Sunshine, cables, bills and batteries: design a solar-plus-grid system for a small island community.
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Palm Bay (a fictional island community) pays high electricity bills and loses power during storms. The Palm Bay Electricity Company has funds for a solar array with battery storage to supply the school and clinic. The board wants to know:
The same ideas keep appearing. Each row shows one shared topic and where you meet it in your lessons.
Appliances use energy (kWh); panels convert sunlight with an efficiency; food chains pass on only part of their energy too.
High-voltage transmission wastes less energy as heat. The same electricity ideas run through circuits, bills and electrolysis.
Sunlight over a day follows a sine-shaped curve that Add Maths can model.
Battery capacity falls by a fixed percentage each year, a geometric pattern solved with logarithms.
A backup generator releases carbon dioxide; Biology and Chemistry explain the effect on climate and ecosystems.
The board needs to know what the community pays now and how long a solar system would take to pay for itself.
Energy per day = 1.5 × 4 = 6 kWh. In 30 days = 6 × 30 = 180 kWh. [2]
Cost = 180 × $0.35 = $63.00. [1]
(a) 12 000 ÷ 150 = 80 months = 6 years 8 months. [2]
(b) Value = 12 000 × 0.9³ = 12 000 × 0.729 = $8 748. [3: use of 0.9, power of 3, answer]
Increase = 60 kWh. Percentage increase = 60 ÷ 400 × 100 = 15%. [2]
Task total: 10 marks
Solar output rises and falls with the sun. The battery bank slowly loses capacity each year.
(a) The maximum value of sine is 1, so the maximum power is 800 W, when 15t = 90°, that is t = 6, at noon. [2]
(b) 800 sin(15t) = 400, so sin(15t) = 0.5. [1] 15t = 30° or 150°, so t = 2 or t = 10. [1] That is 8:00 a.m. and 4:00 p.m. [1]
10 × 0.95ⁿ < 8, so 0.95ⁿ < 0.8. [1]
Take logs: n log 0.95 < log 0.8, and since log 0.95 is negative, n > log 0.8 ÷ log 0.95. [1]
n > (−0.0969) ÷ (−0.02228) = 4.35. [1]
So after 5 years. [1]
Task total: 9 marks
Power must be sent from the solar farm to the village through cables with resistance. The engineer compares two voltages.
(a) I = P ÷ V = 10 000 ÷ 200 = 50 A. [1]
(b) P(lost) = I²R = 50² × 2 = 5000 W. [1] (half of the power is wasted as heat)
(c) I = 10 000 ÷ 20 000 = 0.5 A; P(lost) = 0.5² × 2 = 0.5 W. [2]
(d) A step-up transformer raises the voltage so the current is much smaller, so less energy is lost as heat in the cables (I²R). [1]
Note: the 200 V figure is only for comparison; real systems use many more steps.
Vs ÷ Vp = Ns ÷ Np, so Ns = 100 × 20 000 ÷ 200 = 10 000 turns. [2]
Power in = 5 × 1000 = 5000 W. Efficiency = 900 ÷ 5000 × 100 = 18%. [2]
Task total: 10 marks
During cloudy spells a gas generator will run. How much energy does it release and how much carbon dioxide?
(a) M(CH₄) = 16 g/mol; moles = 16 000 ÷ 16 = 1000 mol. [1]
(b) Energy = 1000 × 890 = 890 000 kJ = 890 MJ. [2]
(c) 1 mol CH₄ gives 1 mol CO₂; M(CO₂) = 44 g/mol; mass = 1000 × 44 = 44 000 g = 44 kg. [2]
(d) Exothermic: ΔH is negative, so heat energy is given out to the surroundings. [1]
Hydrogen at the cathode and oxygen at the anode. [1] Volume ratio H₂ : O₂ = 2 : 1. [1]
Carbon dioxide (CO₂). [1] Effect: raises global temperatures, melts ice and raises sea level, causes more extreme weather, acidifies oceans. [1]
Task total: 10 marks
The ecologist compares energy flow in nature with the energy flow in the power system and weighs the environmental effects of the project.
(a) 10% of 20 000 = 2000 kJ. [1]
(b) 10% of 2000 = 200 kJ. [1]
(c) Any two: heat released by respiration; energy used for movement and life processes; energy lost in waste (faeces and urine); parts that are not eaten (bones, roots). [2]
(a) Any two: coral bleaching; sea level rise and loss of coastal habitats (mangroves, beaches); more intense hurricanes and drought; changes in distribution or breeding times of species. [2]
(b) Trees take in carbon dioxide for photosynthesis [1] and convert it into carbohydrates, which are stored in wood, leaves and roots as a carbon store (carbon sink) [1]; they also release oxygen. [1]
(c) The carbon dioxide released when bagasse is burned is about the same as the carbon dioxide the sugar-cane absorbed by photosynthesis while it grew, so there is little net addition. [2]
Task total: 11 marks
Smart meters send each household’s readings to the company. The data officer analyses them in a spreadsheet and the network manager considers risks.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Month | kWh | Cost ($) | 0.35 | |
| 2 | Jan | 210 | |||
| 3 | Feb | 180 | |||
| 4 | Mar | 195 |
The tariff ($ per kWh) is in cell E1.
(a) =B2*$E$1 [2: multiplication and an absolute reference to E1, because the tariff must not move when copied].
(b) Jan $73.50, Feb $63.00, Mar $68.25. [1]
(c) =SUM(C2:C4) (= $204.75) [2]; =AVERAGE(B2:B4) (= 195 kWh) [2].
A column (or bar) chart, because it compares values across categories (months). [1]
(a) A WAN (or the Internet / mobile network). [1]
(b) Any two: no need to send staff to read meters; readings are more accurate and frequent; customers can see their usage and save energy; faults are detected faster. [2]
(c) Hackers could read or change customers’ data. Reduce it with encryption, strong passwords or a firewall. [1]
Task total: 12 marks
Prepare a board paper of one to two pages (or a 5-slide pitch) giving a clear yes or no and the evidence. Include the community’s energy demand and cost, the payback period, the solar output curve (draw it from the equation), the cable-loss comparison, the generator’s emissions and the battery lifetime.
| Criterion | What a top answer shows | Marks |
|---|---|---|
| Accuracy | Correct calculations with units from all six tasks | 6 |
| Evidence-based decision | Recommendation clearly supported by payback, losses and emissions | 5 |
| Graphs and tables | Neat, labelled, with sensible scales | 3 |
| Risks and sustainability | Considers cost, climate and data-security risks | 4 |
| Communication | Clear and suitable for a board of non-specialists | 2 |
Each of these people uses the subjects in this project every day.
Designs generation, transmission and distribution so electricity arrives safely and efficiently.
Uses: Physics (circuits, transformers), Maths and Add Maths
Pathway: Degree in electrical engineering.
Installs and maintains solar panels, inverters and batteries on homes, schools and farms.
Uses: Physics (electricity, efficiency), Maths (costing, angles)
Pathway: Technical certificate or apprenticeship, then further training.
Studies how much energy buildings use and advises how to cut costs and emissions.
Uses: Maths (bills, percentages), IT (spreadsheets), Chemistry (fuels)
Pathway: Degree in engineering, environmental science or economics.
Writes the programs and databases that read smart meters and balance supply and demand.
Uses: IT (programming, databases, networks), Add Maths
Pathway: Degree in computer science or software engineering.
Measures the effect of energy projects on air, climate and ecosystems.
Uses: Biology, Chemistry, Maths (statistics)
Pathway: Degree in environmental science or biology.