Reading a power rating

1. Every mains appliance carries a data plate giving the supply it is designed for, $230V$ at $50Hz$ in the United Kingdom, and its power rating in watts or kilowatts.
2. The power rating is the energy the appliance transfers each second while it is working normally, so a rating of $2000W$ means $2000J$ every second.
3. Ratings are quoted either way round, since $1kW=1000W$, so $2000W$ and $2.0kW$ are the same rating.
4. Typical UK figures are an electric shower at $9.0kW$, a kettle at $3.0kW$, a hair dryer at $2.0kW$, a laptop at $65W$, a fridge at $100W$ and an LED lamp at $8W$.
5. A larger power rating means energy is transferred faster, not that more energy is used in total, because the total energy also depends on how long the appliance runs.
6. A fridge with a small rating runs for many hours a day, while a kettle with a large rating runs for only a few minutes, so the fridge can easily use more energy over a day.
7. Some appliances switch themselves on and off, so the rating gives the power while the appliance is actually working rather than an average over the day.

Current drawn by appliances

1. The current an appliance draws from the mains follows from the power equation $P=IV$, where $P$ is in watts, $I$ is in amperes and $V$ is in volts.
2. Rearranging for the current gives $I=\frac{P}{V}$, and for a UK mains appliance the potential difference used is $V=230V$.
3. Because the supply potential difference is fixed, the current is decided by the power rating alone: the larger the rating, the larger the current.
4. A $2.0kW$ hair dryer therefore draws a far larger current than a $65W$ laptop charger plugged into the same socket.
5. The current matters because it decides how thick the flex must be, how warm the flex becomes in use, and which fuse should be fitted in the plug.
6. A power in kilowatts must be converted to watts before substituting, so $2.0kW$ becomes $2000W$, otherwise the current comes out $1000$ times too small.

Choosing a fuse

1. A fuse is chosen so that it carries the appliance's normal working current without melting, yet melts quickly if a fault makes the current much larger.
2. The standard cartridge fuses fitted in a UK plug are rated at $3A$, $5A$ and $13A$.
3. The working current is found first from $I=\frac{P}{V}$, and the fuse chosen is then the smallest standard rating above that working current.
4. A fuse rated below the working current would melt every time the appliance was switched on, so the appliance would never work.
5. A fuse rated far above the working current is also unsafe, because a fault current could flow for a long time, overheating the flex and starting a fire before the fuse melted.
6. A $2.0kW$ hair dryer drawing $8.7A$ therefore takes a $13A$ fuse, while a $460W$ television drawing $2.0A$ takes a $3A$ fuse.
7. A $3.0kW$ kettle draws $\frac{3000}{230}=13A$, which sits right at the limit of the standard range, so it is fitted with the $13A$ fuse because no larger plug fuse is made.

The kilowatt-hour

1. The joule is an inconveniently small unit for household energy, since a single kettle boiling transfers a few hundred thousand joules and a whole house uses a few thousand million in a quarter.
2. Domestic energy is therefore measured in kilowatt-hours, and one kilowatt-hour is the energy transferred by an appliance of power $1kW$ working for $1hour$.
3. Energy in kilowatt-hours is found from $E=P\times t$ with the power $P$ in kilowatts and the time $t$ in hours, which is the same equation as $E=Pt$ in joules and seconds but with larger units.
4. Converting to joules uses $1kW=1000W$ and $1hour=3600s$, so $1kWh=1000\times 3600=3.6\times 10^{6}J$.
5. A time given in minutes is converted to hours by dividing by $60$, so $12minutes=\frac{12}{60}=0.20h$.
6. The electricity meter in a house counts kilowatt-hours, and one kilowatt-hour is what a bill calls a unit of electricity.

Cost of electricity

1. The cost of running an appliance is the energy it transfers multiplied by the price of one unit, so cost $=$ energy in $kWh$ $\times$ price per $kWh$.
2. The price is quoted in pence per kilowatt-hour, for example $27p$ per unit, and multiplying by an energy in kilowatt-hours gives a cost in pence.
3. Dividing a cost in pence by $100$ converts it to pounds, so $1458p$ is £14.58\pounds14.58£14.58.
4. Two appliances at the same price per unit can be compared directly by their energy in kilowatt-hours, since the price cancels out of the comparison.
5. A standing charge on a bill is a fixed daily amount that does not depend on the energy used, so it is added after the energy cost has been worked out.
6. Reducing a cost means reducing the energy, which can be done by lowering the power rating, shortening the time of use, or both.

Comparing appliances

1. Comparing two appliances means comparing the energy each transfers over the time it is actually used, not their power ratings alone.
2. A filament lamp rated at $60W$ and an LED lamp rated at $8W$ give out a similar amount of light, so the LED does the same useful job for a much smaller power.
3. Left on for $1000h$, the filament lamp transfers $E=0.060\times 1000=60kWh$ while the LED lamp transfers $E=0.008\times 1000=8kWh$.
4. The saving of $52kWh$ is worth $52\times 27=1404p$, which is £14.04\pounds14.04£14.04 over the life of one lamp.
5. Time can outweigh power completely: a $100W$ fridge running all day transfers $0.100\times 24=2.4kWh$, while a $3.0kW$ kettle used for $10minutes$ transfers only $3.0\times \frac{10}{60}=0.50kWh$.
6. The fridge, with a rating $30$ times smaller, therefore uses nearly five times as much energy in a day as the kettle.