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

current

提示It is the quantity an ammeter reads.

为什么In 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

提示Multiply the two readings together.

为什么P = 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

提示One of the two quantities appears twice over.

为什么In 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

提示Square before you multiply.

为什么P = 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

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

为什么Rearranging 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

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

为什么Rearranging 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

提示A kettle left on for longer costs more to run.

为什么In 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

提示Neither number is yet in the unit the equation needs.

为什么Convert 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

提示A volt is a joule for every coulomb.

为什么In 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

提示Each coulomb transfers 12 J.

为什么E = 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

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

为什么The 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

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

为什么Charge 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

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

为什么Power 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

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

为什么In 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

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

为什么Power 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

提示The cables on pylons run at hundreds of thousands of volts.

为什么The 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

提示The potential difference must be raised before the long journey begins.

为什么The 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

提示In an ideal transformer the power going in equals the power coming out.

为什么Use 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.