Generated ERQ

✓ passed A.3 Work, energy and power × B.5 Current and circuits 10 marks SL 3 passes 100.93s $0.6432

## ERQ · 10 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 portable electric heater is connected to a household mains supply of 230 V. The heater contains a single resistive element and is labelled "2.00 kW at 230 V". When switched on, the element warms a small room, and the manufacturer claims that the heater transfers thermal energy to the surrounding air at a constant rate equal to its rated power. A student uses the heater for 15 minutes and treats the heater as a closed system that converts all electrical energy directly into thermal energy delivered to the room air. The resistance of the element at its normal working temperature is to be taken as constant in parts (a)–(c). ### Part (a) Define [2 marks] · AO1 · Topic: A.3 Work, energy and power Define *power* and state its SI unit. ### Part (b) Calculate [3 marks] · AO2 · Topic: A.3 Work, energy and power Using the manufacturer's claim, calculate the thermal energy, in MJ, delivered to the room air during the 15-minute period. ### Part (c) Show that [3 marks] · AO2 · Topic: A.3 Work, energy and power + B.5 Current and circuits The heater is connected directly to the 230 V mains supply. Show that the resistance of the heating element at its working temperature is about 26 Ω. ### Part (d) Discuss [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The calculation in part (b) assumes the heater delivers thermal energy to the room air at a constant rate of 2.00 kW from the instant it is switched on. Discuss one reason why this assumption is not realistic, and comment on whether your answer in (b) is an overestimate or an underestimate of the actual thermal energy delivered to the air. --- ## Mark Scheme ### Part (a) [2 marks] — Define - M1: Power is the rate of doing work / rate of energy transfer (per unit time) [no ECF] - M2: SI unit is the watt (W) OR J s⁻¹ [no ECF] ### Part (b) [3 marks] — Calculate - M1: Recognises E = Pt with correct conversion t = 15 × 60 = 900 s [no ECF] - M2: Substitution: E = 2000 × 900 [ECF from (a) not applicable] - M3: E = 1.80 × 10⁶ J = 1.80 MJ (accept 1.8 MJ) [no ECF] ### Part (c) [3 marks] — Show that - M1: Identifies P = V²/R (or equivalent route via P = VI and V = IR) [no ECF] - M2: Rearranges to R = V²/P and substitutes: R = (230)² / 2000 [no ECF] - M3: R = 26.45 Ω ≈ 26 Ω (student-derived value must lie in 26.4–26.5 Ω before rounding) [no ECF] ### Part (d) [2 marks] — Discuss (model critique: limitation + implication for (b)) *Pathway A — transient warm-up of element:* - M1a: Identifies that when switched on, the element is cold and must itself absorb thermal energy before reaching working temperature, so not all electrical energy is delivered to the air at the rated rate from t = 0 / the assumption of constant 2.00 kW transfer to the air from switch-on is invalid - M2a: Therefore the answer in (b) is an **overestimate** of the thermal energy actually delivered to the air during the 15 minutes (some energy is stored as internal energy of the element) *Pathway B — temperature dependence of resistance:* - M1b: Identifies that the resistance of the element is lower when cold than when hot, so the initial electrical power dissipated P = V²/R exceeds 2.00 kW (or, the rated 2.00 kW only applies at working temperature, not throughout) - M2b: Therefore the answer in (b) is an **underestimate** of the thermal energy delivered, because the heater dissipates more than 2.00 kW during the warm-up phase *Pathway C — heat losses through casing / conduction to surroundings other than room air:* - M1c: Identifies that some thermal energy is transferred to the casing, walls, or lost by conduction rather than being delivered to the room air, so the heater is not a perfectly closed system delivering all energy to the air - M2c: Therefore the answer in (b) is an **overestimate** of the thermal energy delivered specifically to the room air Award M1 for any one valid limitation of the constant-2.00-kW-to-air model AND M2 for the matching directional comment on (b)'s validity. M2 is only awarded if it is consistent with the M1 mechanism chosen. ### Marker notes - Alternative method accepted for (c): P = VI gives I = 2000/230 = 8.70 A, then R = V/I = 230/8.70 = 26.4 Ω. - Show-that target in (c): R = 26.45 Ω given to 4 sig figs; student-derived 26.4–26.5 Ω acceptable before rounding to 26 Ω. - (d) accept any one of the three pathways above; do not award M2 if the direction of the error contradicts the mechanism in M1. - Do not credit vague statements such as "the heater is not 100% efficient" without identifying where the energy goes or why the rate is not constant.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) AO1 Define with command term 'Define'; (b) AO2 Calculate with command term 'Calculate'; (c) AO2 Show that with command term 'Show that'; (d) AO3 Suggest with command term 'Suggest'. The progression from recall→application→analysis→evaluation is properly sequenced, and all command terms align with their intended cognitive levels.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 structure for 'Suggest'. The command term requires 'a proposal + a brief physics-based justification,' but M1 and M2 are not clearly separated into these two components. M1 conflates the proposal with partial justification (using 'so' and 'OR'), and M2 restates and expands the same reasoning rather than providing distinct justification. The structure should have M1 = clear proposal statement alone, and M2 = explicit physics warrant linking to a principle (e.g., P = V²/R).

