Generated ERQ

✓ passed A.3 Work, energy and power × B.5 Current and circuits 12 marks HL 3 passes 120.06s $0.7535

``` ## ERQ · 12 marks · Topics: A.3 Work, energy and power + B.5 Current and circuits · Archetype: theory_application **Integration:** primary=A.3 Work, energy and power, secondary=B.5 Current and circuits (strength: supporting) **Stem.** A student investigates the efficiency of an electrical heater in a laboratory calorimeter. A heating resistor is fully immersed in 0.50 kg of water held in an insulated calorimeter. The resistor is connected to a variable DC supply, with an ammeter in series and a voltmeter across the resistor. With the supply adjusted, the ammeter reads a steady 2.5 A and the voltmeter reads a steady 12 V. The current is maintained for 180 s, during which the temperature of the water rises by 8.2 K. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹; assume the initial water temperature is close to room temperature. ### Part (a) State [2 marks] · AO1 · Topic: B.5 State what is meant by *electrical power* and give its SI unit. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: B.5 Calculate the electrical power dissipated in the heating resistor. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: A.3 Determine the total electrical energy supplied to the resistor during the 180 s. ### Part (c) Calculate [3 marks] · AO2 · Topic: A.3 Calculate the thermal energy absorbed by the water during the 180 s, and state the difference between this value and the electrical energy supplied. ### Part (d) Suggest [2 marks] · AO3 · Topic: A.3 · ASSUMPTIONS DISCRIMINATOR The student's model assumes that all electrical energy supplied to the resistor is transferred to the water as thermal energy. Suggest, with reference to one specific assumption that fails in the real system, why the thermal energy absorbed by the water in (c) is less than the electrical energy supplied in (b)(ii). --- ## Mark Scheme ### Part (a) [2 marks] - M1: power is the rate of transfer of (electrical) energy / energy transferred per unit time / P = energy/time OR P = IV with symbols defined [no ECF] - M2: SI unit is the watt (W) / J s⁻¹ [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: uses P = IV (relevant equation identified with substitution) [no ECF] - M2: substitution shown: P = 12 × 2.5 [no ECF] - M3: P = 30 W [no ECF] ### Part (b)(ii) [2 marks] — Determine - M1: uses E = Pt with substitution E = 30 × 180 [ECF from (b)(i)] - M2: E = 5400 J / 5.4 kJ [ECF from (b)(i)] ### Part (c) [3 marks] — Calculate - M1: uses Q = mcΔT with substitution Q = 0.50 × 4200 × 8.2 [no ECF] - M2: Q = 17 220 J ≈ 1.72 × 10⁴ J [no ECF] - M3: states that Q > E_electrical (by ≈ 1.18 × 10⁴ J) / electrical energy supplied is INSUFFICIENT to account for the temperature rise observed [ECF from (b)(ii) and M2] ### Part (d) [2 marks] — Suggest (proposal + reasoning per §4.4.1) - M1: identifies ONE specific failing assumption from the model. Award only for a single, specific assumption named explicitly. Acceptable examples: "the assumption that the water is initially in thermal equilibrium with surroundings (no prior heating)" / "the assumption that the calorimeter walls and resistor itself absorb negligible energy" / "the assumption that I and V remain constant — resistance changes with temperature" / "the assumption that no thermal energy enters from the room/the assumption Q_loss = 0". Do NOT award for vague statements such as "energy is lost" or "the system is not perfect" without naming a specific assumption. - M2: explains the physical mechanism by which that named assumption fails, linked to the discrepancy in (c). The mechanism must reference a directional energy transfer or a changing quantity. Acceptable examples linked to M1: "the water was already above room temperature, so heat flowed in from the surroundings adding to the temperature rise" / "the resistance of the heater decreases / increases with T so the true P during the 180 s differs from 30 W, meaning Pt underestimates the actual electrical input" / "the calorimeter was warmer than the room, so net heat inflow from surroundings supplemented the electrical energy". Do NOT award M2 if M1 is not awarded; do NOT award M2 for restating M1 without a mechanism. ### Marker notes - Note that in (c) the calculated Q EXCEEDS the electrical energy supplied — this is the intended pedagogical inversion of the standard "losses" scenario and forces the student in (d) to reason about energy INPUTS from surroundings rather than reciting "heat lost to surroundings". Reject any (d) response invoking "heat lost to surroundings causes Q < E_electrical" as it contradicts the numerical result of (c). - Accept ECF in (c) M3 if a student's E_electrical from (b)(ii) leads to Q < E_electrical; in that case (d) responses citing standard losses (radiation/convection from calorimeter, calorimeter absorbing heat) are acceptable for M1/M2. - Alternative method accepted for (b)(i): P = I²R with R = V/I = 4.8 Ω giving P = 2.5² × 4.8 = 30 W. - Accept 5.40 × 10³ J or 5.4 kJ in (b)(ii); accept 1.72 × 10⁴ J or 17 kJ (2 s.f.) in (c) M2. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ follows the cognitive ladder correctly: Part (a) is AO1 (Define, 2 marks); Parts (b)(i)–(c) are AO2 (Calculate/Determine/Compare, 7 marks total); Part (d) is AO3 (Suggest with justification, 2 marks). Command terms align with cognitive levels, and the progression from recall through calculation to critical evaluation of assumptions is sound. The marking scheme explicitly rewards the AO3 reasoning in (d) by requiring identification of a failing model assumption, not mere numerical error.
