Electricity

The bill is for energy, not power

Look at an appliance and it will tell you its power: 3 kW on a kettle, 60 W on a lamp. Look at an electricity bill and it charges you for something else entirely. ⚠️ YOUR BILL IS NOT A BILL FOR POWER. IT IS A BILL FOR ENERGY. And the difference between those two words is the whole of this topic's arithmetic. POWER IS A RATE. It says how fast an appliance draws energy while it is running, and it never changes: a 3 kW kettle is a 3 kW kettle whether you boil it once or never. ENERGY IS AN AMOUNT. It depends on the power AND on how long the thing was left on. ⚠️ Which is why a 3 kW kettle boiled for two minutes costs less than a 60 W lamp left on all week, even though the kettle is fifty times the more powerful of the two. Power alone tells you nothing about cost. Everything else in this topic hangs off that chain. Current and voltage give you power. Power and time give you energy. Energy and price give you cost. ⚠️ And the same relationship, read backwards, is why the National Grid runs its cables at hundreds of thousands of volts. So learn the chain once, and the questions stop being separate.

Words for what a circuit carries

Six quantities and their units. Definitions only, with nothing worked out.

Find the source of the potential difference

This circuit contains a cell, a resistor and a lamp. Tap the component that PROVIDES the potential difference driving the current round the circuit.

A rate, an amount, and a price

Three columns, and each one is the input to the next. Almost every domestic electricity question sits somewhere along this chain.

The kettle and the lamp

A 3 kW kettle is boiled for two minutes a day. A 60 W lamp is left on continuously all week. A student says the kettle must cost far more, because it is fifty times as powerful. What is wrong with that reasoning?

• Power is a rate, so it only tells you how fast energy is drawn. Cost depends on the energy transferred, which is power multiplied by time, and the lamp runs for thousands of times longer
• Nothing is wrong: the kettle draws more power, so it must cost more
• The kettle produces heat and the lamp produces light, and heat is not charged for
• The lamp is on standby rather than running, so it draws no energy

Working out which equation you need

This specification is unusually mathematical, and it says so: recall, rearrangement and substitution of the equations are what separate the top grade. The algebra is never the hard part. Choosing the equation is. ⚠️ THERE ARE ONLY THREE QUANTITIES IN A SIMPLE CIRCUIT AND ONE RELATIONSHIP BETWEEN THEM. Potential difference equals current times resistance: V = IR. Rearranged, I = V / R and R = V / I. So work in this order, every time. ONE: list what the question has given you, with units. Two of the three quantities will be there. TWO: rearrange BEFORE you substitute. Put the unknown on its own first, then put the numbers in. Rearranging with numbers already in place is where errors breed. THREE: check the units belong together. Amps with volts and ohms; watts with volts and amps; kilowatts with HOURS if you want kilowatt-hours. Two worked examples. A component with 6 V across it carrying 2 A has resistance 6 / 2, which is 3 ohms. And an appliance rated at 1 kW left on for 5 hours transfers 1 x 5, which is 5 kWh. ⚠️ And check the size of your answer. A domestic appliance drawing thousands of amps, or a household using a millionth of a kilowatt-hour, means a unit has gone astray.

Rearrange for the resistance

A lamp has a potential difference of 12 V across it and carries a current of 0.5 A. Rearrange the relationship before substituting, and work out the resistance of the lamp in ohms. Give the number only.

Find the power of the appliance

An appliance is connected to the 230 V mains supply and draws a current of 10 A. Work out its power in watts. Give the number only.

How many kilowatt-hours

A 2 kW heater is left running for 3 hours. Work out the energy it transfers, in kilowatt-hours. Give the number only.

Why the pylons carry hundreds of thousands of volts

Mains sockets deliver about 230 V. The cables slung between pylons carry hundreds of thousands. That looks like a strange choice, since high voltage is exactly what makes those cables lethal. It follows directly from the chain you have just learned. ⚠️ Power is current times potential difference. So for a FIXED amount of power, raising the voltage lowers the current - the same energy per second, carried by a smaller flow. And it is the CURRENT that wastes energy in a cable. A wire has resistance, and pushing current through resistance heats it. The more current, the more energy lost as heat before it reaches anybody's house. So the Grid does something that sounds backwards. A transformer steps the voltage up as electricity leaves the power station, so it can travel at low current across the country losing very little. Another transformer steps it back down near where it is used, to a voltage that is safe in a building. ⚠️ Notice that no energy is being created or saved by the transformers themselves. They are trading voltage against current so that the journey is cheaper. Same power, different combination. And it explains the danger. The cables are lethal precisely because of the voltage that makes them efficient, which is why they are strung out of reach on pylons rather than buried at the roadside.

Match each part to the job it does

True about mains electricity

Select the TWO statements that are true.

• A fuse protects a circuit by melting and breaking it when the current becomes too large
• The earth wire normally carries no current, and only does so if something has gone wrong
• A fuse works by slowing the current down to a safe level
• The National Grid uses high voltage because high voltage is safer than low voltage

The circuit numbers run

Five questions on the quantities, the units and the chain. Three lives.

Spot the true electricity facts

Tap the TWO statements that are true.

• A kilowatt-hour is a unit of energy, not of power
• It is the current in a transmission cable that wastes energy as heat
• An appliance with a higher power rating always costs more to run
• The earth wire carries current continuously during normal use

Complete the electricity facts

Current is measured in units called _____, and potential difference in units called _____. Resistance is measured in _____. The rate at which an appliance transfers energy is its power, measured in _____, and multiplying that by the time it runs for gives the energy transferred.

Three decisions about the bill

Three pieces of reasoning to judge. Each answer has to carry the explanation, not just the verdict.

• A household wants to cut its bill and decides to stop using the 3 kW kettle, while leaving several 60 W lamps on all day. Is that the right target?
• A student calculates the energy used by a 2000 W appliance running for 3 hours and writes 6000 kWh. What has gone wrong?
• Someone suggests the National Grid would be safer if it transmitted at 230 V all the way, since that is what sockets deliver. What would actually happen?

Explain what you are actually paying for

A friend has looked at an electricity bill and cannot see why the kettle is not the most expensive thing in the house. Write them the explanation, and take it as far as the pylons.

• Explain the difference between power and energy, saying which one is a rate and which an amount
• Explain how the power of an appliance is worked out from the current and the potential difference
• Explain how energy is worked out from power and time, and why electricity is sold in kilowatt-hours
• Use those ideas to explain why a low-power appliance left on for a long time can cost more than a high-power one used briefly
• Finish by explaining why the National Grid transmits at very high voltage, referring to current and to energy wasted as heat