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Power, efficiency and energy resources - Science Year 10

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Introduction

Calculate power, energy and efficiency, compare energy resources across several criteria, and test a fictional time-resolved supply/storage schedule. Year 10 placement is editorial within the GCSE pathway.

Calculate power, energy, efficiency and equivalent-service savings

Energy transfer and power answer different questions. Energy is measured in joules; power is how quickly energy transfers, measured in watts. One watt is one joule per second. A higher-power device can transfer the same energy in less time, but power alone does not prove that it needs less total energy or has a greater useful fraction. Match the task, duration and boundary before comparing equipment.

$P = \frac{E}{t}, E = P t$

Use an original idealised pump record: 6000 J enters the stated device boundary during 8.00 s, with 3600 J assigned to the intended useful mechanical output and 2400 J to other, eventually dissipative routes. Average input power is 750 W and useful average power 450 W. The two power rates concern the same eight-second operation. Total energy is conserved; less useful energy is not deleted from the complete account.

$η = \frac{E_{u}}{E_{i n}} = \frac{P_{u}}{P_{i n}}$

Here eta is efficiency as a fraction, u marks the useful output for the defined task and in marks the input. The original case gives 0.600, or 60.0 percent. The power ratio is equivalent only when the compared rates cover the same appropriate operation or operating conditions. A process can conserve total energy without being one hundred percent efficient for its useful purpose. What counts as useful depends on that purpose; warming a room intentionally differs from unwanted motor warming during pumping.

A kilowatt-hour is an energy unit, not a power unit or a kilowatt divided by an hour. One kilowatt acting for one hour transfers 3.60 million joules. Use watts with seconds for joules, or kilowatts with hours for kilowatt-hours. Converting one quantity while leaving the other in an incompatible unit can introduce a factor of one thousand or 3600.

For a separate original classroom comparison, stipulate twenty old lamps rated 40 W each and twenty replacement lamps at 18 W each, with equivalent delivered lighting, comfort and required operating time. Over 5.00 hours, old input is 0.800 kW times five equals 4.00 kWh; replacement input is 0.360 kW times five equals 1.80 kWh. Saving is 2.20 kWh, or 55.0 percent of the original input. Equivalent useful service is an explicit assumption, not something inferred from lower wattage alone.

For a separate fictional 2.00 MW wind installation producing 12.0 MWh over twenty-four hours, average output is 0.500 MW and the period’s capacity factor is 25.0 percent. That does not mean it operated at a constant quarter power every second or was available only one quarter of the time. Rated power, actual energy, operating availability and time variation are distinct evidence. The wind photograph elsewhere on this page is not the source of this fictional installation’s rating.

Review stores and transfer pathways, then distinguish transferred energy from rate and useful fraction using the original pump case. Explain why energy conservation does not guarantee perfect task efficiency. The equations and original lighting comparison provide the offline alternative. Original: Cognito, GCSE Physics - Energy Stores, Transferring Energy & Work Done. The written explanations and native tasks work without sound or the external player.

Compare resources using reliability, impact and cost boundaries

An energy resource must be evaluated for a particular service and timescale. Renewable means replenished through relevant natural processes on a human timescale, not free, impact-free or automatically available whenever demand rises. Non-renewable resources include finite fossil fuels and nuclear fuels. Electricity is an energy carrier; it is not a primary fuel that appears independently of the generation and storage processes supplying it.