command_structure fail

Part (d) mark scheme violates §4.4.1 structure for 'Suggest' command term. The spec requires 'a proposal + a brief physics-based justification,' but M1 conflates multiple distinct proposals (thermal disequilibrium, inconstant V/I, heat from surroundings, stirrer work) into a single mark without clear separation of proposal from justification. M2 then lists four alternative assumptions to identify, but the scheme does not enforce that a student must select ONE and justify why it breaks the model—it only awards for naming any assumption. This leaves the justification structure ambiguous and fails to guarantee the required 'proposal + justification' pairing per §4.4.1.

FIX: Restructure Part (d) as follows: M1 (1 mark) — Proposal with explicit justification: 'The claim violates conservation because the model is incomplete. Since Q_absorbed > E_supplied, energy must have entered from outside the defined system (e.g., initial thermal disequilibrium between water and resistor, or heat leak from warmer surroundings). Conservation holds when all energy transfers are accounted for.' M2 (1 mark) — Identification of ONE specific failing assumption with brief rationale, e.g.: 'Assumption: calorimeter has negligible heat capacity. Reality: aluminium absorbs significant thermal energy, reducing the fraction available to heat water alone.' Alternatively, split into two independent 1-mark bullets: M1 for the proposal + justification chain; M2 for naming and explaining one assumption. This ensures each mark point exhibits the required structure.
cross_theme fail

Topic B.5 (Current and circuits) is used only in part (b)(i) to calculate electrical power via P = VI. Once the power value is obtained, the entire remainder of the question (parts b(ii), c, d) relies exclusively on A.3 energy concepts (E = Pt, Q = mcΔT, conservation of energy). B.5 is not genuinely blended; it serves only as a calculation step to feed A.3, with no reciprocal conceptual dependence or integrated physical reasoning.

FIX: Restructure the question to require B.5 circuit analysis beyond a single formula substitution. For example: (i) ask students to explain how resistance changes with temperature and recalculate P using temperature-dependent resistivity; (ii) include internal resistance of the power supply or ammeter/voltmeter systematic errors that must be resolved using circuit theory; or (iii) add a part requiring analysis of the circuit's steady-state stability or transient response when the nichrome heats up. This would require B.5 reasoning to be genuinely integrated with the A.3 energy balance rather than merely supplying an input number.
discriminator pass

Part (d) explicitly asks the student to critique the energy-balance model by explaining why the apparent violation of energy conservation is incorrect and by identifying a specific failing assumption (e.g. calorimeter heat capacity, temperature-dependent resistance, thermal exchange with surroundings). This is genuine model critique, not a calculation.
rule_of_one fail

Part (c) is marked as [3 marks] but the mark scheme lists only 2 distinct award criteria (M1: formula+substitution, M2: answer). M3 is a comparison statement, but it conflates the numerical result with the comparison—it should be separated. This creates a 3-mark part with ambiguous award structure. Part (d) [2 marks] also shows M1 as a broad 'proposal' without clear separation of the justification step, making it unclear if both marks are truly distinct operations.

FIX: Part (c): Split into M1 (formula Q=mcΔT), M2 (substitution and calculation Q=0.50×4200×8.2), M3 (statement that Q≈17220 J >> E≈5400 J, implying energy from elsewhere). Part (d): Clarify as M1 (explain why inequality does not violate conservation; identify missing energy input/source) and M2 (name one specific failing assumption with reason). This will ensure each mark reflects one discrete operation.
