Connect power, time, energy and cost
Energy in kWh = power in kW × time in h; cost = energy × tariff.
Continue where you stopped
The core idea
Electricity · Lesson 6 of 6 · about 25–35 min
What you need to understand
Energy in kWh = power in kW × time in h; cost = energy × tariff.
Definitions
- kilowatt-hour
- the energy transferred by 1 kW operating for 1 hFor example: Electricity bills record energy in kWh, not power.
- electricity bill
- a record of electrical energy used during a stated billing periodFor example: The usage figure is recorded in kilowatt-hours.
Key idea
- LookA 60 W fan runs for 5 h. Electricity costs $0.30 per kWh. Find the cost.
- ThinkEnergy in kWh = power in kW × time in h; cost = energy × tariff.
- DoCalculate energy and cost, interpret bill information, and justify one specific action through its effect on power or operating time.
Review the full electricity topic picture if you need the visual overview.
Explanation
To find electrical energy in kilowatt-hours, convert power to kilowatts and multiply by time in hours. A kilowatt is power; a kilowatt-hour is energy.
A bill may show cumulative meter readings, so subtract the previous reading from the current reading to find use during the billing period. Multiply energy use by the tariff. A useful saving action reduces unnecessary power or operating time while still providing the required service.
Pause and say it: Energy in kWh = power in kW × time in h; cost = energy × tariff.
Common mistake
Tempting wrong idea: The voltage and power ratings on a label are meter readings taken at the present moment.
Why it fails: The power rating is fixed by the manufacturer and does not change while the appliance runs. It gives the power during normal use; multiplying by the operating time gives the energy used, and multiplying that by the tariff gives the cost.
Use this instead: A label states the appliance's intended operating voltage and rated power, not a live measurement.
Practical work
What to show: Calculate energy and cost, interpret bill information, and justify one specific action through its effect on power or operating time.
Before you finish: Check that the billing period and tariff refer to the same readings.
Practical link: The topic investigation is taught in “Choose the meter job before connecting it”.
6. Worked Examples
Modelled example 1
Calculate energy use and cost
Problem
A 60 W fan runs for 5 h. Electricity costs $0.30 per kWh. Find the energy used and cost.
Study the worked solution
Calculate billed energy
Method
Convert watts to kilowatts and multiply by time in hours.
Reason
Power in kW × time in h gives electrical energy in kWh.
Working
60 W = 0.060 kW; energy = 0.060 × 5 = 0.30 kWh
Apply the tariff
Method
Multiply the energy use by cost per kWh.Reason
Cost depends on the amount of energy used, not power alone.
Working
cost = 0.30 kWh × 0.30/kWh =0.09
Guided practice 2
Calculate a bill from meter readings
Problem
An electricity meter changes from 1840 kWh to 1960 kWh. The tariff is $0.25 per kWh. Find the billing-period energy use and energy charge.
Find use before applying the tariff
Hints
Hint 1: meter difference
Subtract the earlier cumulative reading from the later one.
Hint 2: charge
Multiply billing-period energy by cost per kWh.
View solution step by step
Find the energy used
Method
Subtract the earlier meter reading from the later reading.
Reason
The difference between cumulative readings is the billing-period energy use.
Working
1960 kWh − 1840 kWh = 120 kWhApply the tariff
Method
Multiply the billing-period energy by the cost per kWh.
Reason
The tariff prices each kilowatt-hour used.Working
120 kWh × 0.25/kWh =30.00
Challenge 3
Cost a changed operating schedule
Problem
A 1.2 kW heater is left on unnecessarily for 30 minutes each day over 20 days. Electricity costs $0.32 per kWh. Calculate the avoidable energy and cost, then state one specific saving action.
Connect power, time, tariff and action
Hints
Hint 1: total time
Convert 30 minutes to hours, then multiply by the number of days.
Hint 2: units and tariff
Multiply kW by h for kWh, then multiply the result by the cost per kWh.
View solution step by step
Combine the operating time
Method
Convert the daily operating time to hours and find the total time.
Reason
A kWh calculation requires time expressed in hours.
Working
30 min = 0.5 h; total time = 0.5 h × 20 = 10 h
Calculate energy and cost
Method
Multiply power by total time, then apply the tariff.
Reason
Power × time gives energy, and the tariff converts that energy to cost.
Working
energy = 1.2 kW × 10 h = 12 kWh; cost = 12 × 0.32 =3.84
Remove the stated waste
Method
Choose an action that reduces the unnecessary operating time.
Reason
A timer or shutdown routine would reduce the unnecessary operating time.
Working
Switch the heater off when heating is no longer required.
Guided practice
Try it with support
A 0.460 kW appliance runs for 3.0 h. Find its energy use and cost at $0.30 per kWh.
- Multiply power in kW by time in hours, then use the tariff.
Check the guided answer
Answer: Energy = 0.460 × 3.0 = 1.38 kWh. Cost = 1.38 × $0.30 = $0.414, or about $0.41.
Check: Keep kW and kWh distinct: one is power and the other is energy.
Practise and continue
Practise this
A bill shows a previous meter reading of 215 kWh and a current reading of 248 kWh. Find the billed use and its cost at $0.30 per kWh.
Need a hint?
- Subtract the meter readings before applying the tariff.
Check your answer
Answer: The billed use is 248 − 215 = 33 kWh, costing 33 × $0.30 = $9.90.
Check: Check that the billing period and tariff refer to the same readings.
Think like a scientist
Two fans provide the same airflow, but one has a lower power rating. What extra information is needed before claiming it will cost less over a month?
Check the reasoning
Their operating times and the electricity tariff are also needed; actual use may outweigh the difference in power rating.
Remember: A useful saving claim connects power, time and the required outcome.
One-minute check
- Hide the page and explain connect power, time, energy and cost in your own words.
- Give a new example that is different from the worked example.
- Correct this common mistake: “The voltage and power ratings on a label are meter readings taken at the present moment.”