Resource group	Supply characteristic	Important evaluation questions
Coal, oil and natural gas	Finite chemical fuels; output can be controlled within plant constraints	Combustion emissions, extraction, fuel supply and price
Nuclear fuel	Finite resource; useful sustained output, with outages and operating constraints	Fuel cycle, waste, construction, decommissioning and safety
Wind and solar PV	Renewable flows with weather/time-dependent output	Forecasting, land/materials, network and flexibility needs
Reservoir hydro	Renewable water cycle; some controllable output when water is available	Rainfall, reservoir limits, river ecology and displaced land uses
Tidal and wave	Tides are predictable but periodic; waves depend on conditions	Site suitability, ecology, equipment and integration
Geothermal	Useful relatively steady resource at suitable sites	Site/flow management, development cost and local impacts
Biomass	Potentially renewable with sustained regrowth and supply	Land use, combustion, carbon accounting and alternative uses

Wind and solar PV have variable output, but forecasting, geographical diversity, demand flexibility, interconnection, storage and other resources can help integrate them. Calling every variable source useless misses this system context. Equally, adding annual wind or solar energy does not by itself guarantee enough power at every moment. Reservoir hydro can offer controllable output under suitable conditions, while run-of-river installations have different constraints; neither has unlimited water.

Fossil-fuel generation can be dispatchable within technical and fuel constraints, but combustion has greenhouse-gas and pollutant implications. Nuclear generation uses a finite fuel through nuclear processes, not ordinary chemical burning, and requires consideration of the fuel cycle, waste and decommissioning. Low direct operating carbon emissions do not mean zero life-cycle environmental impact. No resource label alone establishes total impact, cost or guaranteed reliability.

Biomass is not automatically carbon-neutral: regrowth, time, land use, processing and alternative uses matter. Geothermal and hydro need site and flow management. Tidal timing is predictable but periodic, which is different from a constant output matched to demand. An honest comparison uses more than one criterion and states the relevant place, period, output quality and limitations of the evidence.

Costs also need a common comparison boundary. Use this separate original fictional example in invented cost units, not pounds or a current electricity tariff. Projects A and B are both assumed to deliver 500 MWh per year for twenty years with unchanged performance. A costs 180000 units initially and 8000 per year to run; B costs 260000 initially and 4000 per year. Each simple undiscounted total is 340000 units for 10000 MWh, or 34 units per delivered MWh.

That equality does not decide the best project. This deliberately incomplete calculation omits financing, discounting, degradation, end-of-life costs, network effects and the timing or firmness of delivery. It is not a full levelised-cost study, investment recommendation or quoted market price. A lower capital cost is not automatically a lower lifetime cost, and identical average costs do not establish identical reliability or environmental performance.

Review then evaluate: Cognito — KS3 Physics - Energy Resources. This is a foundation recap of resource types; the original cost and time-resolved supply tasks here provide the Year 10 extension. Offline fallback: compare two rows of the original resource table using reliability, impact, cost boundary and ability to meet a stated demand.

Test demand and storage with a time-resolved energy ledger

Enough energy across a period does not guarantee enough power when it is needed. A storage system has an energy capacity, such as MWh, and separate charge/discharge power limits, such as MW. A ten-megawatt-hour device cannot automatically deliver ten megawatts; its power rating and available state of charge also matter. Storage shifts previously supplied energy and has real losses; it is not a new primary resource that generates free extra energy.

The following original fictional schedule covers six consecutive one-hour intervals, not an entire day or the real UK electricity system. All power values are interval averages. The final column is an available fixed 23 MW supply block in this simplified comparison, not a guarantee for a named real power station. Wind and solar values are supplied available outputs; unused potential may be curtailed.

One-hour interval	Demand in MW	Available wind in MW	Available solar in MW	Available fixed block in MW
1	20	8	0	23
2	30	10	4	23
3	40	6	15	23
4	50	4	10	23
5	40	8	1	23
6	20	12	0	23

The six-hour available supply sums to 216 MWh and demand to 200 MWh. Consider a storage device starting empty, with capacity 10 MWh, maximum charging power 5 MW and maximum discharging power 5 MW. Stipulate an ideal round-trip efficiency of one hundred percent solely to isolate timing and capacity limits. Real losses would require additional accounting. Assume surplus is charged whenever allowed, and deficits are served by discharge whenever possible, without future borrowing.

