Power and the watt

Definition

Power

The rate at which energy is transferred.

Definition

Watt

The unit of power, equal to one joule of energy transferred every second.

Power tells you how quickly energy is transferred, not how much energy is transferred in total.
Power is measured in watts ( $W\text{W}$ ), and a power of $W1\ \text{W}$ means that $J1\ \text{J}$ of energy is transferred every second, so $J/s1\ \text{W} = 1\ \text{J/s}$ .
Larger powers are given in kilowatts ( $kW\text{kW}$ ), where $W1\ \text{kW} = 1000\ \text{W}$ .
The equation that links them is $transferredtime\text{power} = \dfrac{\text{energy transferred}}{\text{time}}$ , or $\dfrac{E}{t}$ , with power in $W\text{W}$ , energy in $J\text{J}$ and time in $s\text{s}$ .
Rearranging gives $transferred=power×time\text{energy transferred} = \text{power} \times \text{time}$ , or $\times t$ , and $transferredpower\text{time} = \dfrac{\text{energy transferred}}{\text{power}}$ , or $\dfrac{E}{P}$ .
The rearranged form shows that the energy an appliance transfers depends on two things, its power and the time it is switched on for.
Time must be converted into seconds before substituting, so $5$ minutes becomes $\times 60 = 300\ \text{s}$ , and a power in kilowatts must be converted into watts.

Power ratings of appliances

Definition

Power rating

The power at which an appliance is designed to transfer energy when it is operating normally.

Every electrical appliance carries a power rating, printed on a label on its base or back, often next to the supply voltage, such as $V230\ \text{V}$ , $kW3\ \text{kW}$ on a kettle.
The power rating tells you how many joules the appliance takes in from the mains or a battery each second when it is working normally.
Electric shower: about $kW9\ \text{kW}$ , because cold water must be heated almost instantly as it flows through.
Kettle: about $kW3\ \text{kW}$ , enough to boil a full kettle in a few minutes.
Hairdryer: about $kW2\ \text{kW}$ on its hottest setting.
Microwave oven: about $W800\ \text{W}$ .
Television: about $W100\ \text{W}$ .
Laptop charger: about $W60\ \text{W}$ .
LED lamp: about $W8\ \text{W}$ .
The appliances with the highest power ratings are those that heat things, especially water, because large amounts of energy have to be transferred to a thermal energy store in a short time.
Appliances that only produce light, sound or small movements have much lower power ratings.
Many appliances have more than one setting, and each setting has its own power.
1. A hairdryer on its cool setting runs only its motor at a few hundred watts, while on its hot setting the heating element is also switched on and the power rises to about $kW2\ \text{kW}$ .
2. A microwave oven set to $W600\ \text{W}$ instead of $W800\ \text{W}$ transfers less energy to the food each second, so the food takes longer to heat up.

Power and changes in stored energy

When an appliance is in use, its power rating tells you how quickly the energy stores linked to it are changing.
In a $kW3\ \text{kW}$ kettle, energy is transferred electrically at $J3000\ \text{J}$ every second, and most of it goes into the thermal energy store of the water, so the temperature of the water rises quickly.
A $kW2\ \text{kW}$ kettle holding the same water transfers energy at only $J2000\ \text{J}$ every second, so the thermal energy store of the water increases more slowly and the water takes longer to boil.
Both kettles have to transfer about the same total energy to boil the same water, so the higher-power kettle does it in less time.
In a fan, the power rating sets how quickly energy is transferred to the kinetic energy stores of the blades and the air.
In a battery-powered device, the power tells you how quickly the chemical energy store of the battery decreases, which is why a phone running a game at high brightness goes flat much sooner than a phone left on standby.
The power rating describes the rate at which energy is taken in, so the useful store always increases a little more slowly than this, because part of the energy is wasted.
For any appliance, a higher power rating means more energy is transferred in the same time, and leaving an appliance on for longer transfers more energy at the same power.
A low-power appliance left on for a long time can therefore transfer more energy than a high-power appliance used for a few minutes.

Measuring the power of an appliance

Definition

Joulemeter

An instrument that measures the total energy transferred to an electrical appliance, in joules.

