Electrical Energy & Power Bills
Average Sydney household (AGL data, 2023): 18 kWh/day at 30.2 c/kWh — annual electricity bill $1,984. A 6.6 kW rooftop solar system generates 26.4 kWh/day (average), fully offsetting consumption with 8.4 kWh exported to the grid each day at the feed-in tariff. Physics on the bill: E = Pt, billed in kWh = kW × h.
A 2500 W electric hot water system runs for 3 hours per day.
Predict 1: How many kWh of electricity does it use per day?
Predict 2: If electricity costs 32 c/kWh, what is the daily running cost?
1 kilowatt-hour (kWh) is equal to:
Know
- $E\ (\text{kWh}) = P\ (\text{kW}) \times t\ (\text{h})$
- $\text{Cost} = E\ (\text{kWh}) \times \text{tariff}\ (\$/\text{kWh})$
- 1 kWh = 3.6 × 10⁶ J = 3.6 MJ
- Power bills use kWh because joules are impractically small
Understand
- Why electricity is billed in kWh rather than joules
- How to compare the running costs of different appliances
- How solar PV reduces net energy consumption and bills
Can Do
- Calculate electricity cost for any appliance given power, time, and tariff
- Convert between kWh and joules
- Estimate and compare annual household energy bills
Core Content
Open an electricity bill and look at the usage section. It shows how many kilowatt-hours (kWh) you used in the quarter, multiplied by the tariff (cents per kWh), plus a fixed daily supply charge. The metre in your home's switchboard literally counts kWh — it records how many kilowatts of demand you drew, multiplied by how many hours you drew it for. A 2 kW electric jug running for 0.05 hours uses exactly 0.1 kWh = 360,000 J. The formulae below translate that reading into a dollar figure.
$E\ (\text{kWh}) = P\ (\text{kW}) \times t\ (\text{hours})$
$\text{Cost} (\$) = E\ (\text{kWh}) \times \text{tariff}\ (\$/\text{kWh})$
Note: $P$ must be in kilowatts and $t$ must be in hours for the kWh formula to work.
A household uses: 1800 W TV for 4 h/day, 2400 W kettle for 0.2 h/day, 200 W fridge for 24 h/day. Tariff = $0.32/kWh. Find the monthly cost (30 days).
- TV: $E = 1.8 \times 4 = 7.2\ \text{kWh/day}$
- Kettle: $E = 2.4 \times 0.2 = 0.48\ \text{kWh/day}$
- Fridge: $E = 0.2 \times 24 = 4.8\ \text{kWh/day}$
- Total/day = 12.48 kWh/day; Monthly = $12.48 \times 30 = 374.4\ \text{kWh}$
- Cost = $374.4 \times 0.32 = \$119.81/\text{month}$
Electrical energy in billing units: $E\ (\text{kWh}) = P\ (\text{kW}) \times t\ (\text{h})$; cost = $E \times \text{tariff}\ (\$/\text{kWh})$. Note: $P$ must be in kilowatts and $t$ in hours; $1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$.
Pause — copy the highlighted formulas into your book before moving on.
To calculate energy in kWh, you multiply power in watts by time in hours.
A 500 W appliance running for 2 hours uses 1 kWh of electrical energy.
Electricity tariff = 32 c/kWh. Calculate the daily running cost of each appliance:
- A 1500 W electric hot water system running 2 hours per day
- A 100 W LED TV running 5 hours per day
- A 4500 W air conditioner running 3 hours per day
A 3000 W spa heater runs for 2.5 hours. At 32 c/kWh, the cost is:
A Sydney home uses 20 kWh/day. A 5 kW solar system generates 18 kWh/day. Import tariff = 32 c/kWh, feed-in tariff = 7 c/kWh.
- Without solar: calculate the annual electricity bill.
- With solar: the house self-consumes 18 kWh and imports 2 kWh. Calculate the annual cost of imported electricity.
- Calculate the annual savings compared to having no solar.
Three of these correctly describe kilowatt-hours. Pick the odd one out.
A 2000 W appliance running for 3 hours uses _____ kWh of electrical energy.
