D. Physics: Principles and Applications of Electricity · Electricity: Charges, Circuits and EnergyElectricity Versus Electrical Energy: Power and the Kilowatt-Hour
D2.7 D1.2 A2.4About 65 minutes
Learning goals- I can explain the difference between electricity and electrical energy.
- I can explain that charges are not used up in a circuit, but energy is transferred and transformed.
- I can calculate power with P = V × I and P = E ÷ t.
- I can calculate electrical energy in joules and in kilowatt-hours, and estimate its cost.
Words to know
electricity
The general name for all the effects of electric charges, at rest (static electricity) or moving (current electricity).
electrical energy
The energy carried by electric charges and transferred to loads in a circuit, where it is transformed into other forms. Measured in joules (J) or kilowatt-hours (kWh).
power (P)
The rate at which energy is transferred or transformed: P = E ÷ t. For electrical devices, P = V × I. Unit: the watt (W); 1 W = 1 J/s.
kilowatt (kW)
1000 watts.
kilowatt-hour (kWh)
The energy transferred when 1 kW of power is used for 1 hour. 1 kWh = 3 600 000 J (3.6 MJ). Electricity bills charge for kWh.
energy transformation
A change of energy from one form into another, such as electrical energy into light and thermal energy in a lamp.
What are you really paying for?
People say "we used a lot of electricity this month" or "save electricity". But the electrons in your home's wires were there before you moved in, and they are still there. You do not buy electrons. So what does the bill measure?
It measures electrical energy. The two words, electricity and electrical energy, are used loosely in everyday talk, but in science they mean different things.
Electricity and electrical energy
Electricity is the whole family of effects caused by electric charges: static charge on a balloon, a spark, lightning, and current in a wire are all electricity.
Electrical energy is the energy that charges carry or transfer. In a circuit:
- The source (battery, generator) gives energy to the charges.
- The charges carry it around the circuit.
- The loads transform it into other forms: light, thermal energy, sound, motion.
- The charges return to the source, ready to be given more energy. The charges are not used up; the energy is transferred.
So when you "use electricity", what you actually use is electrical energy, which is changed into other forms. The current (how many charges pass per second) is the same going into a lamp as coming out of it; it is the energy that is left behind in the lamp.
| Electricity | Electrical energy |
|---|
| What it is | The effects of electric charges at rest or in motion | The energy carried and transferred by charges |
| Includes | Static charge, sparks, lightning, current | What a battery stores (as chemical energy) and delivers; what a toaster transforms |
| Measured as | Charge (C), current (A), potential difference (V) | Joules (J) or kilowatt-hours (kWh) |
| Is it used up? | Charges are not used up | Energy is transformed into other forms (and is conserved overall) |
Power: how fast energy is transferred
A 1500 W kettle and a 9 W LED bulb both use electrical energy, but the kettle transforms it far faster. Power is the rate of energy transfer:
P = E ÷ t (watts = joules per second)
For an electrical device, power also equals potential difference times current:
P = V × I
This makes sense: V is energy per coulomb, and I is coulombs per second, so V × I is energy per second. The watt is named after James Watt, a Scottish engineer.
Worked exampleExample 1: Power from V and I
A hair dryer draws 10 A from a 120 V outlet. What is its power?
- P = V × I
- P = 120 V × 10 A = 1200 W
P = 1200 W = 1.2 kW. The hair dryer transforms 1200 J of electrical energy every second.
Energy in joules and in kilowatt-hours
Rearranging P = E ÷ t gives E = P × t.
- With P in watts and t in seconds, E is in joules.
- With P in kilowatts and t in hours, E is in kilowatt-hours (kWh). This is the unit on electricity bills, because joules are tiny: 1 kWh = 1000 W × 3600 s = 3 600 000 J.
Cost = energy used (kWh) × price per kWh
In Ontario, the price per kWh depends on the price plan and the time of day, and a bill also includes delivery and other charges. In the examples below we use simple made-up prices so that the math is clear.
Worked exampleExample 2: A kettle in joules and in kWh
A 1500 W kettle runs for 4.0 minutes. How much electrical energy does it transform? Give the answer in joules and in kWh.
- Joules: t = 4.0 × 60 = 240 s. E = P × t = 1500 W × 240 s = 360 000 J.
- kWh: P = 1.5 kW, t = 4.0 ÷ 60 = 0.0667 h. E = 1.5 kW × 0.0667 h = 0.10 kWh.
- Check: 0.10 kWh × 3 600 000 J/kWh = 360 000 J ✓
The kettle transforms 360 000 J, which is 0.10 kWh.
Worked exampleExample 3: The cost of a light left on
A 9 W LED bulb is left on for 6 hours a day for 30 days. Assume a price of 10¢ per kWh. What does it cost?
- Time: 6 h/day × 30 days = 180 h
- Energy: E = P × t = 0.009 kW × 180 h = 1.62 kWh
- Cost = 1.62 kWh × 10¢/kWh = 16.2¢
About 16¢ for the month. An old 60 W incandescent bulb giving similar light would use 0.060 × 180 = 10.8 kWh, costing about $1.08, nearly 7 times as much.
Unit check
- P = V × I: volts × amps = watts.
- E = P × t: watts × seconds = joules; kilowatts × hours = kWh.
- Divide watts by 1000 to get kW; divide minutes by 60 to get hours.
- 1 kWh = 3.6 million joules.
Hands-on activityHome energy detective
You need: a notebook, a calculator, and the labels on 5 devices or appliances in your home (look on the back or bottom; many are near the cord).
