Lesson 6 of 8Principles & Applications of Electricity

Unit 4 · Lesson 6 of 8

Electrical Energy, Power and Cost

Electricity is the general name for the effects of electric charges; electrical energy is the energy that moving charges carry and that loads transform. Power is how fast that energy is transformed. Learn P = VI and E = Pt, why utilities measure energy in kilowatt-hours, how to calculate the cost of running an appliance, and how time-of-use pricing works in Ontario.

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Key things to remember

1Electricity is the general term for effects of electric charges; electrical energy is the energy carried by moving charges and transformed by loads.
2Power is the rate of energy transformation: $P = \frac{E}{t}$ and $P = V I$ , measured in watts (1 W = 1 J/s).
3Energy: $E = Pt$ . In joules, use watts and seconds; in kilowatt-hours, use kilowatts and hours.
4 $1 kWh = 3.6 \times 1 0^{6} J$ ; kW measures power, kWh measures energy.
5Cost = energy (kWh) × price per kWh.

Every month or two, an Ontario home gets an electricity bill. It does not charge for amperes or volts, and it does not charge for "electricity" as a thing you can pile up. It charges for energy, counted in kilowatt-hours. To understand that bill, and to save money on it, you need to know the difference between power and energy, and how to calculate each one. A space heater and an LED bulb can both run all evening, but one of them costs far more. In this lesson you will find out exactly how much more.

Electricity vs electrical energy

Electricity is a general word for everything involving electric charges, whether still (static electricity) or moving (current electricity). Electrical energy is the energy carried by moving charges, which loads transform into other forms: light in a lamp, thermal energy in a toaster, kinetic energy in a fan, sound in a speaker. The charges themselves are not used up. The electrons in your home's wiring were already in the copper and they stay in the circuit; in fact, with alternating current they mostly jiggle back and forth. What the power plant sends you, and what you pay for, is the energy.

Power: how fast energy is transformed

Power is the rate at which energy is transformed. Its symbol is $P$ and its unit is the watt (W): 1 W means 1 joule of energy every second. A kilowatt (kW) is 1000 W. A 10 W LED bulb transforms 10 J of electrical energy every second; a 1500 W kettle transforms 1500 J every second. Power in a circuit is also easy to find from the meters: multiply the potential difference (joules per coulomb) by the current (coulombs per second) and you get joules per second.

P = \frac{E}{t} P = V I E = P t

P in watts (W), E in joules (J), t in seconds (s), V in volts (V), I in amperes (A).

Fig 1Two formula triangles. The left one is Ohm's law (V = IR). The right one is for power: cover what you want to get P = VI, I = P/V or V = P/I. The extra power formulas shown under it are for later physics courses.

Kilowatt-hours

A joule is a tiny amount of energy, so a home's monthly use would be hundreds of millions of joules. Utilities use a bigger unit, the kilowatt-hour (kWh): the energy transformed by a 1 kW device running for 1 hour. To get energy in kWh, use $E = P \times t$ with power in kilowatts and time in hours. Then multiply by the price per kWh to get the cost. Be careful: kW is a unit of power (how fast), and kWh is a unit of energy (how much). It is like the difference between a car's speed in km/h and the distance it travels in km.

1 kWh = 1000 W \times 3600 s = 3600000 J cost = E (kWh) \times price per kWh

One kilowatt-hour is 3.6 million joules.

Appliance	Typical power	Time used	Energy
LED light bulb	10 W = 0.010 kW	5 h	0.05 kWh
Laptop	50 W = 0.050 kW	4 h	0.2 kWh
Television	100 W = 0.10 kW	3 h	0.3 kWh
Electric kettle	1500 W = 1.5 kW	6 min = 0.1 h	0.15 kWh
Space heater	1500 W = 1.5 kW	4 h	6 kWh
Clothes dryer	5000 W = 5.0 kW	1 h	5 kWh

Typical values; real appliances vary. Devices that make heat use the most energy, especially when they run for hours.

How Ontario prices electricity

Most Ontario homes have a smart meter that records how much energy is used in each hour. Households can choose a price plan. On time-of-use pricing, electricity costs more on weekdays during on-peak hours, when the whole province uses the most, and less overnight and on weekends. Other plans charge one price up to a set amount each month and a higher price after that, or offer an extra-low price overnight. Prices change over time, so questions in this course give you an example rate, such as 10 cents per kWh. Shifting jobs like laundry to off-peak times saves money and eases the load on the grid at its busiest times.

Standby power adds up

Many devices draw a little power even when they look "off": TVs, game consoles, chargers left in the wall and anything with a glowing light or clock. Each one may use only a few watts, but it runs 24 hours a day, every day. Unplugging devices or using a power bar with a switch cuts this standby (or "phantom") load.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1

A kettle draws 12.5 A from a 120 V outlet. What is its power, in watts and in kilowatts?

Example 2

That 1.5 kW kettle runs for 4.0 minutes to boil water. How much electrical energy does it use, in kWh and in joules?

Example 3

A 60 W incandescent bulb and a 9 W LED bulb give about the same light. Each runs 5.0 h a day for 30 days. At an example price of 10 cents per kWh, how much does each cost to run, and how much does the LED save?

Where marks get lost

Mixing up kW and kWh. A kilowatt is a rate (power); a kilowatt-hour is an amount (energy). Your bill charges for kWh.
Using minutes in E = Pt when the answer should be in kWh. Convert minutes to hours by dividing by 60 (30 min = 0.5 h).
Multiplying watts by hours and calling the answer kWh. 100 W × 3 h = 300 Wh, which is 0.3 kWh; divide watts by 1000 first.
Saying you pay the power company for electrons or for current. The charges stay in the circuit; you pay for the electrical energy they deliver.
Thinking a device with a high power rating always costs more than one with a low rating. Cost depends on power AND time: a 10 W device left on all month can cost more than a 1500 W kettle used for a few minutes a day.

Flashcards 9

Electricity

Electrical energy

Power (P)

Power in a circuit

+ 5 more

Practice

Which unit is used on an electricity bill to measure the amount of energy used?

A lamp connected to 120 V draws a current of 0.50 A. What is its power, in watts?

A 1200 W hair dryer runs on a 120 V outlet. What current does it draw, in amperes?

A 2.0 kW electric heater runs for 3.0 hours. How much energy does it use, in kWh?

kWh

A 100 W television is on for 30 minutes. How much energy does it use, in kWh? Give your answer to three decimal places.

kWh

A 1500 W space heater runs for 4.0 hours. At an example price of 12 cents per kWh, how much does this cost, in cents?

cents

A 10 W LED bulb is on for 1.0 minute. How much electrical energy does it transform, in joules?

Match each quantity to the unit you would usually use for it.

Power of an appliance

Energy on a home electricity bill

Energy in SI base units

Price of electricity

Which statement best describes the difference between electricity and electrical energy?

A device uses 1 kW of power for 1 hour. Name the unit of energy that equals exactly this amount.

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