13.5–13.7P, 13.10TransformersHigher tier
Physics only, and Higher tier only — not on the Combined Science specification
A basic transformer consists of a primary coil and a secondary coil wound on an iron core. Iron is used as it is easily magnetised. Knowledge of laminations and eddy currents in the core is not required.
You should be able to explain how the effect of an alternating current in one coil in inducing a current in another is used in transformers:
1. An alternating current in the primary coil produces a continually changing magnetic field. 2. The iron core carries that changing field to the secondary coil. 3. The secondary coil experiences a changing magnetic field, so by the generator effect a potential difference is induced across it.
The current must be alternating. A steady direct current would produce a steady field, nothing would be changing at the secondary, and no potential difference would be induced — which is why transformers only work on ac.
The ratio of the potential differences across the primary and secondary coils of a transformer, Vp and Vs, depends on the ratio of the number of turns on each coil, np and ns:
Vp / Vs = np / ns
potential difference, Vp and Vs, in volts, V. This equation is given on the Physics equation sheet.
In a step-up transformer Vs is greater than Vp — the secondary has more turns. In a step-down transformer Vs is less than Vp — the secondary has fewer turns.
You should be able to explain how the ratio of the potential differences across the two coils depends on the ratio of the number of turns on each.
Worked example
A transformer has 200 turns on the primary and 5000 turns on the secondary. The primary potential difference is 230 V. Calculate the secondary potential difference.
- Write the equation: Vp / Vs = np / ns.
- Rearrange for Vs: Vs = Vp × ns ÷ np.
- Substitute: Vs = 230 × 5000 ÷ 200.
- 5000 ÷ 200 = 25, and 230 × 25 = 5750.
- Check the type: the secondary has more turns, so this is a step-up transformer and Vs should be larger — it is.
Answer: 5750 V — a step-up transformer.
If transformers were 100% efficient, the electrical power output would equal the electrical power input:
Vs × Is = Vp × Ip
where Vs × Is is the power output at the secondary coil and Vp × Ip is the power input at the primary coil. Power input and output are in watts, W. This equation is also given on the Physics equation sheet.
You should be able to calculate the current drawn from the input supply to provide a particular power output.
Worked example
A transformer supplies 5750 V at 0.20 A from a 230 V input. Assuming 100% efficiency, calculate the input current.
- Power output = Vs × Is = 5750 × 0.20 = 1150 W.
- If the transformer is 100% efficient, the power input equals the power output.
- So Vp × Ip = 1150 W.
- Ip = 1150 ÷ 230.
- Check: the potential difference was stepped up, so the current must be stepped down — and 5 A is much larger than 0.20 A, as expected for the low-voltage side.
Answer: 5.0 A
You should be able to apply the equation linking the potential differences and number of turns in the two coils of a transformer to the currents and the power transfer involved, and relate these to the advantages of power transmission at high potential differences.
That last point ties back to the National Grid. Because the power is essentially unchanged, stepping the potential difference up necessarily steps the current down. The power wasted heating the transmission cables is given by P = I² R, so a smaller current wastes far less energy — and because the current is squared, the saving is dramatic. The potential difference is stepped down again before it reaches homes, because hundreds of thousands of volts would be far too dangerous to use.
Common mistake
A transformer does not increase the power. If it steps the potential difference up, it steps the current down by the same factor — the power output can never exceed the power input.
- Transformer
- a device with a primary coil and a secondary coil wound on an iron core, in which an alternating current in one coil induces a current in the other
13.8–13.9, 13.11PThe National Grid
The National Grid is a system of cables and transformers linking power stations to consumers. Electrical power is transferred from power stations to consumers using the National Grid.
Step-up transformers are used to increase the potential difference from the power station to the transmission cables. Step-down transformers are then used to decrease, to a much lower value, the potential difference for domestic use.
You should be able to explain why the National Grid system is an efficient way to transfer energy. The construction and operation of transformers is covered under electromagnetic induction, and is Higher tier only — here you need only what a step-up and a step-down transformer do.
The explanation rests on the two power equations from earlier in this sub-topic, used together.
The power that has to be delivered is fixed. Because P = V I, transmitting that same power at a much higher potential difference means a much smaller current in the cables.
The power wasted heating the cables is given by P = I² R. Because the current is squared, reducing the current reduces the wasted power dramatically — cutting the current to a tenth cuts the wasted power to a hundredth.
So stepping the potential difference up for transmission, and back down for use, wastes far less energy than transmitting at a low potential difference would. The potential difference is stepped down again at the end because 400 000 V would be far too dangerous to bring into a house.
Worked example
Explain, in terms of the two power equations, why the current in transmission cables is kept low.
- The power to be transmitted is fixed by demand.
- P = V I, so for a fixed power a higher potential difference means a lower current.
- The power dissipated in the cables themselves is P = I² R, where R is the resistance of the cables.
- Because the current is squared, halving the current cuts the wasted power to a quarter.
- Therefore transmitting at high potential difference and low current wastes much less energy as heating of the cables.
Answer: A higher transmission potential difference gives a lower current for the same power, and because the wasted power goes as the square of the current, a lower current wastes far less energy in heating the cables.
Common mistake
Step-up transformers do not increase the power transmitted. They increase the potential difference and decrease the current, keeping the power essentially the same — the saving comes entirely from less energy being wasted in the cables.
- National Grid
- a system of cables and transformers linking power stations to consumers
- Step-up transformer
- a transformer that increases the potential difference from the power station to the transmission cables, which reduces the current and so the energy wasted in heating the cables
- Step-down transformer
- a transformer that decreases the potential difference to a much lower, safer value for domestic use
Before you practise
- An alternating current in the primary coil makes a changing magnetic field in the core, which induces an alternating potential difference in the secondary.
- It only works with alternating current — direct current gives a steady field and induces nothing.
- A step-up transformer has more turns on the secondary; a step-down has fewer.
- potential difference across primary ÷ potential difference across secondary = turns on primary ÷ turns on secondary.
- For a 100% efficient transformer, power in equals power out.
- Step-up transformers raise the voltage for transmission; step-down transformers lower it again for homes.
- High voltage means low current for the same power, and the energy wasted heating the cables depends on the current SQUARED.