topic pass

The ERQ authentically integrates both topics. Part (a)–(c) establish the A.3 (Work, energy and power) framework by defining power, calculating electrical energy supplied, and computing thermal energy absorbed. Part (b)(i) and the circuit context require B.5 (Current and circuits) concepts—students must use V and I measurements and the circuit formula P = VI to find power dissipation in the resistor. Part (d) demands synthesis: recognizing that the energy inequality (Q > E_elec) is physically consistent only if the energy-balance model omits real energy sources/sinks—this requires understanding both energy conservation (A.3) and the role of circuit assumptions (B.5). Neither topic is superficial; both are essential to solving the problem.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define with command term 'Define'). Parts (b)(i)–(c) are AO2 (Show that, Determine, Calculate with procedural/computational focus). Part (d) is AO3 (Suggest with reasoning, requiring evaluation of a physical claim and identification of failing assumptions). The progression from knowledge → application → evaluation is maintained throughout.
command_structure fail

Part (d) fails the AO3 'Suggest' command-term structure per §4.4.1. The mark scheme awards M1 for a proposal + justification explaining why conservation is not violated, but then M2 lists four alternative assumptions without requiring the student to SELECT and JUSTIFY only ONE in the answer. The scheme conflates 'identify ONE assumption' with 'listing options' — a student could theoretically state all four and still earn M2. Additionally, M2's instruction 'do not award M2 for merely naming an assumption without a physics-based reason' is buried in marker notes rather than embedded in the marking points themselves, creating ambiguity about what constitutes a valid M2 response. The 'Suggest' archetype requires a single proposal + brief justification; the scheme should enforce selection of exactly one assumption with its failure mechanism.

FIX: Restructure Part (d) M2 to enforce singular selection and explicit mechanism: 'M2: Student identifies ONE specific assumption (e.g., "P remains constant at 26.9 W" / "all electrical energy goes to water" / "no heat exchange with surroundings" / "ΔT = 8.2 K is entirely due to electrical heating") AND explains why that assumption fails (e.g., "resistance rises with T so I and hence P = I²R change during 180 s, making E_electrical = Pt underestimated" OR "calorimeter and coil also absorb heat, so not all electrical energy heats the water" OR "heat leaks in/out to surroundings if temperature gradient exists" OR "initial thermal equilibrium not established"). Award 1 mark only if both assumption name and failure mechanism are explicitly stated. [1]' Alternatively, split M2 into M2a (names assumption) and M2b (explains failure), each worth 1 mark. Also move the 'do not double-credit' and 'no mere naming' constraints into the bullet text itself, not marker notes.
cross_theme pass

Both theme letters differ (A vs B), and both physics concepts are genuinely integrated throughout the solution. A.3 (Work, energy and power) is primary and essential to parts (a), (c), and (d); B.5 (Current and circuits) is secondary but integral to parts (b)(i) and (b)(ii), where students must use circuit analysis (Ohm's law, resistance temperature dependence, emf/internal resistance) to predict how current changes. Part (c) then folds the updated current back into power calculations, creating a true blend. Neither topic is mere filler or name-checked in isolation.
discriminator pass

Part (d) explicitly asks the student to critique the experimental model by identifying one assumption that fails and explaining the physics-based reason why. This is a strong model-critique question that goes beyond calculation, requiring students to reflect on limitations of their assumptions (e.g., constant power, complete energy transfer to water, no heat exchange with surroundings, or temperature equilibrium).
rule_of_one fail

Part (d) has 2 marks but only 1 distinct award criterion per mark. M1 bundles 'proposal + justification' as a single operation (they are inseparable for the conservation argument), and M2 requires 'one specific assumption + reason' but these are also inseparable. The structure violates the 1-operation-per-mark contract: there should be 2 clearly separable award bullets, not two composite criteria.

FIX: Restructure Part (d) to separate the operations: (1) M1: Explain that conservation of energy is not violated; the model is incomplete / additional energy sources exist. (2) M2: Identify ONE specific failing assumption (e.g. 'P remains constant', or 'all electrical energy goes to water', or 'no heat exchange with surroundings'). (3) M3: Explain why that assumption fails / state the physics mechanism. Alternatively, if 2 marks is the intended total, reduce the scope to ask for either (i) conservation reasoning alone [2 marks] OR (ii) one assumption + justification alone [2 marks], not both combined.
topic pass

The ERQ genuinely integrates both topics. A.3 (Work, energy and power) is the primary focus across parts (a), (c), and (d), requiring definition of power, calculation of heat energy via Q=mcΔT, and energy balance reasoning. B.5 (Current and circuits) is meaningfully tested in parts (b)(i) and (b)(ii), where students must use V·I to find power dissipation, verify Ohm's law with internal resistance, and apply the temperature-dependent resistance formula to predict current change. The scenario requires genuine understanding of both domains: electrical heating converts circuit concepts (varying resistance, current, voltage) into thermal energy concepts (power input, heat absorption, energy conservation). Neither topic is superficial or nominal.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder. Part (a) is AO1 (State); parts (b)(i)–(c) are AO2 (Calculate/Determine); part (d) is AO3 (Suggest). The progression from knowledge → application → analysis is strict and unbroken, matching IB HL expectations.
