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Worked Examples by MYP Criterion

The following worked examples are organised according to the four MYP Sciences Assessment Criteria. Each example demonstrates the type of thinking and communication expected at each level. Click a criterion tab to explore the example and mark scheme.

A
Criterion A: Knowing and Understanding
Recalling, defining, selecting, and applying formulae to solve structured problems

A1 — Finding Power from Voltage and Current

Problem
An electric iron operates at a mains voltage of 220 V and draws a current of 6.5 A. Calculate the power consumed by the iron and identify the energy conversion that takes place.
1
Identify knowns: V = 220 V, I = 6.5 A. Required: P.
2
Select formula: P = I × V (current and voltage both known).
3
Substitute: P = 6.5 A × 220 V.
4
Calculate: P = 1 430 W = 1.43 kW.
5
Energy conversion: Electrical energy → thermal (heat) energy. The resistance of the iron's heating element converts electrical work into heat via the Joule effect.
✓ P = 1 430 W (1.43 kW)  |  Conversion: Electrical → Thermal
▸ Mark Scheme
  • Correct formula stated: P = IV [1]
  • Correct substitution with units: P = 6.5 × 220 [1]
  • Correct answer: 1 430 W (accept 1.43 kW) [1]
  • Correct energy conversion identified [1]

A2 — Using P = I²R (Joule Heating)

Problem
A resistor of resistance 40 Ω carries a current of 3.5 A. Calculate: (a) the power dissipated, and (b) the heat energy produced in 5 minutes.
1
Part (a): P = I²R = (3.5)² × 40 = 12.25 × 40 = 490 W.
2
Part (b) — Convert time: t = 5 min = 5 × 60 = 300 s.
3
Calculate energy: W = P × t = 490 W × 300 s = 147 000 J (147 kJ).
✓ P = 490 W  |  Heat energy = 147 000 J = 147 kJ
▸ Mark Scheme
  • Formula P = I²R stated [1]
  • Correct squaring of current: (3.5)² = 12.25 [1]
  • P = 490 W [1]
  • Time correctly converted to seconds: 300 s [1]
  • W = 147 000 J (accept 147 kJ) [1]
B
Criterion B: Inquiring and Designing
Formulating research questions, hypotheses, and experimental designs with variables and methods

B1 — Designing an Experiment to Verify P = IV

Research Question
How does the electrical power dissipated in a resistor change as the voltage across it is varied from 2 V to 12 V, when the resistance remains constant?

Hypothesis: If the voltage across a fixed resistor is increased, then the power dissipated will increase proportionally according to P = V²/R. Specifically, doubling the voltage should quadruple the power, since P ∝ V². The graph of P vs. V will be a parabola (non-linear, increasing).

Variables:

  • Independent: Voltage across the resistor (V), varied from 2 V to 12 V in steps of 2 V.
  • Dependent: Power dissipated (W), calculated from P = I × V after measuring current.
  • Controlled: Resistance value (fixed resistor, e.g. 10 Ω), room temperature, wire gauge, circuit connections.

Equipment: Variable DC power supply (0–15 V), fixed resistor (10 Ω ± 5%, 10 W rated), digital ammeter (range 0–2 A), digital voltmeter (range 0–15 V), connecting wires, switch.

Method (summary):

1
Connect the resistor in series with the ammeter; connect the voltmeter in parallel across the resistor. Include a switch for safety.
2
Set the power supply to 2 V. Close the switch. Record the voltmeter reading (V) and ammeter reading (I). Calculate P = IV.
3
Open the switch. Increase voltage to 4 V. Repeat step 2. Continue up to 12 V in 2 V increments.
4
Repeat the entire trial three times and average the results to improve reliability.
5
Plot P (y-axis) vs. V² (x-axis). A straight line through the origin would confirm P = V²/R.
⚠️
Safety: Do not exceed the rated power of the resistor. Keep current below 2 A. Open the switch between readings to prevent overheating. Never touch the resistor while current flows.
▸ Mark Scheme
  • Focused, testable research question formulated [2]
  • Prediction/hypothesis linked to formula with justification [2]
  • All three variables correctly identified and described [2]
  • Sufficient, appropriate equipment listed [2]
  • Method sufficient to collect reliable data (repeats, range) [2]
  • Safety consideration specific to the experiment [1]
  • Graphical linearisation strategy noted (P vs V²) [1]
C
Criterion C: Processing and Evaluating
Collecting, processing, and interpreting data; identifying errors and drawing valid conclusions

C1 — Analysing Experimental Data

Scenario
A student conducted the experiment from B1 with a 10 Ω resistor and obtained the data below. Analyse the results, calculate P for each trial, identify any anomalous results, and draw a conclusion comparing with the theoretical value.