FIX: Restructure Part (d) M1 and M2 as follows: M1 (proposal): 'When first switched on, the cold element has resistance 22 Ω, which is lower than its steady operating resistance of ~26 Ω.' M2 (physics-based justification): 'Since P = V²/R and V is constant, lower resistance means higher initial power dissipation. Alternatively, some of the initial electrical energy is absorbed by the element to raise its temperature rather than transferred to the room air, so the rate of thermal transfer to the air is initially lower than the 2.00 kW assumption.' Marker note should clarify that either mechanism (higher initial P, or diversion of energy to element warm-up) is acceptable, but the proposal and justification must be logically distinct.
cross_theme pass

Both A.3 (Work, energy and power) and B.5 (Current and circuits) are genuinely integrated throughout the question. Part (c) explicitly requires the circuit relationship P = V²/R to calculate resistance, and part (d) uses the physical consequence of resistance change (from 22 Ω to 26 Ω) to explain why power delivery varies, linking circuit behavior directly to energy transfer. Neither topic is merely name-checked; both are essential to solving the problem.
discriminator pass

Part (d) explicitly asks the student to 'Suggest, with reference to the resistance values given in the stem, why the actual thermal energy transferred to the air during the first few seconds of operation differs from the value calculated in (b).' This is a clear model-critique question: it asks the student to identify and justify a limitation of the assumption that power remains constant at 2.00 kW throughout operation. The student must recognize that the model's assumption breaks down due to the resistance change and warm-up transient, satisfying the dimension's requirement for critique of modeling assumptions.
rule_of_one fail

Part (d) has 2 marks but only 1 distinct operation listed in each bullet. The mark scheme describes a proposal + justification structure, but M1 and M2 are not independent award criteria with separate operations—they are two components of a single evaluative judgment. For a 2-mark 'Suggest' question, we need 2 separable operations (e.g., identify phenomenon + explain consequence), not a single integrated response. The scheme conflates the two marks into one holistic rubric rather than two discrete checkpoints.

FIX: Restructure Part (d) mark scheme to separate two distinct operations: (M1) Identify that cold resistance (22 Ω) is lower than operating resistance (~26 Ω), OR recognize that the element must absorb energy to warm up. (M2) Explain the consequence: either initial current/power is higher than rated value (since P = V²/R increases as R decreases), OR initial thermal energy transfer to air is less than steady-state because energy goes into heating the element itself. This ensures each mark corresponds to one independent award point.
topic pass

The ERQ successfully tests both A.3 (Work, energy and power) and B.5 (Current and circuits) through genuine integration, not superficial mention. Part (c) requires applying P = V²/R (circuits concept) to calculate resistance at steady state; part (d) explicitly demands reasoning about how the resistance change (B.5) affects initial power dissipation and energy distribution (A.3). The scenario's physics demands understanding of both topics working together.

Iteration 1 — failed

ao_ladder pass

The ERQ strictly obeys the cognitive ladder. Part (a) is AO1 (Define—lowest tier); parts (b) and (c) are AO2 (Calculate/Show that—middle tier); part (d) is AO3 (Suggest with physics justification—highest tier). Complexity and command terms progress logically from recall through procedural application to reasoned explanation.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 'Suggest' structure. The scheme provides two acceptable M1 proposals but does not explicitly pair each with its corresponding M2 justification. The wording 'the M2 justification must match the chosen M1 mechanism' is a compliance instruction, not a marking point structure. The mark scheme must exhibit clear 'proposal + physics-based justification' pairing(s) as explicit bullet structures, not as conditional instructions to markers.

FIX: Restructure Part (d) to show two distinct M1–M2 pairs, each self-contained: *Pathway A:* M1a (proposal: resistance is lower at start) → M2a (justification: P = V²/R, so lower R yields higher initial power). *Pathway B:* M1b (proposal: energy diverted to heating element itself) → M2b (justification: by energy conservation, rate to air = electrical power − dU_element/dt, so initially rate to air < 2.00 kW). Then award M1 for either pathway AND M2 for the corresponding justification. Alternatively, rewrite as a single integrated M1 (both mechanisms stated together) + M2 (single overarching justification), but the current conditional-instruction format does not satisfy §4.4.1's explicit structure requirement.
cross_theme pass

Both A.3 (Work, energy and power) and B.5 (Current and circuits) are genuinely integrated throughout the question. Part (c) requires both P = V²/R (circuits) and energy principles (work/energy) to derive the resistance. Part (d) explicitly uses both conceptual frameworks: resistance temperature-dependence (circuits) and energy conservation/thermal transfer (work and energy). The topics are not merely name-checked; they are functionally intertwined in solving the problem.
discriminator fail

Part (d) is the final section and nominally asks students to 'suggest why' the thermal transfer rate differs from the assumed constant 2.00 kW. However, this is fundamentally a mechanism-identification and justification task (AO3), not a model-critique question. It asks students to explain a real-world deviation from the idealized assumption, but does not ask them to evaluate, critique, or discuss limitations of the model itself — e.g. 'Discuss why treating the heater as delivering constant power is unrealistic', 'Explain one limitation of the assumption that...', or 'Suggest how the model could be improved'. The question stops at explaining the physics of the deviation rather than stepping back to evaluate the validity or assumptions of the original model.

