Compare multiappliance daily energy and costs
Add energy across appliances and compare long low-power use with shorter high-power operation.
Section P4.2.5 · Electrical energy and electrical power
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Calculate kWh and energy cost.
- Read multiple power–time accounts.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 1.2 kWh plus 0.4 kWh?
What you will learn
- Add separately calculated appliance energies.
- Compare costs over the same interval and stated tariff.
Total amounts instead of unmatched rates
Calculate each appliance's energy for its own operating duration, then add the kWh amounts. A 0.8 kW appliance for 1.5 h uses 1.2 kWh; a 0.1 kW appliance for 4 h uses 0.4 kWh. Total use is 1.6 kWh. At a fictional 0.25 currency units/kWh, their combined energy charge is 0.40 currency units.
Adding the powers and multiplying by one selected duration is valid only when the appliances run simultaneously for that same complete interval under matching conditions. Separate durations in the question must be retained. An appliance used on several days requires the supplied pattern for each day's total.
Compare power and duration together
A low input rate can still accumulate a noticeable amount over a long time. A 0.01 kW standby load for 20 h uses 0.2 kWh. A 1 kW load for 0.25 h uses 0.25 kWh. The second is one hundred times as powerful, but uses only 1.25 times the energy over these different stated durations.
Use the same tariff and time boundary for a fair cost comparison. This arithmetic does not establish a home's actual usage or savings; real operating patterns, cycling, measurement and billing terms must be supplied. Keep the example's fictional prices separate from actual purchasing or tariff advice.
Sources for this lesson
Pause and explain
Compare 0.01 kW for 20 h with 1 kW for 0.25 h.
Worked example
Total energy and energy charge for 0.8 kW over 1.5 h and 0.1 kW over 4 h at fictional 0.25 currency units/kWh.
Show the worked solution
- First energy = 1.2 kWh; second = 0.4 kWh.
- Total = 1.6 kWh.
- Energy charge = 1.6 × 0.25 = 0.40 currency units.
Answer 1.6 kWh; 0.40 currency units.
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Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Total energy for 0.8 kW over 1.5 h and 0.1 kW over 4 h.
Give me a hint
Find both power–duration products before adding.
Compare my reasoning
- First: 1.2 kWh.
- Second: 0.4 kWh.
- Total: 1.6 kWh.
1.6 kWh.
Look for these in your work
- Retain both times.
- Add compatible energy amounts.
Price that 1.6 kWh total at a fictional 0.25 currency units/kWh. Compare the individual energy charges.
Give me a hint
Apply the same tariff to each amount and check their sum.
Compare my reasoning
- First cost = 1.2 × 0.25 = 0.30.
- Second cost = 0.4 × 0.25 = 0.10.
- Combined energy charge = 0.40 currency units.
0.30 and 0.10; total 0.40 currency units.
Look for these in your work
- Use the same price.
- Check the separate charges sum.
Compare a 0.01 kW standby load for 20 h with a 1 kW load for 0.25 h. Find their energy ratio, second divided by first.
Give me a hint
Compute energy first rather than using the power ratio alone.
Compare my reasoning
- Standby energy = 0.2 kWh.
- Other energy = 0.25 kWh.
- Ratio = 0.25/0.2 = 1.25.
0.2 kWh; 0.25 kWh; energy ratio 1.25.
Look for these in your work
- Include both durations.
- Keep energy ratio separate from the power ratio.
Common mistakes
- Keep each duration.
- A power ratio is not necessarily the energy ratio.
- Do not infer real usage from fictional examples.
What can you explain now?
What should be added when appliances have different operating times?
Compare with the explanation
Their separate energy amounts.
Each appliance's power acts over its own stated time, giving compatible kWh amounts to total.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Total energy and supplied costs for different appliances and explain how long low-power operation compares with short high-power use.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.