Table C1.1 — Raw Data: Voltage, Current, and Calculated Power

V (V)I₁ (A)I₂ (A)I₃ (A)Ī (A)P = IV (W)P_theory = V²/R (W)% Error
2.00.200.210.200.200.400.400.0%
4.00.400.390.400.401.601.600.0%
6.00.590.600.610.603.603.600.0%
8.00.770.780.790.786.246.402.5%
10.00.950.940.820.97*9.7010.003.0%
12.01.181.191.181.1814.1614.401.7%

* I₃ at 10 V = 0.82 A is anomalous; excluded from mean. Mean recalculated from I₁ and I₂ only.

Anomalous result: The reading I₃ = 0.82 A at 10 V is significantly below the other two trials (0.95 and 0.94 A). This was excluded from the mean because it lies more than 10% from the average of the other trials. A possible cause is a loose connection during that trial.

Trend: Power increases with voltage in a non-linear (parabolic) fashion, consistent with P = V²/R. When voltage doubled from 2 V to 4 V, power quadrupled from 0.40 W to 1.60 W, confirming P ∝ V².

Percentage error analysis: Errors increase at higher voltages (8–12 V), likely due to the resistance of the resistor increasing slightly as it heats up — a systematic effect not controlled in this experiment.

✓ Conclusion: Results support P = V²/R. Experimental power values agree within 3% of theoretical values for most readings. Anomalous result at 10 V, Trial 3 was identified and excluded. The relationship P ∝ V² was confirmed.
▸ Mark Scheme
  • Mean current correctly calculated for each voltage [2]
  • Anomalous result identified (0.82 A) and excluded with justification [2]
  • P = IV correctly calculated for each row [2]
  • % error calculated and compared to theoretical values [2]
  • Trend correctly described as parabolic / P ∝ V² [2]
  • Conclusion supported by specific data values [1]
  • Limitation identified (resistance increases with temperature) [1]
D
Criterion D: Reflecting on the Impacts of Science
Evaluating societal, environmental, and ethical dimensions of scientific knowledge and its applications

D1 — Extended Response: Power, Energy and Society

Essay Question (12 marks)
Evaluate how an understanding of electrical power and energy consumption can help individuals and governments make decisions that are both economically and environmentally responsible. Refer to the physics principles of P = IV and W = Pt, and discuss at least one real-world context with specific reference to Kazakhstan.

Model Response (extract):

An understanding of electrical power — defined as the rate of energy transfer (P = IV) — is foundational to energy literacy. When consumers recognise that a device's power rating in watts represents continuous joule consumption per second, they can calculate true running costs using W = Pt. For example, leaving a 2 kW panel heater running for 8 hours daily consumes 16 kWh. At Kazakhstan's 2025 residential tariff of approximately 30.56 KZT/kWh, this amounts to 489 KZT per day, or roughly 14,700 KZT per month — a significant household expense during Kazakh winters.

At the governmental level, the physics principle P = I²R reveals why high-voltage power transmission is economically critical. For a fixed power output P, increasing transmission voltage reduces current I. Since power loss in transmission lines equals I²R, even a tenfold increase in voltage reduces line losses by a factor of one hundred. Kazakhstan's national grid operator KEGOC transmits electricity at up to 1,150 kV — one of the highest transmission voltages in the world — precisely to minimise these losses across the country's vast territory (spanning over 2,700 km east to west).

From an environmental perspective, understanding that fossil fuel power plants convert chemical energy to electrical energy at roughly 35–45% efficiency — the rest being dissipated as waste heat (W = I²Rt at power station level) — motivates the transition to renewable sources. Kazakhstan, which generated 89% of its electricity from fossil fuels in 2022, has committed to raising its renewable share to 15% by 2030. Citizens who understand the physics of power loss, efficiency, and energy costing are better positioned to support such policy transitions.

The ethical dimension involves equity: Kazakhstan's electricity tariffs are among the world's lowest (37% of the global average), a result of historical state subsidies. While this makes energy accessible, it reduces the incentive to conserve electricity — illustrating how physics knowledge, economic policy, and social values are inseparable in the challenge of sustainable energy management.

✓ This response demonstrates: physics principles cited correctly (P = IV, I²R, W = Pt) | real-world connection to Kazakhstan | societal and environmental impact discussed | ethical dimension addressed | scientific vocabulary used throughout.
▸ Mark Scheme
  • Correct and relevant use of at least two physics formulae [2]
  • Clear link between physics and a societal/economic impact [2]
  • Specific reference to Kazakhstan with accurate context [2]
  • Environmental dimension discussed with scientific reasoning [2]
  • Ethical dimension addressed (equity, policy, responsibility) [2]
  • Response is structured, uses scientific vocabulary, and is evidence-based [2]

4

Interesting Facts — The World

🌩️ Natural Power
A Lightning Bolt Delivers ~1 Billion Joules

A single lightning discharge lasts only 1–2 milliseconds yet delivers approximately 10⁹ J of energy. This corresponds to an instantaneous power exceeding 500 gigawatts — roughly half the total electrical generating capacity of the United States, released in an instant.

