Cost-Benefit Analysis of Energy Devices — Grade 9 Science

Wait — so a tiny LED saves you money and the planet, but how do you prove it with numbers instead of vibes? Let’s put on our scientist hats (and maybe a tiny economist beret).

You already learned about types of energy devices and how to read efficiency and power ratings. You also practiced using Ohm's law and the relationships between voltage, current, and resistance to calculate power in circuits (remember P = VI and P = I²R?). Now we'll use those ideas to decide which device is really worth buying: the flashy new gadget, or the old, energy-sucking relic under your bed.

What is a cost-benefit analysis for energy devices?

A cost-benefit analysis (CBA) compares the costs of buying and operating a device with the benefits (mainly money saved on energy bills, plus environmental benefits and convenience). For energy devices the important pieces are:

• Initial cost: what you pay up front (purchase, installation)
• Running cost: energy used each hour → converts to money (and emissions)
• Maintenance and replacement: bulbs, filters, repairs
• Lifespan: how many hours/years it works
• Non-monetary benefits: lower CO₂ emissions, better light quality, less noise

Why this matters: choices we make in school, home, or future engineering projects depend on lifetime cost, not just the price tag.

Quick reminder: connect to circuits and power

Use these formulas you already know:

• Power: P = V × I (watts)
• Power (another form): P = I² × R
• Energy used: E = P × t (watt-hours or kilowatt-hours)

Energy companies bill in kilowatt-hours (kWh). To get kWh: convert watts to kilowatts (divide by 1000) and multiply by hours used.

Micro explanation: If two devices run on the same voltage, the one that draws more current (higher I) uses more power (P = VI), and thus more energy over time.

Step-by-step: How to do the cost-benefit analysis

1. Find the power rating (W) on the device.
2. Choose a realistic daily use (hours per day) and convert to yearly hours.
3. Calculate yearly energy: energy (kWh/year) = power (kW) × hours/year.
4. Multiply by the cost per kWh (check your local rate) for yearly running cost.
5. Add maintenance/replacement costs per year.
6. Compare total yearly cost of each device and compute annual savings.
7. Compute payback period = extra_initial_cost ÷ annual_savings.

Real example: 60 W incandescent vs 10 W LED (practical, grade 9 friendly)

Assumptions:

• Use per day = 4 hours
• Electricity price = $0.20 per kWh
• Incandescent: 60 W, lifespan 1,000 hours, cost $1
• LED: 10 W, lifespan 25,000 hours, cost $5

Calculations:

• Yearly hours = 4 × 365 = 1,460 h
• Incandescent energy/year = 0.06 kW × 1,460 h = 87.6 kWh → cost = 87.6 × 0.20 = $17.52
• LED energy/year = 0.01 kW × 1,460 h = 14.6 kWh → cost = 14.6 × 0.20 = $2.92
• Annual energy savings = $17.52 − $2.92 = $14.60
• Extra initial cost for LED = $5 − $1 = $4
• Payback period = 4 ÷ 14.60 ≈ 0.27 years ≈ 3.3 months

Replacement story:

• In one year the incandescent uses up 1,460 of its 1,000 hours → it needs replacements; you'd need about 1.46 bulbs per year (cost ≈ $1.46/year). LED lasts far longer, so replacement cost per year is tiny.

Environmental bonus (quick calc): if electricity emits 0.5 kg CO₂ per kWh, switching one bulb saves (87.6 − 14.6) × 0.5 ≈ 36.5 kg CO₂ per year.

Conclusion: the LED pays back the extra purchase price fast and keeps saving for years — a classic win-win.

Another quick example: small space heater vs electric radiator

A space heater 1,500 W used 2 hours/day vs a newer 1,200 W efficient model.

• Old heater energy/day = 1.5 kW × 2 h = 3 kWh → yearly = 1,095 kWh → cost at $0.20/kWh = $219
• New heater yearly = 1.2 × 2 × 365 = 876 kWh → cost = $175.20
• Annual savings ≈ $43.80
• If the new unit costs $40 more upfront, payback ≈ 40 ÷ 43.8 ≈ 0.9 years

Small improvements add up — but always check if the higher-efficiency model truly uses less power for the same heating effect (that can depend on insulation and thermostat).

Things students often misunderstand — let’s clear them up

• “Higher watt means brighter or better.” Not always. For devices that convert electricity to light, higher watt often means more light for old tech (like incandescent). For LEDs, lower watt can give the same brightness because they are more efficient.
• “If something is efficient, it will cost less right away.” Not always: efficient devices can cost more up front but save money over time. That’s why we use payback and lifetime cost.
• “Electricity cost is only the power rating.” No — you must multiply by hours used and the energy rate (kWh price). Also include replacements and maintenance.

Quick checklist for your own experiment or homework

• Get power rating from the label (W)
• Decide daily hours and compute yearly hours
• Use local cost per kWh
• Don’t forget replacement costs and lifespan
• Calculate payback and lifetime savings
• Mention environmental impact if asked

Key takeaways (the things you’ll actually remember at 2 a.m.)

• Energy cost = power × time → convert to kWh and multiply by price. That’s the backbone.
• Efficiency and power ratings matter — they tell you how much useful output you get per unit of energy.
• Initial price is not the whole story — think lifetime cost and payback period.
• Small everyday choices (like switching a bulb) can save money fast and cut emissions.

"Buying cheaper now can cost you more later — and your electric bill will happily remind you every month."

Go run one of these calculations at home: pick a lamp or a fan, find its power, estimate hours per week, and compute the yearly cost. Show your family the math — you might become the household energy whisperer.

Tags: beginner, humorous, science, education