking points
- States that as the motor's coil rotates within the magnetic field, it is itself acting like a generator, so by Faraday's law it induces an EMF.
- States that, by Lenz's law, this induced EMF (back EMF) opposes the applied (supply) voltage that is driving the current in the first place.
- States that the net driving voltage across the coil's resistance is therefore (supply voltage − back EMF), which decreases as back EMF increases.
- States that since back EMF increases with the motor's rotational speed, the current drawn by the motor decreases as its speed increases.
Examiner tip: This is why a motor draws its largest current the instant it starts (back EMF is zero at zero speed) and a much smaller current once running freely at full speed — a stalled (jammed) motor can draw dangerously large currents for exactly this reason.
28.
Marking analysis: A learner attempts the following task: “Explain, using Lenz's law, why a spinning electric motor generates a 'back EMF' that opposes the supply voltage driving it, and state what happens to the current drawn by the motor as its speed increases.” Their response addresses only this point: “States that as the motor's coil rotates within the magnetic field, it is itself acting like a generator, so by Faraday's law it induces an EMF.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that as the motor's coil rotates within the magnetic field, it is itself acting like a generator, so by Faraday's law it induces an EMF. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that, by Lenz's law, this induced EMF (back EMF) opposes the applied (supply) voltage that is driving the current in the first place. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that the net driving voltage across the coil's resistance is therefore (supply voltage − back EMF), which decreases as back EMF increases. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: States that since back EMF increases with the motor's rotational speed, the current drawn by the motor decreases as its speed increases. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that as the motor's coil rotates within the magnetic field, it is itself acting like a generator, so by Faraday's law it induces an EMF.
- Identifies the missing requirement: States that, by Lenz's law, this induced EMF (back EMF) opposes the applied (supply) voltage that is driving the current in the first place.
- Identifies the missing requirement: States that the net driving voltage across the coil's resistance is therefore (supply voltage − back EMF), which decreases as back EMF increases.
- Identifies the missing requirement: States that since back EMF increases with the motor's rotational speed, the current drawn by the motor decreases as its speed increases.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
29.
A coil of 80 turns and area 0.012 m² rotates at constant angular speed 25 rad s⁻¹ in a uniform magnetic field of flux density 0.35 T. Its flux linkage is NBA cos(ωt). (a) Determine the maximum induced emf. (b) Calculate the magnitude of the emf when ωt = 30°. (c) The coil is connected to a 6.0 Ω resistor and internal resistance is negligible. Calculate the instantaneous power in the resistor at this angle. (d) State one change that doubles the maximum emf without changing the field.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses Faraday's law to obtain ε = NBAω sin(ωt). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Calculates εmax = 80(0.012)(0.35)(25) = 8.4 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Calculates ε = 8.4 sin 30° = 4.2 V. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Uses P = ε²/R to obtain P = 4.2²/6.0 = 2.94 W (about 2.9 W). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Develop this part of the answer: States a valid change such as doubling the number of turns, coil area, or angular speed. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Differentiate the flux linkage before substituting the angle; maximum flux and maximum induced emf occur a quarter-cycle apart.
Marking points
- Uses Faraday's law to obtain ε = NBAω sin(ωt).
- Calculates εmax = 80(0.012)(0.35)(25) = 8.4 V.
- Calculates ε = 8.4 sin 30° = 4.2 V.
- Uses P = ε²/R to obtain P = 4.2²/6.0 = 2.94 W (about 2.9 W).
- States a valid change such as doubling the number of turns, coil area, or angular speed.
Examiner tip: Differentiate the flux linkage before substituting the angle; maximum flux and maximum induced emf occur a quarter-cycle apart.
30.
Marking analysis: A learner attempts the following task: “A coil of 80 turns and area 0.012 m² rotates at constant angular speed 25 rad s⁻¹ in a uniform magnetic field of flux density 0.35 T. Its flux linkage is NBA cos(ωt). (a) Determine the maximum induced emf. (b) Calculate the magnitude of the emf when ωt = 30°. (c) The coil is connected to a 6.0 Ω resistor and internal resistance is negligible. Calculate the instantaneous power in the resistor at this angle. (d) State one change that doubles the maximum emf without changing the field.” Their response addresses only this point: “Uses Faraday's law to obtain ε = NBAω sin(ωt).” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses Faraday's law to obtain ε = NBAω sin(ωt). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Calculates εmax = 80(0.012)(0.35)(25) = 8.4 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Calculates ε = 8.4 sin 30° = 4.2 V. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Uses P = ε²/R to obtain P = 4.2²/6.0 = 2.94 W (about 2.9 W). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Requirement 5: Identifies the missing requirement: States a valid change such as doubling the number of turns, coil area, or angular speed. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses Faraday's law to obtain ε = NBAω sin(ωt).
- Identifies the missing requirement: Calculates εmax = 80(0.012)(0.35)(25) = 8.4 V.
- Identifies the missing requirement: Calculates ε = 8.4 sin 30° = 4.2 V.
- Identifies the missing requirement: Uses P = ε²/R to obtain P = 4.2²/6.0 = 2.94 W (about 2.9 W).
- Identifies the missing requirement: States a valid change such as doubling the number of turns, coil area, or angular speed.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.