A joulemeter is connected between the supply and the appliance, and its display counts up the joules transferred to the appliance while it is switched on.
Timing the same period with a stopwatch gives the time, so the power can be calculated from $\dfrac{E}{t}$ .
Comparing the measured power with the power rating on the label checks whether the appliance is working as designed.

Example

Energy transferred by a kettle

A kettle with a power rating of $kW3.0\ \text{kW}$ is switched on for $2.5$ minutes.
Convert the power into watts and the time into seconds: $W3.0\ \text{kW} = 3000\ \text{W}$ and $2.5 \times 60 = 150\ \text{s}$ .

\times t

\times 150

450\,000\ \text{J}

This energy is transferred electrically from the mains, and most of it ends up in the thermal energy store of the water.

Example

Comparing a shower and a lamp

An electric shower rated at $W9000\ \text{W}$ is used for $8$ minutes, and an LED lamp rated at $W8\ \text{W}$ is left on for $24$ hours.
Energy transferred by the shower, using $\times 60 = 480\ \text{s}$ :

\times 480 = 4\,320\,000\ \text{J}

Energy transferred by the lamp, using $24 \times 60 \times 60 = 86\,400\ \text{s}$ :

\times 86\,400 = 691\,200\ \text{J}

The shower transfers about six times as much energy as the lamp, even though it is on for a far shorter time, because its power rating is more than a thousand times greater.

Example

How long a phone battery lasts

A fully charged phone battery stores about $J54\,000\ \text{J}$ in its chemical energy store.
Time for the battery to empty while the phone is used for messages at a power of $W1.5\ \text{W}$ :

\frac{E}{P} = \frac{54\,000}{1.5} = 36\,000\ \text{s}

Time for the battery to empty while the phone runs a game at a power of $W6.0\ \text{W}$ :

\frac{E}{P} = \frac{54\,000}{6.0} = 9000\ \text{s}

Dividing by $3600$ gives $10$ hours for messaging and $2.5$ hours for gaming, because the higher power empties the chemical energy store four times as quickly.

Practical

Using a joulemeter to find power

Aim: to measure the energy transferred to several low-voltage electrical appliances in a measured time, and use the readings to calculate the power of each one.
Apparatus: a low-voltage power supply, a joulemeter, a stopwatch, connecting leads, and a set of low-voltage appliances such as a $V12\ \text{V}$ filament lamp, a small electric motor with a fan blade, a $V12\ \text{V}$ immersion heater in a beaker of water and a small buzzer.
Method, setting up:
- Connect the power supply to the input terminals of the joulemeter, and connect the first appliance to the output terminals, so that every joule reaching the appliance passes through the meter.
- Set the power supply to the voltage marked on the appliance and keep it switched off.
- Press the reset button so that the joulemeter reads $J0\ \text{J}$ , and check whether its display shows joules or kilojoules.
Method, taking readings:
- Switch on the power supply and start the stopwatch at the same moment.
- Let the appliance run for exactly $2$ minutes, watching that the reading on the joulemeter rises steadily.
- Switch off the supply as the stopwatch reaches $s120\ \text{s}$ , then record the final joulemeter reading in a results table.
- Reset the joulemeter and repeat the run twice more for the same appliance, then repeat the whole procedure for each of the other appliances.
Variables: the independent variable is the appliance being tested, the dependent variable is the energy transferred, and the control variables are the time each appliance runs for and the voltage of the supply.
Results: record the appliance, the three energy readings in joules, the mean energy and the time in seconds, then calculate the power of each appliance, and you should find that the immersion heater gives the largest reading and the buzzer the smallest.
Maths: calculate the mean energy for each appliance, then use $\dfrac{E}{t}$ , so a mean of $J2880\ \text{J}$ in $s120\ \text{s}$ gives $\dfrac{2880}{120} = 24\ \text{W}$ .
Watch out: starting and stopping the stopwatch late adds a reaction-time error, so a long timing period makes this error a smaller fraction of the total, and the repeat readings should agree closely before a mean is taken.
Safety: the immersion heater must be fully under water before it is switched on, the heater and lamp stay hot after use and should not be touched, and mains appliances are only ever tested by your teacher with a plug-in meter designed for the purpose.

