Edexcel IGCSE Physics · Spec 6.8-6.9
Transformers: Using the Equations
Worked examples using the transformer equations.
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Transformers: Using the Equations
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Explained
Transformer calculations, and the order you must work in
A transformer changes the size of an alternating voltage. Two coils are wound on the same iron core, and the ratio of turns on the two coils decides what happens to the voltage.
Two equations cover everything you will be asked. The first links voltages to turns. The second says that for an ideal transformer, the power going in equals the power coming out.
The turns equation
Primary voltage divided by secondary voltage equals primary turns divided by secondary turns.
Read it as a statement about proportions. More turns on the secondary than the primary gives a higher output voltage, and that is a step up transformer. Fewer turns gives a lower output voltage, and that is a step down transformer.
Because it is a ratio, you can check your answer without redoing it. If the secondary has three times as many turns, the secondary voltage should be three times as large. If your answer went the wrong way, you have inverted the fraction.
The power equation
For an ideal transformer, primary voltage times primary current equals secondary voltage times secondary current.
This has a consequence students often find surprising. Stepping the voltage up steps the current down by the same factor, because the power cannot increase. That is exactly why the national grid transmits at very high voltage: the current is small, and since the energy wasted heating the cables depends on the current squared, small current means small losses.
Real transformers are not quite ideal. Some energy is wasted heating the core and the coils, so the output power is slightly less than the input power.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme for a transformer calculation splits three marks between substitution, rearrangement and evaluation, and says the substitution and rearrangement can come in either order. Then it adds the line that matters: substitution into an incorrectly arranged formula scores zero.
So a rearrangement done wrongly in your head, before any numbers appear, takes the method marks with it. Writing the equation as it stands, putting the numbers in, and only then solving for the missing quantity keeps the credit available even if the arithmetic slips.
The same mark scheme is relaxed about notation. It allows recognisable symbols and any rearrangement, condones coils written for turns, condones the letter T for turns, and allows 1 and 2 in place of input and output. What it will not do is award marks for a formula that was already wrong when the numbers went in.
A worked example
A transformer has 1000 turns on the primary and 300 on the secondary, with 230 V across the primary. Write the equation, substitute, and solve: 230 divided by the secondary voltage equals 1000 divided by 300, so the secondary voltage is 300 multiplied by 230 divided by 1000, which is 69 V.
Check it against the proportions. The secondary has fewer turns, so it should have a lower voltage, and 69 V is lower than 230 V. The answer is consistent.
If the question then asks for the secondary current given the primary current, switch to the power equation rather than the turns equation, and expect the current to have gone up because the voltage went down.
Spec 6.8-6.9
What you need to know
- Use Vp over Vs equals Np over Ns
- Find a missing voltage or number of turns
- Use the power equation for an ideal transformer
Active recall
Quick check
Answer each question before opening the answer.
What is the transformer turns-and-voltage equation?
Vp ÷ Vs = np ÷ ns (primary/secondary voltage ratio equals the turns ratio).
For a 100% efficient transformer, what equation relates the power?
Vp × Ip = Vs × Is (power in = power out).
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