Electricity and magnetism, Year 10: power, energy and the National Grid

current

HintIt is the quantity an ammeter reads.

The whyIn symbols, P = V I, with P in watts, V in volts and I in amperes. AQA expects this equation to be recalled. It says that a device is powerful if a large amount of charge passes each second, or each coulomb transfers a lot of energy, or both.

2300

HintMultiply the two readings together.

The whyP = V × I = 230 × 10. This equation must be recalled. The answer, 2.3 kW, is typical of a household heater or kettle.

power = current² × resistance

HintOne of the two quantities appears twice over.

The whyIn symbols, P = I² R. It comes from putting V = I R into P = V I, and AQA expects it to be recalled in its own right. It is the equation to use when the potential difference is not known.

20 W

HintSquare before you multiply.

The whyP = I² × R = 2² × 5 = 4 × 5. Only the current is squared. This energy heats the resistor, which is why resistors and wires warm up when they carry a current.

5 A

HintRearrange the equation that links these three quantities so the unknown is on its own.

The whyRearranging P = V I gives I = P ÷ V = 60 ÷ 12. Checking back: 12 V × 5 A = 60 W. This rearrangement is how the correct fuse or cable for an appliance is chosen.

0.2 A

HintGet the squared quantity on its own first; the final step is a root.

The whyRearranging P = I² R gives I² = P ÷ R = 2 ÷ 50 = 0.04, and the square root of 0.04 is 0.2. Checking back: 0.2² × 50 = 0.04 × 50 = 2 W.

time

HintA kettle left on for longer costs more to run.

The whyIn symbols, E = P t, with E in joules, P in watts and t in seconds. AQA expects the equation to be recalled. The energy an appliance transfers depends on both its power rating and how long it is switched on.

360 000 J

HintNeither number is yet in the unit the equation needs.

The whyConvert first: 2 kW = 2000 W and 3 minutes = 180 s. Then E = P × t = 2000 × 180. Working in watts and seconds is what gives an answer in joules.

energy transferred = charge flow × potential difference

HintA volt is a joule for every coulomb.

The whyIn symbols, E = Q V, with E in joules, Q in coulombs and V in volts. AQA expects it to be recalled. It says that work is done whenever charge flows, and that each coulomb transfers a number of joules equal to the potential difference.

240

HintEach coulomb transfers 12 J.

The whyE = Q × V = 20 × 12. This equation must be recalled. The energy is transferred from the supply to the lamp, and from there to the surroundings as light and heating.

From the chemical store of the battery to the kinetic store of the fan

HintName where the energy starts and where the useful part of it ends up.

The whyThe battery does electrical work as charge flows through the motor, and the motor turns the blades. Some energy is also dissipated, heating the motor and the air. AQA expects pupils to describe how appliances transfer energy from batteries or the mains to the kinetic energy of motors or to heating devices.

90 J

HintFirst find how much charge has gone through; then what each coulomb delivered.

The whyCharge flow Q = I × t = 0.5 × 60 = 30 C. Energy E = Q × V = 30 × 3. The same answer comes from finding the power, P = V × I = 1.5 W, and multiplying by the 60 s.

The National Grid

HintTwo words: the first means 'belonging to the whole country', the second is a network of crossing lines.

The whyPower stations feed electrical power in, and homes, schools and factories take it out, often hundreds of kilometres away. Because everything is linked, a town is not left dark when a single station shuts down.

A step-up transformer

HintIts name says which way the potential difference goes, as on a staircase.

The whyIn the National Grid these sit between the power stations and the transmission cables. Raising the potential difference lowers the current needed to carry the same power. AQA does not require knowledge of how the device is built.

For the same power the current is smaller, so less energy is wasted heating the cables

HintThe long wires have resistance; ask what makes them warm up.

The whyPower is potential difference × current, so the same power can be carried by a high potential difference and a low current. The heating in a cable depends on the current squared (P = I² R), so a small current wastes very little. That is why the Grid is an efficient way to transfer energy.

To lower the potential difference to a much safer value for domestic use

HintThe cables on pylons run at hundreds of thousands of volts.

The whyThe very high potential difference that makes transmission efficient would be extremely dangerous in a house and would destroy ordinary appliances. Step-down transformers reduce it, in stages, to about 230 V for homes.

Between the power stations and the transmission cables

HintThe potential difference must be raised before the long journey begins.

The whyThe order is: power station, step-up transformer, transmission cables, step-down transformer, consumer. The potential difference is raised for the long-distance part of the journey only, and lowered again at the far end.

20 A

HintIn an ideal transformer the power going in equals the power coming out.

The whyUse Vp × Ip = Vs × Is, so 230 × 2 = 23 × Is and Is = 460 ÷ 23. Stepping the potential difference down by a factor of ten steps the current up by the same factor. This equation is given on the AQA equation sheet and is Higher tier only.