Common Mistake

Do not mix up power and energy, because energy is measured in joules and power is measured in watts.
Do not assume that the appliance with the higher power rating always transfers more energy, because the total also depends on how long each appliance is used.
Do not substitute a time in minutes into $\times t$ , because the equation needs time in seconds to give energy in joules.

Exam technique

Explaining a power rating

When you explain what a power rating means, turn it into joules per second, for example by writing that a $W2000\ \text{W}$ heater transfers $J2000\ \text{J}$ of energy every second.
Link the rating to the store that changes, for example the thermal energy store of the water in a kettle or the kinetic energy store of a fan.
You must recall the power equation, so in a calculation write the equation, show the converted values, then give the answer with its unit, because each stage can earn a mark even if the final answer is wrong.

Self review

Define power.
State how many joules a $kW1.5\ \text{kW}$ heater transfers each second.
Explain why a $kW3\ \text{kW}$ kettle boils water faster than a $kW2\ \text{kW}$ kettle.
Calculate the energy transferred by a $W60\ \text{W}$ laptop charger in $10$ minutes.
Describe how a joulemeter and a stopwatch are used to find the power of an appliance.

Power and the watt

Definition

Power

The rate at which energy is transferred.

Definition

Watt

The unit of power, equal to one joule of energy transferred every second.

Power tells you how quickly energy is transferred, not how much energy is transferred in total.
Power is measured in watts ( $W\text{W}$ ), and a power of $W1\ \text{W}$ means that $J1\ \text{J}$ of energy is transferred every second, so $J/s1\ \text{W} = 1\ \text{J/s}$ .
Larger powers are given in kilowatts ( $kW\text{kW}$ ), where $W1\ \text{kW} = 1000\ \text{W}$ .
The equation that links them is $transferredtime\text{power} = \dfrac{\text{energy transferred}}{\text{time}}$ , or $\dfrac{E}{t}$ , with power in $W\text{W}$ , energy in $J\text{J}$ and time in $s\text{s}$ .
Rearranging gives $transferred=power×time\text{energy transferred} = \text{power} \times \text{time}$ , or $\times t$ , and $transferredpower\text{time} = \dfrac{\text{energy transferred}}{\text{power}}$ , or $\dfrac{E}{P}$ .
The rearranged form shows that the energy an appliance transfers depends on two things, its power and the time it is switched on for.
Time must be converted into seconds before substituting, so $5$ minutes becomes $\times 60 = 300\ \text{s}$ , and a power in kilowatts must be converted into watts.

Power ratings of appliances

Definition

Power rating

The power at which an appliance is designed to transfer energy when it is operating normally.

Every electrical appliance carries a power rating, printed on a label on its base or back, often next to the supply voltage, such as $V230\ \text{V}$ , $kW3\ \text{kW}$ on a kettle.
The power rating tells you how many joules the appliance takes in from the mains or a battery each second when it is working normally.
Electric shower: about $kW9\ \text{kW}$ , because cold water must be heated almost instantly as it flows through.
Kettle: about $kW3\ \text{kW}$ , enough to boil a full kettle in a few minutes.
Hairdryer: about $kW2\ \text{kW}$ on its hottest setting.
Microwave oven: about $W800\ \text{W}$ .
Television: about $W100\ \text{W}$ .
Laptop charger: about $W60\ \text{W}$ .
LED lamp: about $W8\ \text{W}$ .
The appliances with the highest power ratings are those that heat things, especially water, because large amounts of energy have to be transferred to a thermal energy store in a short time.
Appliances that only produce light, sound or small movements have much lower power ratings.
Many appliances have more than one setting, and each setting has its own power.
1. A hairdryer on its cool setting runs only its motor at a few hundred watts, while on its hot setting the heating element is also switched on and the power rises to about $kW2\ \text{kW}$ .
2. A microwave oven set to $W600\ \text{W}$ instead of $W800\ \text{W}$ transfers less energy to the food each second, so the food takes longer to heat up.