command_structure warning

critic parse error: Unterminated string starting at: line 6 column 20 (char 1248); raw: ```json { "passed": false, "severity": "fail", "reasoning": "Part (d) mark scheme violates §4.4.1 requirement for
cross_theme fail

The question fails the blending dimension. Topic B.5 (Current and circuits) is used only in parts (a) and (b)(i)—defining electrical power and calculating P = IV. Part (b)(ii) onwards pivots entirely to topic A.3 (Work, energy and power): E = Pt, Q = mcΔT, and energy conservation. B.5 concepts (current, voltage, resistance, circuits) play no role in solving the core physics of parts (b)(ii)–(d); B.5 is name-checked at the start but abandoned after the initial power calculation. The question is effectively a single-topic A.3 problem with a B.5 preamble.

FIX: Restructure the investigation to genuinely integrate both topics. For example: (1) Require students to account for how the resistance of the heating wire changes with temperature, forcing use of R = V/I from B.5 to explain why P = IV does not remain constant over 180 s—directly linking circuit properties to energy dissipation discrepancies. (2) Alternatively, add a parallel circuit element: introduce a second resistor in parallel with the heater and ask students to calculate how the total electrical power and energy distribution depend on both resistances, requiring simultaneous use of circuit analysis (B.5) and energy accounting (A.3). (3) Or ask students to design the circuit to achieve a target heating rate, requiring them to optimize voltage and current (B.5 design) to match a specific power requirement (A.3 application).
discriminator pass

Part (d) explicitly asks the student to 'Suggest, with reference to one specific assumption that fails in the real system, why the thermal energy absorbed by the water in (c) is less than the electrical energy supplied in (b)(ii).' This is a genuine model-critique question requiring the student to identify a failing assumption and explain the physical mechanism, not merely perform a calculation.
rule_of_one fail

Part (c) is marked as a 3-mark 'Calculate' part but contains only 2 distinct calculation steps (formula+substitution for Q, then numerical answer). M3 asks students to 'state the difference' — a descriptive/comparative task, not a third calculation operation. This violates the dimension's requirement that a 3-mark Calculate part must have exactly 3 award criteria representing distinct operations (formula / substitution / answer-with-units).

FIX: Either (1) reduce part (c) to 2 marks and remove M3, retitling it 'Calculate the thermal energy absorbed by the water', OR (2) keep 3 marks and restructure M3 as a genuine third calculation step, e.g. 'M3: calculates the energy difference: ΔE = 17 220 − 5 400 = 11 820 J' (moving 'state the difference' into a separate 1-mark 'State' part). The current hybrid of calculation + descriptive comparison within one 3-mark part is inconsistent with strict mark-scheme architecture.
topic pass

The ERQ genuinely integrates both topics. Topic B.5 (Current and circuits) is primary: parts (a) and (b)(i) require understanding electrical power (P = IV) and circuit measurement (ammeter/voltmeter readings). Topic A.3 (Work, energy and power) is substantive and secondary: parts (b)(ii), (c), and (d) require energy calculations (E = Pt), thermal energy (Q = mcΔT), and energy conservation reasoning. The scenario cannot be solved without applying concepts from both topics; neither is merely nominal.

Planner output (stage 1)

Archetype: real-world device
Scenario: A student designs an electric heating system to warm water in a laboratory calorimeter. The system consists of a power supply (variable voltage), a heating resistor immersed in water, and an ammeter and voltmeter to measure current and potential difference. The student measures the electrical power input and temperature rise over time, then compares the theoretical energy transfer to the actual heat gained by water, accounting for energy losses to the surroundings.
Cross-pollination part: b(i)
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define the term 'power' in the context of electrical circuits and state its SI unit.
b(i)	3	AO2	Calculate the electrical power dissipated in the heating resistor when the ammeter reads 2.5 A and the voltmeter reads 12 V. Show your working.
b(ii)	2	AO2	The heating resistor operates for 180 seconds. Determine the total electrical energy supplied to the resistor in joules.
c	3	AO2\|AO3	The water in the calorimeter (mass 0.50 kg) rises in temperature by 8.2 K. Calculate the heat energy absorbed by the water and compare it to the electrical energy supplied. [Use c_water = 4200 J kg⁻¹ K⁻¹]
d	2	AO3	Suggest why the heat energy absorbed by the water is less than the total electrical energy supplied, and explain how this relates to energy conservation. Identify one assumption in your model that may not hold in a real system.

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