A household uses 30 kWh per day. The electricity tariff is 30 c/kWh. The quarterly bill (90 days) before any rebates is:
ApplyBand 3(3 marks) 3. A household uses: a 2400 W electric oven for 1 hour per day, a 250 W refrigerator for 24 hours per day, and a 1000 W washing machine for 1.5 hours per day. The electricity tariff is 32 c/kWh. Calculate the daily energy use in kWh and the daily cost.
AnalyseBand 4(3 marks) 4. A 60 W incandescent globe is replaced by a 10 W LED globe that produces the same light output. Both run for 8 hours per day at 32 c/kWh. (a) Calculate the daily energy saving in kWh. (b) Calculate the daily cost saving in cents. (c) Calculate the annual saving and comment on whether the switch is cost-effective.
EvaluateBand 6(4 marks) 5. A student claims: "Solar panels reduce your electricity bill to zero." Using the concepts of energy consumption, solar generation, feed-in tariffs, and standing charges, evaluate this claim for an average Sydney household consuming 18 kWh/day with a 6.6 kW solar system generating 24 kWh/day (summer).
Show all answers
Activity 1 — Model Answers
- $E = 1.5 \times 2 = 3.0\ \text{kWh}$; cost = $3.0 \times 32 = 96\ \text{c} = \$0.96$
- $E = 0.1 \times 5 = 0.5\ \text{kWh}$; cost = $0.5 \times 32 = 16\ \text{c}$
- $E = 4.5 \times 3 = 13.5\ \text{kWh}$; cost = $13.5 \times 32 = 432\ \text{c} = \$4.32$
Activity 2 — Model Answers
- Without solar: $20 \times 365 = 7300\ \text{kWh/year}$; $7300 \times 0.32 = \$2336/\text{year}$
- With solar: imports $2\ \text{kWh/day} \times 365 = 730\ \text{kWh/year}$; $730 \times 0.32 = \$233.60/\text{year}$
- Savings = $2336 - 234 = \$2102/\text{year}$ (plus any feed-in credit if excess is exported)
Short Answer — Model Answers
Q3 (3 marks): Oven: $2.4 \times 1 = 2.4\ \text{kWh}$. Fridge: $0.25 \times 24 = 6.0\ \text{kWh}$. Washer: $1.0 \times 1.5 = 1.5\ \text{kWh}$. Total = 9.9 kWh/day. Cost = $9.9 \times 0.32 = \$3.17/\text{day}$.
Q4 (3 marks): (a) Saving per day: $(60 - 10)/1000 \times 8 = 0.4\ \text{kWh}$. (b) $0.4 \times 32 = 12.8\ \text{c/day}$. (c) Annual: $12.8 \times 365/100 = \$46.72/\text{year}$. An LED globe costs ~$5–10; payback is only 2–3 months — highly cost-effective.
Q5 (4 marks): The claim is an overstatement. In summer, a 6.6 kW system generating 24 kWh/day exceeds the 18 kWh consumption; the excess 6 kWh is exported at a low feed-in tariff (~7 c/kWh). However: (1) Standing charges ($0.80–1.20/day) are paid regardless of solar generation. (2) In winter, solar generation drops significantly (e.g. 10 kWh/day), requiring 8 kWh of imports daily. (3) Overnight consumption requires full grid import. Net result: solar can reduce the annual bill by 60–80% but rarely reaches zero due to standing charges and seasonal/daily variability. The claim ignores these factors.
Five timed questions on electricity bills and energy costs.
⚔ Enter the arenaAGL's 2023 data shows the average Sydney household uses 18 kWh/day at 30.2 c/kWh — an annual bill of 18 × 365 × $0.302 = $1,984. A 6.6 kW solar system generates 26.4 kWh/day on average, fully covering that 18 kWh and exporting 8.4 kWh to the grid each day. Without solar, that household spends nearly $2,000 per year; with solar, the consumption cost falls to near zero (though standing charges remain). This is E = Pt applied to a real household.
Now check your Think First answers: a 2500 W hot water system running 3 h/day uses E = 2.5 kW × 3 h = 7.5 kWh/day. At 32 c/kWh, daily cost = 7.5 × $0.32 = $2.40.