Power and changes in stored energy

When an appliance is in use, its power rating tells you how quickly the energy stores linked to it are changing.
In a $kW3\ \text{kW}$ kettle, energy is transferred electrically at $J3000\ \text{J}$ every second, and most of it goes into the thermal energy store of the water, so the temperature of the water rises quickly.
A $kW2\ \text{kW}$ kettle holding the same water transfers energy at only $J2000\ \text{J}$ every second, so the thermal energy store of the water increases more slowly and the water takes longer to boil.
Both kettles have to transfer about the same total energy to boil the same water, so the higher-power kettle does it in less time.
In a fan, the power rating sets how quickly energy is transferred to the kinetic energy stores of the blades and the air.
In a battery-powered device, the power tells you how quickly the chemical energy store of the battery decreases, which is why a phone running a game at high brightness goes flat much sooner than a phone left on standby.
The power rating describes the rate at which energy is taken in, so the useful store always increases a little more slowly than this, because part of the energy is wasted.
For any appliance, a higher power rating means more energy is transferred in the same time, and leaving an appliance on for longer transfers more energy at the same power.
A low-power appliance left on for a long time can therefore transfer more energy than a high-power appliance used for a few minutes.

Measuring the power of an appliance

Definition

Joulemeter

An instrument that measures the total energy transferred to an electrical appliance, in joules.

A joulemeter is connected between the supply and the appliance, and its display counts up the joules transferred to the appliance while it is switched on.
Timing the same period with a stopwatch gives the time, so the power can be calculated from $\dfrac{E}{t}$ .
Comparing the measured power with the power rating on the label checks whether the appliance is working as designed.

Example

Energy transferred by a kettle

A kettle with a power rating of $kW3.0\ \text{kW}$ is switched on for $2.5$ minutes.
Convert the power into watts and the time into seconds: $W3.0\ \text{kW} = 3000\ \text{W}$ and $2.5 \times 60 = 150\ \text{s}$ .

\times t

\times 150

450\,000\ \text{J}

This energy is transferred electrically from the mains, and most of it ends up in the thermal energy store of the water.

Example

Comparing a shower and a lamp

An electric shower rated at $W9000\ \text{W}$ is used for $8$ minutes, and an LED lamp rated at $W8\ \text{W}$ is left on for $24$ hours.
Energy transferred by the shower, using $\times 60 = 480\ \text{s}$ :

\times 480 = 4\,320\,000\ \text{J}

Energy transferred by the lamp, using $24 \times 60 \times 60 = 86\,400\ \text{s}$ :

\times 86\,400 = 691\,200\ \text{J}

The shower transfers about six times as much energy as the lamp, even though it is on for a far shorter time, because its power rating is more than a thousand times greater.

Example

How long a phone battery lasts

A fully charged phone battery stores about $J54\,000\ \text{J}$ in its chemical energy store.
Time for the battery to empty while the phone is used for messages at a power of $W1.5\ \text{W}$ :

\frac{E}{P} = \frac{54\,000}{1.5} = 36\,000\ \text{s}

Time for the battery to empty while the phone runs a game at a power of $W6.0\ \text{W}$ :

\frac{E}{P} = \frac{54\,000}{6.0} = 9000\ \text{s}

Dividing by $3600$ gives $10$ hours for messaging and $2.5$ hours for gaming, because the higher power empties the chemical energy store four times as quickly.

