11 2.3 Electric power and energy
Energy-efficiency label. Appliances such as refrigerators carry a label that shows the energy rating and the monthly energy consumption, so that buyers can choose appliances that consume less (the highest rating, shown by the green arrow, A, means the highest efficiency and lowest consumption).
Electric power (P) is the rate at which an appliance consumes electric energy, i.e. the energy it consumes per second.
P = E / t, so E = P × t
Unit of power: watt (W) = 1 joule per second. "A 9 W LED lamp" uses 9 joules of electrical energy every second.
The joule is a very small unit of energy, so in household billing the larger unit kilowatt-hour (kW·h) is used: 1 kW·h = 1000 W × 3600 s = 3.6 × 10⁶ J.
Cost of electric energy. Follow four steps:
- Power in kW = power in W ÷ 1000.
- Find the number of operating hours.
- Energy in kW·h = power in kW × hours.
- Cost = energy in kW·h × price per kW·h.
(The price per kW·h used in the book's example is 1.55 Egyptian pounds. For your own calculations use the price given in the question.)
Worked example 7: comparing two lamps
A CFL of 20 W and an LED of 12 W give about the same light. Compare the monthly (30-day) costs if each is used 12 h per day at 1.55 pounds per kW·h. Hours = 30 × 12 = 360 h. CFL: 0.020 kW × 360 = 7.2 kW·h; cost = 7.2 × 1.55 = 11.16 pounds. LED: 0.012 × 360 = 4.32 kW·h; cost = 4.32 × 1.55 = 6.70 pounds. Saving = about 4.46 pounds per month per lamp. The LED is more efficient.
Worked example 8: a kettle
A 1500 W kettle is used 0.5 h per day. What is the weekly energy and cost at 1.55 pounds per kW·h? P = 1.5 kW. Hours per week = 0.5 × 7 = 3.5 h. Energy = 1.5 × 3.5 = 5.25 kW·h. Cost = 5.25 × 1.55 = 8.1375, about 8.14 pounds.
Worked example 9: equal energy
Appliance X has power 2000 W, appliance Y has 1000 W. X runs for 3 hours. How long must Y run to use the same energy? E = 2 kW × 3 h = 6 kW·h; time for Y = 6 / 1 = 6 hours. The lower the power, the longer it takes to use the same energy.
- Typical powers (for reference): electric heater 1–2 kW; iron 1–2.5 kW; air conditioner 1.5–2.5 kW; laptop about 50 W; fan 50–100 W; television about 100 W.
- Heating appliances and air conditioners consume the most energy.
- Increasing the operating hours (cause) increases the energy and the cost (effect).