1
🧠 Biology vs. Technology
Your Brain Runs on 20 Watts

The human brain — capable of consciousness, creativity, and complex reasoning — operates on roughly 20 W. The world's most powerful AI supercomputers consume 20–100 megawatts to approach a fraction of the brain's capability, making the brain arguably the most power-efficient information processor known.

2
⚡ Engineering History
The War of Currents (1880s)

Edison promoted direct current (DC); Tesla championed alternating current (AC). AC won because transformers can step up voltage for long-distance transmission, reducing I²R losses. This is pure physics: a 10× voltage increase reduces current 10-fold and line losses 100-fold. The principle is unchanged in today's grids.

3
☀️ Solar Energy
Earth Receives 1361 W per Square Metre

The solar constant (power delivered by sunlight at Earth's orbit) is 1,361 W/m². A commercial solar panel at 22% efficiency generates ~300 W/m². In theory, covering 500 km × 500 km of the Sahara with such panels would meet total global electricity demand — a striking demonstration of P = power density × area.

4
🏭 Industrial Scale
The Three Gorges Dam: 22.5 Gigawatts

The world's largest power station — China's Three Gorges Dam — has an installed capacity of 22,500 MW. Running at full capacity for one hour, it generates 22,500 MWh = 22.5 million kWh. At the 2025 Chinese residential rate (~0.08 $/kWh), that hour of output is worth approximately $1.8 million.

5
🔬 James Watt's Legacy
1 Horsepower = 746 Watts

James Watt defined "horsepower" to market his steam engines to customers familiar with horses. He calculated that a mill horse could lift 33,000 foot-pounds of weight per minute. When the SI unit of power was introduced in 1960, it was named the watt in his honour: 1 W = 1 J/s.

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5

Focus on Kazakhstan 🇰🇿

🏔️
Why Kazakhstan? As the ninth-largest country by area, Kazakhstan faces unique challenges in electricity generation, transmission across vast distances, and transitioning from a coal-dominated energy mix. Understanding electrical power is directly relevant to national policy, household budgets, and environmental goals.
💡 Tariffs 2025
Among the World's Lowest Electricity Prices

Kazakhstan's residential electricity tariff is approximately 30.56 KZT/kWh (~$0.061) as of 2025 — just 37% of the global average. This low price is partly a legacy of Soviet-era subsidies and abundant coal reserves. While affordable for households, it historically reduced incentives for energy efficiency, making physics literacy even more important for informed consumption.

1
📈 Rising Tariffs
26% Increase in One Year (2024)

Despite being low globally, electricity prices in Kazakhstan rose by nearly 26% in 2024 — with North Kazakhstan (+20%) and East Kazakhstan (+19.8%) among the hardest-hit regions. New maximum tariffs were approved for 2026–2032, with production costs ranging from 9.40 to 23.25 KZT/kWh depending on the power station. This makes understanding kWh consumption increasingly relevant for Kazakh households.

2
⏰ Time Zone Decision
One Nation, One Time Zone (March 2024)

On 1 March 2024, Kazakhstan merged its two time zones (UTC+5 and UTC+6) into a single UTC+5. For Astana and Almaty, clocks moved back one hour. Scientists from the Fesenkov Astrophysical Institute and the Institute of Genetics and Physiology supported the change, citing biological rhythm benefits. However, a Demoscope poll in December 2024 found 53% of Kazakhstanis opposed the change, citing darker mornings, disrupted sleep, and economic disruption.

3
⚡ Physics + Time Zones
How UTC Affects Electricity Demand

The time zone change has a direct electrical power consequence: when clocks in Astana moved back one hour, morning darkness now extends further into working hours. Studies in chronobiology suggest artificial lighting demand increases, adding load to the power grid during peak hours. This illustrates how a political decision — shifting time zones — has a measurable impact on electrical power consumption patterns, directly governed by P = IV in millions of circuits simultaneously.

4
🏭 Power Generation
Coal Dominates at 75.86 TWh (2024)

Kazakhstan produced the majority of its electricity from coal in 2024, with thermal power stations in Ekibastuz generating over 9.3 billion kWh in Pavlodar region alone — 60.7% of national output from just three regions. Ekibastuz GRES-1, one of the world's largest coal power stations, operates at up to 4,000 MW installed capacity — a figure directly calculable as P = 4,000,000 W.

5
🌱 Green Transition
Target: 15% Renewables by 2030

Kazakhstan has committed to raising its renewable energy share to 15% of generation by 2030 (from ~10.9% in 2023: wind 1.51%, solar 1.41%, hydro 8.00%). Clean energy investment reached $1.32 billion in 2024 — a 213% increase from 2023. The physics of solar and wind power (P = power density × area × efficiency) underpins all renewable energy calculations.

