Turns and potential difference
Definition
Turns ratio
The number of turns on the primary coil of a transformer compared with the number of turns on its secondary coil.
- Each coil of a transformer is made of a number of turns, which are complete loops of wire around the iron core.
- The iron core carries the same changing magnetic field through every turn of both coils.
- Every turn therefore has the same potential difference induced across it, whichever coil it belongs to.
- The turns of a coil are joined one after another, like cells connected in series, so the potential differences across the individual turns add up.
- The total potential difference across a coil is therefore proportional to the number of turns it has.
- In the primary coil, the supply potential difference is shared equally between its turns, which sets the potential difference per turn for the whole transformer.
- The ratio of the potential differences across the two coils is equal to the ratio of their numbers of turns, which is called the turns ratio.
- A secondary coil with twice as many turns as the primary coil has twice the potential difference across it.
- A secondary coil with half as many turns as the primary coil has half the potential difference across it.
- This simple link holds for an ideal transformer, in which all of the magnetic field from the primary coil passes through the secondary coil and no energy is wasted.
Step-up and step-down transformers
Definition
Step-up transformer
A transformer with more turns on its secondary coil than on its primary coil, so its output potential difference is greater than its input potential difference.
Definition
Step-down transformer
A transformer with fewer turns on its secondary coil than on its primary coil, so its output potential difference is smaller than its input potential difference.
- A step-up transformer has more turns on its secondary coil than on its primary coil.
- The output potential difference of a step-up transformer is therefore greater than its input potential difference.
- A step-down transformer has fewer turns on its secondary coil than on its primary coil.
- The output potential difference of a step-down transformer is therefore smaller than its input potential difference.
- A transformer with the same number of turns on both coils gives an output potential difference equal to its input.
- The transformer inside a microwave oven is a step-up transformer, raising the 230 V230\ \text{V}230 V mains to a few thousand volts.
- The transformer inside a doorbell supply is a step-down transformer, lowering the 230 V230\ \text{V}230 V mains to a few volts.
Practical
Investigating the turns on a transformer
- Aim: to find how the output potential difference of a transformer depends on the number of turns on its secondary coil.
- Apparatus: a U-shaped soft-iron core with a yoke and clamp, a reel of insulated wire, a low-voltage a.c. supply, two a.c. voltmeters (or multimeters set to a.c. volts), connecting leads and a switch.
- Method:
- Wind 505050 turns of insulated wire neatly onto one limb of the core to make the primary coil, and connect it to the a.c. supply through the switch, with a voltmeter across it.
- Wind 101010 turns of wire onto the other limb, all in the same direction, to make the secondary coil, and connect the second voltmeter across its ends.
- Clamp the yoke firmly across the top of the core so the iron forms a closed loop.
- Close the switch, set the supply so the primary voltmeter reads 2.0 V2.0\ \text{V}2.0 V, and record the secondary potential difference.
- Open the switch, add 101010 more turns to the secondary coil, and repeat, keeping the primary potential difference at 2.0 V2.0\ \text{V}2.0 V.
- Continue in steps of 101010 turns up to 100100100 turns.
- Plot the secondary potential difference against the number of secondary turns, and draw a line of best fit.
- Variables: the independent variable is the number of turns on the secondary coil, the dependent variable is the secondary potential difference, and the control variables are the primary potential difference, the number of turns on the primary coil, the core and the supply frequency.
- Results:
- The secondary potential difference rises in equal steps as turns are added, giving a straight line through the origin, so the output is directly proportional to the number of secondary turns.
- With fewer than 505050 secondary turns the output is smaller than the input, as in a step-down transformer, and with more than 505050 it is larger, as in a step-up transformer.
- The measured outputs are slightly smaller than the turns ratio predicts, because some of the magnetic field leaks out of the core and some energy is transferred to the thermal store of the core and coils.
- Watch out: turns wound in the wrong direction cancel part of the induced potential difference, and a loose yoke lets field leak out, so keep the winding direction the same and clamp the yoke tightly.
- Safety: use only a low-voltage a.c. supply, open the switch before changing the number of turns, and let the core cool if it becomes warm.
Common Mistake
- Do not decide whether a transformer steps up or down from the total number of turns, because what matters is whether the secondary coil has more or fewer turns than the primary coil.
- Do not reverse the names: a step-up transformer increases the potential difference and has more turns on its secondary coil.
Exam technique
Explaining the turns ratio
- When explaining why the output depends on the turns, include the two key steps: the same changing magnetic field passes through every turn, and the potential differences across the turns add up along each coil.
- To identify a step-up or step-down transformer, compare the secondary turns with the primary turns, and state the comparison in your answer.
- If a question gives the potential differences instead of the turns, use the same link in reverse, so a larger output potential difference means more turns on the secondary coil.
Self review
- What does the turns ratio of a transformer compare?
- Explain why a coil with more turns has a larger potential difference induced across it.
- How can you tell from the numbers of turns whether a transformer is step-up or step-down?
- A secondary coil has three times as many turns as the primary coil; how does the output potential difference compare with the input?
- Why is the measured output of a real transformer slightly less than the turns ratio predicts?
