Revision NotesExam QuestionsPast Papers
GCSEPhysicsAQARevision NotesMagnetism & ElectromagnetismInduced Potential, Transformers & the National GridTransformer Equations

Transformer Equations (AQA GCSE Physics)

Revision Note

Katie M

Author

Katie M

Last updated

Did this video help you?

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:

fraction numerator potential space difference space across space primary over denominator potential space difference space across space secondary end fraction space equals space fraction numerator number space of space turns space on space primary over denominator number space of space turns space on space secondary end fraction

  • This equation can be written using symbols as follows:

V subscript p over V subscript s space equals space N subscript p over N subscript s

  • Where:

    • Vp = potential difference (voltage) across the primary coil in volts (V)

    • Vs = potential difference (voltage) across the secondary coil in volts (V)

    • Np = number of turns on primary coil

    • Ns = number of turns on secondary coil

  • The equation above can be flipped upside down to give:

V subscript s over V subscript p space equals space N subscript s over N subscript 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 open parentheses V subscript s space greater than space V subscript p close parentheses

  • A step-up transformer has more turns on the secondary coil than on the primary coil open parentheses N subscript s space greater than space N subscript p close parentheses

Step-down Transformer

  • A step-down transformer decreases the potential difference of a power source open parentheses V subscript s space less than space V subscript p close parentheses

  • A step-down transformer has fewer turns on the secondary coil than on the primary coil open parentheses N subscript s space less than space N subscript p close parentheses

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 subscript p space equals space 20

  • Number of turns on the secondary coil, N subscript s space equals space 800

  • Potential difference across the primary coil, V subscript p space equals space 500 space straight V

Step 2: Write down the transformer equation

  • There will be less rearranging to do if V subscript s is on the top of the fraction

V subscript s over V subscript p space equals space N subscript s over N subscript p

Step 3: Rearrange the equation to make VS the subject

V subscript s space equals space V subscript p space cross times space N subscript s over N subscript p

Step 4: Substitute the known values into the equation

V subscript s space equals space 500 space cross times space 800 over 20 space equals space 20 space 000 space straight V

Part (b)

  • The potential difference across the secondary coil is larger than across the primary, V subscript s space greater than space V subscript p

  • There are more turns on the secondary coil than on the primary, N subscript s space greater than space N subscript 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:

Vp × Ip = Vs × Is

  • Where:

    • Vp = potential difference across primary coil in volts (V)

    • Ip = current through primary coil in amps (A)

    • Vs = potential difference across secondary coil in volts (V)

    • Is = current through secondary coil in amps (A)

  • The equation above could also be written as:

Ps = Vp × Ip

  • Where:

    • Ps = 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, Vp = 115 V

  • Voltage in secondary coil, Vs = 230 V

  • Current in secondary coil, Is = 5 A

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

Vp × Ip = Vs × Is

Step 3: Substitute in the known values

115 × Ip = 230 × 5

Step 4: Rearrange the equation to find Ip

I subscript p space equals space fraction numerator 230 space cross times space 5 over denominator 115 end fraction

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

Ip = 10 A

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

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

the (exam) results speak for themselves:

    Test yourself

    Did this page help you?

    Previous:TransformersNext:AC & High Voltage Transmission
    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.