Electric Circuits · Grade 10
What is an electricity bill counting — watts or kilowatt hours?
Kilowatt hours, which is a unit of energy and not of power. Power is a rate — how much energy per second — and is measured in watts. Energy is power times time. An appliance of one kilowatt running for an hour has used one kilowatt hour, and that is what you pay for.
Learning objectives
- Calculate the power of a component from the voltage across it and the current through it
- Work out the energy in kilowatt hours used by an appliance that runs for a given number of hours
- Explain why a thin extension cable heats up when a heater is plugged into it
- Compare two appliances by their cost of operation over a year rather than by their purchase price
Power and energy
Power is voltage times current. An appliance running at 230 V drawing 5 A uses 1150 watts, that is about 1.15 kilowatts.
Energy is power times time. On an electricity bill it is convenient to measure it in kilowatt hours: one kilowatt for one hour.
The difference between the two is the difference between speed and distance. Power says how fast energy is being used; a kilowatt hour says how much has been used altogether. A powerful appliance running for a minute can cost less than a weak one running all night.
Two more formulas worth holding
Ohm's law lets you substitute. Power also equals current squared times resistance, and voltage squared divided by resistance.
The first of those is the key to cables heating up. The power wasted in a cable depends on the square of the current: double the current and the heating grows fourfold.
So a thin extension cable heats up when a heater is plugged into it. The cable is thin, its resistance relatively high, the heater draws a large current, and the product becomes heat in the cable instead of in the heater.
Comparing appliances properly
The purchase price is paid once; the electricity is paid every month. A cheap appliance that uses more can cost more within a year.
The calculation is simple: the power in kilowatts, times hours of use per day, times 365, times the price of a kilowatt hour. The right comparison is between those totals, not between the price tags.
Worked examples
An appliance at 230 V draws 2 A. What is its power?
- Power equals voltage times current
- 230 times 2
Answer: 460 watts
A 2000 W heater runs for 3 hours. How many kilowatt hours were used?
- 2000 watts is 2 kilowatts
- Energy equals power times time
- 2 times 3
Answer: 6 kilowatt hours
Why does a thin cable heat up with a heater but not with a lamp?
- The power wasted in the cable is current squared times resistance
- A heater draws far more current than a lamp
- Squaring magnifies the difference
Answer: Because of the large current, which enters the calculation squared
Common mistakes
- Calling the kilowatt hour a unit of power
- A kilowatt is power; a kilowatt hour is power times time, which is energy. It is the unit you are billed for.
- Comparing appliances by purchase price
- The electricity comes back every month. A cheap appliance that uses more can cost more within a year, and the proper comparison includes both.
- Assuming the heat in a cable depends on the voltage
- It depends on the current squared and the cable's resistance. The same voltage with twice the current gives four times the heat, which is the danger in a thin cable.
What to remember
- Power equals voltage times current, measured in watts.
- Energy equals power times time, measured in kilowatt hours.
- Power in a cable equals current squared times resistance.
- Compare appliances by what they cost to run in a year.