Practical

Using a joulemeter to find power

Aim: to measure the energy transferred to several low-voltage electrical appliances in a measured time, and use the readings to calculate the power of each one.
Apparatus: a low-voltage power supply, a joulemeter, a stopwatch, connecting leads, and a set of low-voltage appliances such as a $V12\ \text{V}$ filament lamp, a small electric motor with a fan blade, a $V12\ \text{V}$ immersion heater in a beaker of water and a small buzzer.
Method, setting up:
- Connect the power supply to the input terminals of the joulemeter, and connect the first appliance to the output terminals, so that every joule reaching the appliance passes through the meter.
- Set the power supply to the voltage marked on the appliance and keep it switched off.
- Press the reset button so that the joulemeter reads $J0\ \text{J}$ , and check whether its display shows joules or kilojoules.
Method, taking readings:
- Switch on the power supply and start the stopwatch at the same moment.
- Let the appliance run for exactly $2$ minutes, watching that the reading on the joulemeter rises steadily.
- Switch off the supply as the stopwatch reaches $s120\ \text{s}$ , then record the final joulemeter reading in a results table.
- Reset the joulemeter and repeat the run twice more for the same appliance, then repeat the whole procedure for each of the other appliances.
Variables: the independent variable is the appliance being tested, the dependent variable is the energy transferred, and the control variables are the time each appliance runs for and the voltage of the supply.
Results: record the appliance, the three energy readings in joules, the mean energy and the time in seconds, then calculate the power of each appliance, and you should find that the immersion heater gives the largest reading and the buzzer the smallest.
Maths: calculate the mean energy for each appliance, then use $\dfrac{E}{t}$ , so a mean of $J2880\ \text{J}$ in $s120\ \text{s}$ gives $\dfrac{2880}{120} = 24\ \text{W}$ .
Watch out: starting and stopping the stopwatch late adds a reaction-time error, so a long timing period makes this error a smaller fraction of the total, and the repeat readings should agree closely before a mean is taken.
Safety: the immersion heater must be fully under water before it is switched on, the heater and lamp stay hot after use and should not be touched, and mains appliances are only ever tested by your teacher with a plug-in meter designed for the purpose.

Common Mistake

Do not mix up power and energy, because energy is measured in joules and power is measured in watts.
Do not assume that the appliance with the higher power rating always transfers more energy, because the total also depends on how long each appliance is used.
Do not substitute a time in minutes into $\times t$ , because the equation needs time in seconds to give energy in joules.

Exam technique

Explaining a power rating

When you explain what a power rating means, turn it into joules per second, for example by writing that a $W2000\ \text{W}$ heater transfers $J2000\ \text{J}$ of energy every second.
Link the rating to the store that changes, for example the thermal energy store of the water in a kettle or the kinetic energy store of a fan.
You must recall the power equation, so in a calculation write the equation, show the converted values, then give the answer with its unit, because each stage can earn a mark even if the final answer is wrong.

Self review

Define power.
State how many joules a $kW1.5\ \text{kW}$ heater transfers each second.
Explain why a $kW3\ \text{kW}$ kettle boils water faster than a $kW2\ \text{kW}$ kettle.
Calculate the energy transferred by a $W60\ \text{W}$ laptop charger in $10$ minutes.
Describe how a joulemeter and a stopwatch are used to find the power of an appliance.

7.2.3 Power ratings of domestic appliances

Power and the watt

Power ratings of appliances

Power and changes in stored energy

Measuring the power of an appliance

Energy transferred by a kettle

Comparing a shower and a lamp

How long a phone battery lasts

Using a joulemeter to find power

Explaining a power rating

Review 7.2.3 Power ratings of domestic appliances by teaching Genie

7.2.3 Power ratings of domestic appliances

Power and the watt

Power ratings of appliances

Power and changes in stored energy

Measuring the power of an appliance

Energy transferred by a kettle

Comparing a shower and a lamp

How long a phone battery lasts

Using a joulemeter to find power

Explaining a power rating

Review 7.2.3 Power ratings of domestic appliances by teaching Genie

7.2.3 Power ratings of domestic appliances

Power and the watt

Power ratings of appliances

Power and changes in stored energy

Measuring the power of an appliance

Energy transferred by a kettle

Comparing a shower and a lamp

How long a phone battery lasts

Using a joulemeter to find power

Explaining a power rating

Review 7.2.3 Power ratings of domestic appliances by teaching Genie

7.2.3 Power ratings of domestic appliances Revision Guide

7.2.3 Power ratings of domestic appliances

Power and the watt

Power ratings of appliances

Power and changes in stored energy

Measuring the power of an appliance

Energy transferred by a kettle

Comparing a shower and a lamp

How long a phone battery lasts

Using a joulemeter to find power

Explaining a power rating

Review 7.2.3 Power ratings of domestic appliances by teaching Genie

7.2.3 Power ratings of domestic appliances Revision Guide