In interval one, available supply exceeds demand by 11 MW. Only 5 MWh can be stored during that hour because charging is limited to 5 MW; 6 MWh of potential is unused. In interval two, surplus is 7 MWh, with 5 charged and 2 unused. Storage is now full at 10 MWh. The 4 MWh surplus in interval three is unused because the device has no remaining capacity.

In interval four, demand 50 MW exceeds available supply 37 MW by 13 MW. The device can discharge only 5 MW for the hour, leaving 8 MWh demand unserved and 5 MWh in store. In interval five, the 8 MW deficit is reduced by another 5 MW discharge, leaving 3 MWh unserved and an empty store. In interval six, surplus 15 MWh allows only 5 MWh charging, leaving 10 MWh unused and a final store of 5 MWh.

Across the six-hour model, 189 MWh is served, 11 MWh unserved, 22 MWh available potential curtailed or unused and 5 MWh retained in storage. The available-energy ledger closes: 216 equals 189 plus 22 plus 5. The demand ledger separately closes: 200 equals 189 plus 11. Greater total available energy than total demand did not remove the timing and power constraints. Do not call all 216 MWh actual delivered electricity or count the stored energy again as newly created supply.

This is not a grid reliability certificate. Real planning also considers shorter fluctuations, frequency and voltage, reserves, outages, ramping, transmission, demand response, weather correlations, seasonal storage and uncertainty. A different power rating or energy capacity would change the model’s outcome, but none can be assessed by simply adding nameplate ratings without tracing time and state of charge.

Use the original ledgers to test a specific claim: can it meet the stated demand in each interval, what is assumed constant, where does energy go, which costs or impacts are excluded, and what additional evidence is needed? A professional energy explanation combines correct units, conservation and useful-purpose definitions with a clear account of the system’s actual task and constraints.

Interactive Tasks

Quiz: Test Your Knowledge

What distinguishes power from energy? (Power is the rate of energy transfer, in joules per second) (!Power is a stored amount independent of time) (!Energy is always measured in watts rather than joules) (!A higher power always guarantees higher useful efficiency)

What is the original pump efficiency? (Sixty percent from 3600 useful joules divided by 6000 input joules) (!Forty percent because only the dissipative part can be useful) (!One hundred percent because total energy is conserved) (!Seven hundred fifty percent because input power is seven hundred fifty watts)

What is one kilowatt-hour? (An energy amount equal to 3.60 million joules) (!A kilowatt divided by an hour) (!A power rating of one thousand joules regardless of duration) (!One watt acting for one second)

What saving follows in the original equivalent-service lighting comparison? (2.20 kWh, or fifty-five percent of the original input) (!2.20 kW per hour as the only possible energy unit) (!0.360 kWh because watts and kilowatt-hours are interchangeable) (!A guaranteed equal light output inferred from wattage alone)

What does the fictional wind capacity factor of twenty-five percent mean? (Delivered period energy is one quarter of rating times period duration) (!Output must have been exactly one quarter of rating at every instant) (!The photographed wind site was measured operating only one quarter of the time) (!Every turbine anywhere has identical annual reliability)

Which comparison of renewable resources is sound? (Replenishment does not guarantee zero impact or output whenever demand rises) (!Renewable means no materials, construction or environmental effects) (!All variable output is unusable under every possible system) (!Every hydro reservoir has unlimited water and reversible pumping)

What does the original simple cost comparison establish? (Both assumed projects total 340000 invented units and 34 units per delivered MWh within the stated omissions) (!Project A must be best because its initial price is lower) (!The figures are current UK market tariffs and investment advice) (!Equal average cost proves identical timing, emissions and reliability)

What limits the fictional storage device? (Both its ten-MWh energy capacity and five-MW charge/discharge power limits) (!Only the energy capacity, which automatically fixes every possible power output) (!An ability to borrow tomorrow’s energy before charging) (!No limit because storage creates a primary energy resource)

