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.
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:
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):
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 |
|---|---|---|---|---|---|---|---|
| 2.0 | 0.20 | 0.21 | 0.20 | 0.20 | 0.40 | 0.40 | 0.0% |
| 4.0 | 0.40 | 0.39 | 0.40 | 0.40 | 1.60 | 1.60 | 0.0% |
| 6.0 | 0.59 | 0.60 | 0.61 | 0.60 | 3.60 | 3.60 | 0.0% |
| 8.0 | 0.77 | 0.78 | 0.79 | 0.78 | 6.24 | 6.40 | 2.5% |
| 10.0 | 0.95 | 0.94 | 0.82 | 0.97* | 9.70 | 10.00 | 3.0% |
| 12.0 | 1.18 | 1.19 | 1.18 | 1.18 | 14.16 | 14.40 | 1.7% |
* 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)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 LabA 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 SimulationThough 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| Concept | Core Formula | Unit | Key Insight |
|---|---|---|---|
| Electrical Work | W = QV = IVt | Joule (J) | Energy is transferred by charge moving through a potential difference |
| Electrical Power | P = IV | Watt (W) | Rate of energy transfer; 1 W = 1 J per second |
| Joule Heating | P = I²R | Watt (W) | Power dissipated as heat increases with I²; doubling I quadruples heat |
| Voltage-Power | P = V²/R | Watt (W) | Power proportional to V²; used in high-voltage transmission analysis |
| Energy Billing | E = P × t | kWh | 1 kWh = 3,600,000 J; multiply by tariff for cost |