FIX: Revise part (d) to include explicit model critique. For example: 'Part (d) Discuss [2 marks] · The calculation in (b) assumes the heater delivers thermal energy at a constant rate of 2.00 kW from switch-on. Discuss one reason why this assumption is not realistic, and explain how this affects the validity of your answer to part (b).' This pushes students to not just explain the physics of transient behavior, but to reflect on whether and how the constant-power assumption breaks down and what implications that has.
rule_of_one pass

Each part's mark count matches its award-bullet count: (a) 2 marks / 2 bullets, (b) 3 marks / 3 bullets (formula, substitution, answer-with-units), (c) 3 marks / 3 bullets (formula, substitution, answer), (d) 2 marks / 2 bullets (proposal, justification). The scheme is internally consistent and meets the dimension requirement.
topic pass

The ERQ substantively tests both topics. Part (c) and (d) explicitly require knowledge from both A.3 (power, energy transfer) and B.5 (resistance, circuit relationships P=V²/R, Ohm's law). Part (c) uses the circuit relation P=V²/R to find resistance at operating temperature, while part (d) requires understanding how changing resistance affects power dissipation and energy balance—both concepts are genuinely integrated, not superficial.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) is AO1 with Define; (b) is AO2 with Calculate; (c) is AO2 with Show that; (d) is AO3 with Discuss. Each tier is appropriately sequenced and command terms match the required objectives.
command_structure fail

Part (d) fails the AO3 Discuss requirement. The mark scheme provides three separate pathways (A, B, C) but does not exhibit the mandatory structure for Discuss: at least two perspectives or trade-offs presented within a single coherent response frame. Instead, it offers a choice of one pathway only. Additionally, the 'marker notes' instruction 'accept any one of the three pathways' directly contradicts the IB v5 §4.4.1 requirement that Discuss must evaluate multiple viewpoints/considerations simultaneously. The structure treats this as a selective checklist rather than a genuine multi-perspective discussion.

FIX: Restructure Part (d) to require students to identify and discuss at least two competing/interacting limitations (e.g., Pathway A vs Pathway B: cold-element warm-up causing underestimation of initial power vs. resistance temperature dependence causing overestimation of steady-state power). The mark scheme should then require M1 to present both perspectives, M2 to weigh their relative significance, and M3 to conclude with a net directional comment on (b)'s validity. Alternatively, reframe (d) as an Evaluate question (position + supporting + limiting consideration) if only one mechanism is intended. Keep the three pathways as valid exemplars in 'marker notes' but require the response structure itself to address trade-offs between at least two named physical effects.
cross_theme pass

Both A.3 (Work, energy and power) and B.5 (Current and circuits) are genuinely integrated. Part (c) requires the student to use the power formula P = V²/R (or P = VI combined with Ohm's law), which is a core B.5 concept, to calculate the resistance of the heating element. This calculation is essential to the problem structure, not merely mentioned in passing. Part (b) uses A.3 concepts (E = Pt) to find the thermal energy, and parts (a)–(c) collectively demand understanding of both energy transfer rates and electrical circuit behaviour. The themes A and B are distinct, and both physics concepts are functionally used in solving the problem.
discriminator pass

Part (d) explicitly requires the student to critique the constant-power assumption by discussing one reason why it is not realistic and commenting on whether the answer in (b) is an overestimate or underestimate. This is a clear model-critique dimension that goes beyond calculation, examining limitations and their quantitative implications.
rule_of_one pass

Each part's mark count aligns with its award criteria count: (a) 2 marks / 2 bullets, (b) 3 marks / 3 bullets, (c) 3 marks / 3 bullets, (d) 2 marks / 2 bullets per pathway. The scheme is rigorous and well-structured.
topic pass

The ERQ genuinely integrates both topics. Parts (a)–(b) develop A.3 (power definition, energy calculation via E = Pt). Part (c) explicitly requires B.5 concepts: it mandates use of the power–resistance relationship (P = V²/R or equivalent) derived from circuit theory (Ohm's law, P = VI), which cannot be solved without understanding current and circuits. Part (d) enriches the model critique by considering physical realism (warm-up transients, resistance temperature-dependence, heat losses), all grounded in the interplay between electrical power input and thermal energy transfer. Neither topic is nominal or superficial.

Planner output (stage 1)

Archetype: real-world device
Scenario: A portable electric heater draws current from a household mains supply. The heater's resistance element converts electrical energy into thermal energy over a specified time period. Students must analyse the energy transfer using both mechanical work–energy principles and electrical circuit concepts, then evaluate assumptions about power dissipation in a practical scenario where resistance may vary with temperature.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define
b	3	AO2	Calculate
c	3	AO2	Show that
d	2	AO3	Suggest

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