Why is demand still unserved in the original six-hour model despite larger total available energy? (Timing and storage power/capacity constraints prevent serving every interval) (!The available-energy sum proves every interval must be fully served) (!The wind photograph proves the table is a measured real grid failure) (!Conservation allows arbitrary extra energy during the peak)

Which complete model ledger is correct? (216 available MWh equals 189 served plus 22 unused potential plus 5 finally stored) (!216 available MWh is all delivered, with storage counted again as extra supply) (!200 demand MWh equals 189 served with no remaining difference) (!The eleven unserved MWh are a measured guarantee about the UK grid)

Memory Game

Power	Rate of energy transfer in watts
Efficiency	Useful output divided by input for the defined task
Kilowatt-hour	Energy from one kilowatt acting for one hour
Capacity factor	Period output energy divided by rating times duration
Storage energy capacity	Maximum stored amount for the stated operating model
Dispatchable output	Output controllable within the resource and plant constraints

Drag and Drop

The same useful task is completed in less time	Compare power separately from total energy and useful fraction
Twenty lower-power lamps replace the original set	Require equivalent lighting service before claiming the stipulated savings
A resource is labelled renewable	Still examine timing, impacts, materials and system integration
A store has plenty of energy but a limited discharge rating	Check whether its power can meet the instantaneous deficit
Available supply exceeds total demand over several intervals	Trace each interval and state of charge before claiming full demand is served

Crossword Puzzle

POWER	What quantity is energy transfer per unit time?
EFFICIENCY	What fraction compares useful output with input?
RENEWABLE	What describes a resource replenished on a relevant human timescale?
CAPACITY	What term describes the maximum stored energy amount here?
CURTAILMENT	What can reduce available generation potential that cannot be used?
DEMAND	What electricity requirement must the supply system serve?

LearningApps

Optional extra practice. Choose an appropriate activity with your teacher. If the external collection is unavailable, use the native activities and independent tasks in this course.

Cloze Text

Power measures energy transferred per unit

. Efficiency compares useful output with

. One kilowatt-hour is an energy

. The lighting comparison assumes equivalent useful

. Wind and solar output can be

. Renewable does not mean impact-

. Storage has an energy capacity and a separate power

. Energy not yet stored cannot be borrowed from the

. Available potential may be

. A complete account distinguishes available energy from energy actually

.

Open Tasks

Easy

Define three quantities: Distinguish energy, power and efficiency with units and the useful-purpose boundary.
Read the original pump record: Calculate both average powers and account for every input joule.
Interpret the photographs: Explain why real wind and roof images do not establish ratings or annual yield and why PV is distinct from solar thermal.
Compare resource labels: Distinguish renewable flow, finite fuel and electricity as an energy carrier.

Standard

Calculate equivalent lighting: Find the two five-hour input energies, saving and percentage under the stated equal-service assumption.
Calculate a capacity factor: Find original average output and period capacity factor without claiming constant output or operating availability.
Calculate the fictional cost boundary: Find each project’s twenty-year energy, cost and simple units per delivered MWh, naming omissions.
Trace the first three storage intervals: Calculate surplus, charging, state of charge and unused potential with both power and capacity limits.

Advanced

Complete the six-hour ledger: Trace deficits, final charging, served/unserved demand and all available-energy destinations.
Change one storage assumption: Explain how more energy capacity versus more charging/discharging power would change different constraints without inventing free energy.
Evaluate a resource mix: Use reliability, environmental effects, cost boundaries, site and time rather than a single universal ranking.
Audit a planning claim: Explain why annual totals or added nameplate ratings alone do not certify real grid reliability, including the additional evidence omitted by the original model.

Learning Check

Pump energy and useful fraction: Match the same input/output boundary and eight-second operation.
Lighting and energy units: Convert both ratings and duration consistently and retain equal service.
Capacity factor and resource comparison: Separate ratings, energy and system timing.
Simple fictional cost: Use the common delivery assumption without pretending to calculate a full market value.
Storage sequence: Respect empty start, ten-MWh capacity, five-MW limits and one-hour durations.
Complete conservation and limits: Close the available-energy and demand accounts separately.