- Make a table with columns: device, power (W), hours used per day (estimate), energy per day (kWh), cost per day.
- For each device: energy per day = (W ÷ 1000) × hours. Cost = energy × price. Use 10¢ per kWh for practice, or ask a parent to show you the price per kWh on a real bill.
- Which device uses the most energy per day? Is it the one with the highest power rating, or the one used for the most hours?
- Suggest one change that would cut your household's electrical energy use, and estimate how many kWh it would save in a month.
Model answer: a 100 W TV used 3 h/day uses 0.1 × 3 = 0.3 kWh (3¢ per day at 10¢/kWh). A 1500 W kettle used 10 minutes a day uses 1.5 × (10 ÷ 60) = 0.25 kWh. A device with a lower power rating can still use more energy if it runs for longer.
Safety (grown-up note): Only read labels; leave devices where they are if they are hard to reach, and unplug before turning anything over.
Just for funThe watt is named after James Watt, an engineer famous for improving the steam engine in the 1700s. So every time you check the wattage on an LED bulb, you are honouring a steam-engine expert who died (in 1819) about 60 years before practical electric light bulbs went on sale.
Your turn
1In one or two sentences, explain the difference between electricity and electrical energy.
Electricity is the general name for the effects of electric charges (static or moving). Electrical energy is the energy those charges carry and transfer to loads, measured in J or kWh.
2Is current used up as it passes through a lamp? What is used?
No, the current is the same in and out. The electrical energy is transferred to the lamp and transformed into light and thermal energy.
3A toaster draws 7.5 A from a 120 V outlet. Find its power.
P = V × I = 120 × 7.5 = 900 W.
4A 60 W lamp is on for 2.0 minutes. How much energy does it transform in joules?
E = P × t = 60 W × 120 s = 7200 J.
5A 2.0 kW heater runs for 3.0 hours. How many kWh does it use? What does it cost at 10¢/kWh?
E = 2.0 × 3.0 = 6.0 kWh; cost = 6.0 × 10¢ = 60¢.
6Convert 1 kWh into joules.
1000 W × 3600 s = 3 600 000 J.
More practice: warm-up
1What is the unit of power?
The watt (W): 1 W = 1 J/s.
2Write two formulas for electrical power.
4What unit do electricity bills use for energy?
5Name the energy forms a lamp produces.
Light and thermal energy.
More practice: on your own
1A 12 V car battery supplies 5.0 A to the headlights. What is the power? How much energy is used in 10 minutes?
P = 12 × 5.0 = 60 W. E = 60 W × 600 s = 36 000 J.
2A microwave is rated 1000 W at 120 V. What current does it draw?
I = P ÷ V = 1000 ÷ 120 ≈ 8.3 A.
3A family's fridge uses about 1.2 kWh per day. Estimate its energy use over a 30-day month and the cost at 12¢/kWh.
30 × 1.2 = 36 kWh; 36 × 12¢ = 432¢ = $4.32.
4Two students argue. Ana: "A battery stores electricity." Ben: "A battery stores energy." Who is more accurate? Explain.
Ben. A battery stores chemical potential energy, which it transforms into electrical energy when it drives charges around a circuit. It does not store charge waiting to come out.
5Which uses more energy: a 1500 W kettle for 3 minutes, or a 10 W LED lamp for 8 hours?
Kettle: 1.5 kW × 0.05 h = 0.075 kWh. Lamp: 0.010 kW × 8 h = 0.080 kWh. The lamp uses slightly more, even though its power is 150 times smaller, because it runs much longer.
Challenge
1Show that P = V × I gives units of watts, using the definitions of the volt and the ampere.
1 V = 1 J/C and 1 A = 1 C/s. V × I = (J/C) × (C/s) = J/s, and 1 J/s = 1 W. The coulombs cancel.
2Using P = V × I and V = I × R, show that the power of a resistor can also be written P = I² × R. Then find the power of a 9.6 Ω kettle element carrying 12.5 A.
Substitute V = I × R into P = V × I: P = (I × R) × I = I² × R. P = 12.5² × 9.6 = 156.25 × 9.6 = 1500 W.
3A home uses 750 kWh in a month. A family switches 20 bulbs from 60 W incandescent to 9 W LED. Each bulb is on 4 h/day. Estimate the monthly saving in kWh (30 days) and the percent reduction in the home's use.
Saving per bulb = 51 W. Total = 20 × 51 W = 1020 W = 1.02 kW. Hours = 4 × 30 = 120 h. Saving = 1.02 × 120 ≈ 122 kWh. Percent = 122 ÷ 750 × 100% ≈ 16%.
Quiz
1. Which statement is correct?
2. As current passes through a lamp:
3. A device draws 2.0 A at 120 V. Its power is:
5. A 500 W device runs for 4.0 hours. It uses:
6. Which word best describes a balloon stuck to a wall?
Big idea: Expectation D2.7 asks students to explain the difference between electricity and electrical energy. Electricity is the broad set of phenomena caused by charges; electrical energy is what charges carry and what we pay for. The power and kWh calculations prepare students to evaluate energy use in the next lessons (D1).
Common difficulties:
- "Current gets used up." Current in = current out; energy is what gets transferred.
- Units: W vs kW, minutes vs hours, J vs kWh.
- High power ≠ most energy. A low-power device left on for a long time can use more energy.
How to help: Look at a real electricity bill together and find the kWh used and the price per kWh (Ontario plans include time-of-use, tiered and ultra-low overnight options). Ask your teen which appliances they think use the most energy, then check with labels.