GCSEPhysicsAQARevision NotesMagnetism & ElectromagnetismInduced Potential, Transformers & the National GridTransformer Equations

Transformer Equations (AQA GCSE Physics): Revision Note

Exam code: 8463

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on 2 July 2026

The Transformer Equation

The output potential difference (voltage) of a transformer depends on:
- the number of turns on the primary and secondary coils
- the input potential difference (voltage)

It can be calculated using the equation:

$\frac{potential difference across primary}{potential difference across secondary} = \frac{number of turns on primary}{number of turns on secondary}$

This equation can be written using symbols as follows:

$\frac{V_{p}}{V_{s}} = \frac{N_{p}}{N_{s}}$

Where:
- V_p = potential difference (voltage) across the primary coil in volts (V)
- V_s = potential difference (voltage) across the secondary coil in volts (V)
- N_p = number of turns on primary coil
- N_s = number of turns on secondary coil

The equation above can be flipped upside down to give:

$\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}$

The equations above show that:
- The ratio of the potential differences across the primary and secondary coils of a transformer is equal to the ratio of the number of turns on each coil

Step-up Transformer

A step-up transformer increases the potential difference of a power source $(V_{s} > V_{p})$
A step-up transformer has more turns on the secondary coil than on the primary coil $(N_{s} > N_{p})$

Step-down Transformer

A step-down transformer decreases the potential difference of a power source $(V_{s} < V_{p})$
A step-down transformer has fewer turns on the secondary coil than on the primary coil $(N_{s} < N_{p})$

Worked Example

A transformer has 20 turns on the primary coil and 800 turns on the secondary coil. The input potential difference across the primary coil is 500 V.

a) Calculate the output potential difference across the secondary coil.

b) State whether this is a step-up or step-down transformer.

Answer:

Part (a)

Step 1: List the known quantities

Number of turns on the primary coil, $N_{p} = 20$
Number of turns on the secondary coil, $N_{s} = 800$
Potential difference across the primary coil, $V_{p} = 500 V$

Step 2: Write down the transformer equation

There will be less rearranging to do if $V_{s}$ is on the top of the fraction

$\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}$

Step 3: Rearrange the equation to make V_S the subject

$V_{s} = V_{p} \times \frac{N_{s}}{N_{p}}$

Step 4: Substitute the known values into the equation

$V_{s} = 500 \times \frac{800}{20} = 20 000 V$

Part (b)

The potential difference across the secondary coil is larger than across the primary, $V_{s} > V_{p}$
There are more turns on the secondary coil than on the primary, $N_{s} > N_{p}$
Therefore, this is a step-up transformer

Examiner Tips and Tricks

When you are using the transformer equation make sure you have used the same letter (p or s) in the numerators (top line) of the fraction and the same letter (p or s) in the denominators (bottom line) of the fraction.

There will be less rearranging to do in a calculation if the variable which you are trying to find is on the numerator (top line) of the fraction.

The individual loops of wire going around each side of the transformer should be referred to as turns and not coils.

The Ideal Transformer Equation

An ideal transformer would be 100% efficient
- Although transformers can increase the voltage of a power source, due to the law of conservation of energy, they cannot increase the power output

If a transformer is 100% efficient:

Input power = Output power

The equation to calculate electrical power is:

P = V × I

Where:
- P = power in Watts (W)
- V = potential difference in volts (V)
- I = current in amps (A)

Therefore, if a transformer is 100% efficient then:

V_p × I_p = V_s × I_s

Where:
- V_p = potential difference across primary coil in volts (V)
- I_p = current through primary coil in amps (A)
- V_s = potential difference across secondary coil in volts (V)
- I_s = current through secondary coil in amps (A)

The equation above could also be written as:

P_s = V_p × I_p

Where:
- P_s = output power (power produced in secondary coil) in Watts (W)

Worked Example

A transformer in a travel adapter steps up a 115 V ac mains electricity supply to the 230 V needed for a hair dryer. A current of 5 A flows through the hairdryer.

Assuming that the transformer is 100% efficient, calculate the current drawn from the mains supply.

Answer:

Step 1: List the known quantities

Voltage in primary coil, V_p = 115 V
Voltage in secondary coil, V_s = 230 V
Current in secondary coil, I_s = 5 A

Step 2: Write the equation linking the known values to the current drawn from the supply, I_p

V_p × I_p = V_s × I_s

Step 3: Substitute in the known values

115 × I_p = 230 × 5

Step 4: Rearrange the equation to find I_p

$I_{p} = \frac{230 \times 5}{115}$

Step 5: Calculate a value for I_p and include the correct unit

I_p = 10 A

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent

Transformer Equations (AQA GCSE Physics): Revision Note

The Transformer Equation

Step-up Transformer

Step-down Transformer

Worked Example

Examiner Tips and Tricks

The Ideal Transformer Equation

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Katie M

Reviewer: Caroline Carroll