Worked checks and assessment guidance

Input 6000 J gives average power 750 W; useful 3600 J gives 450 W. The remaining 2400 J is assigned to other eventually dissipative routes. Useful/input is 0.600, or sixty percent, agreeing with the matched power ratio. Conservation does not make the chosen task one hundred percent efficient, and higher power alone does not establish less energy for the same service.
Twenty times forty watts is 0.800 kW; twenty times eighteen is 0.360 kW. Five hours gives 4.00 and 1.80 kWh, saving 2.20 kWh, or fifty-five percent of the original. One kWh equals 3.60 million joules. Equal lighting, comfort and operating time are stipulated rather than inferred from lower wattage. The figures are original, not a measured building audit.
The fictional two-MW installation produces twelve MWh in twenty-four hours, giving average output half a MW and period capacity factor one quarter. This does not prove constant half-MW output or availability only one quarter of the time. Renewable flows still have site, timing, material and impact constraints; finite fuels have their own supply, emission, waste and operating questions. Reservoir hydro and pumped storage are not automatically the same capability.
Each project is assumed to deliver five hundred MWh per year for twenty years, ten thousand total. A is 180000 plus twenty times 8000 equals 340000 invented units; B is 260000 plus twenty times 4000, also 340000. Each simple average is thirty-four units per delivered MWh. Financing, degradation, end costs, network effects and timing are omitted, so this is not a full levelised-cost study or a real tariff/investment recommendation.
Available surpluses or deficits before storage are plus eleven, plus seven, plus four, minus thirteen, minus eight and plus fifteen MWh. Charges are five, five, zero, zero, zero and five; discharges are zero, zero, zero, five, five and zero. End states are five, ten, ten, five, zero and five MWh. Unserved demand is eight then three MWh in the fourth and fifth intervals. Unused potential is six, two, four, zero, zero and ten MWh. The model deliberately uses ideal efficiency and does not borrow future energy.
Total available potential is 216 MWh while demand is 200. Served is 189, unserved eleven, final stored five and unused potential twenty-two. The available ledger is 216 equals 189 plus twenty-two plus five; the demand ledger is 200 equals 189 plus eleven. Larger available energy than total demand therefore does not guarantee every interval is served. This six-hour fictional schedule is not a day-long or real UK grid certificate; losses, reserves, ramping, networks, weather correlations and seasonal behaviour require additional evidence.

Learning evidence

Retain matched-boundary pump calculations, equivalent-service lighting savings, a period-specific capacity factor, an explicitly incomplete fictional cost comparison and the full six-hour storage ledger. Distinguish real illustrations from supplied values, available potential from delivered energy, storage from primary resources and a simplified account from real planning certification.

OER and Wikipedia

Original pump, lighting, wind rating/output, invented-unit cost comparison and six consecutive one-hour supply/storage records. The three unchanged Commons originals and both original Cognito previews were visually inspected; source, licence, byte and native-image checks retained. No photograph is used to assert a measured rating or output.

DfE GCSE combined science, energy scope. OpenStax Physics work and power, concept context. U.S. EIA capacity and generation and electricity storage, general capacity, power/energy and storage concepts only. U.S. statistics are not imported as UK values; all numerical tables here are original fictional models and no real market prices are quoted. Sources checked 13 November 2026.

Additional original video: Cognito — KS3 Physics - Energy Resources, foundation recap, preview and embed verified.

2019 07 26 Trampe Windkraftanlagen DJI 0041.jpg, Daniela Kloth, GFDL 1.2. Unchanged original; caption and learning activities are original.

Solar panels on a roof.jpg, Pujanak, Public domain. Unchanged original; caption and learning activities are original.

Hydroelectric dam.svg, Tennessee Valley Authority; SVG version by Tomia, CC BY 2.5. Unchanged original; caption and learning activities are original.