6

Worked Application — Calculating a Kazakh Electricity Bill

Real-World Problem
A family in Astana uses the following appliances in January (heating season): Calculate the total monthly electricity cost using the 2025 Astana residential tariff of 30.56 KZT/kWh.
1
Heater: E = 2.0 kW × 10 h × 30 days = 600 kWh
2
Lighting: E = 0.08 kW × 6 h × 30 = 14.4 kWh
3
Refrigerator: E = 0.15 kW × 24 h × 30 = 108 kWh
4
TV/devices: E = 0.20 kW × 5 h × 30 = 30 kWh
5
Total: 600 + 14.4 + 108 + 30 = 752.4 kWh/month
6
Cost: 752.4 kWh × 30.56 KZT/kWh = 22,993 KZT ≈ 23 000 KZT/month
✓ Monthly consumption: 752.4 kWh  |  Monthly cost: ≈ 22 993 KZT (~$46 USD)  |  The heater alone accounts for 79.7% of the bill.

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Interactive Simulations

Simulations allow you to explore the relationships between electrical quantities in a risk-free environment. Use the embedded simulation below, then explore the linked external resources for deeper investigation.

Embedded Simulation — Ohm's Law & Power Visualiser

Adjust the sliders to change voltage and resistance. The simulation will calculate current, power, and display a real-time energy meter. The glowing bulb intensity reflects actual power.

⚡ Interactive Circuit: Power & Energy Visualiser — Adjust sliders to explore

External Simulation Resources

🔬
Circuit Construction Kit: DC — PhET Interactive
University of Colorado Boulder · phet.colorado.edu
Free

Build and test DC circuits using virtual batteries, resistors, bulbs, and switches. Attach an ammeter and voltmeter to measure current and voltage, then calculate power and energy. Ideal for verifying P = IV experimentally in a virtual lab. Works on Chromebook, PC, iPad, and tablet.

🔗 Open in PhET (DC Circuit Kit)
🔌
Circuit Construction Kit: DC Virtual Lab
University of Colorado Boulder · phet.colorado.edu
Free

The advanced virtual lab version lets you explore non-ohmic bulbs, fuses, and switches alongside ideal resistors. Graph current and power in real time. Perfect for Criterion C investigations where you need to collect data from multiple voltage settings.

🔗 Open PhET DC Virtual Lab
🌊
Ohm's Law — PhET Interactive
University of Colorado Boulder · phet.colorado.edu
Free

A focused simulation showing the relationship between voltage, current, and resistance using a live formula triangle and dynamic dial displays. Excellent for visualising how changing one variable affects the others — the foundation for understanding all power formulas.

🔗 Open Ohm's Law Simulation
🏠
Energy Skate Park (Power & Energy Transfer)
University of Colorado Boulder · phet.colorado.edu
Free

Though primarily a mechanics simulation, the Energy Skate Park elegantly shows energy transformation and conservation — directly analogous to how electrical energy converts to thermal, light, or mechanical energy in a circuit. Use it to deepen your understanding of energy as a universal quantity.

🔗 Open Energy Skate Park
💡
Simulation Activity Suggestion: Using the PhET DC Circuit Kit, build a circuit with a 12 V battery and a resistor of 6 Ω. Measure I using the ammeter, calculate P = IV, then verify using P = V²/R. Change the resistance to 3 Ω and observe how power doubles. Record all data in a table — this directly supports a Criterion C investigation.

7

Chapter Review

Key Concepts Summary

ConceptCore FormulaUnitKey Insight
Electrical WorkW = QV = IVtJoule (J)Energy is transferred by charge moving through a potential difference
Electrical PowerP = IVWatt (W)Rate of energy transfer; 1 W = 1 J per second
Joule HeatingP = I²RWatt (W)Power dissipated as heat increases with I²; doubling I quadruples heat
Voltage-PowerP = V²/RWatt (W)Power proportional to V²; used in high-voltage transmission analysis
Energy BillingE = P × tkWh1 kWh = 3,600,000 J; multiply by tariff for cost

Self-Check Questions

  1. A 240 V appliance has a resistance of 60 Ω. Calculate its power. [P = V²/R = 960 W]
  2. A current of 4 A flows through a 25 Ω resistor for 3 minutes. Calculate the energy released as heat. [W = I²Rt = 72 000 J]
  3. An appliance uses 2.5 kWh in 5 hours. What is its power rating? [P = E/t = 500 W]
  4. Explain, using the formula P = I²R, why transmission lines are operated at high voltage.
  5. A household in Astana uses 350 kWh in one month. Calculate the cost at 30.56 KZT/kWh. [Cost = 10 696 KZT]
  6. How did Kazakhstan's 2024 time zone change potentially affect electrical power consumption? Use physics reasoning in your answer.