Transformer Calculations

Exam code: 5054

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

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)

$\frac{P . D . across primary coil}{P . D . across secondary coil} = \frac{number of turns on primary coil}{number of turns on secondary coil}$

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

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

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

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

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

b) State what type of transformer this is

Answer

Part (a)

Step 1: List the known quantities

Step 2: Write the equation linking the output potential difference ( $V_{S}$ ) to the known quantities

$\frac{N_{S}}{N_{P}} = \frac{V_{S}}{V_{P}}$

Step 3: Rearrange the equation to make $V_{S}$ the subject

$V_{S} = \frac{N_{S} V_{P}}{N_{P}}$

Step 4: Substitute the known values into the equation

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

Part (b)

The secondary voltage is larger than the primary, therefore this is a step-up transformer

Transformers have a number of roles:
- They are used to increase the potential difference of electricity before it is transmitted across the national grid
- They are used to lower the high voltage electricity used in power lines to the lower voltages used in houses
- They are used in adapters to lower mains voltage to the lower voltages used by many electronic devices

When electricity is transmitted over large distances, the current in the wires heats them, resulting in energy loss
To transmit the same amount of power as the input power the potential difference at which the electricity is transmitted should be increased
- This will result in a smaller current being transmitted through the power lines
- This is because P = IV, so if V increases, I must decrease to transmit the same power
A smaller current flowing through the power lines results in less heat being produced in the wire
- This will reduce the energy loss in the power lines

Electricity is transmitted at high voltage, reducing the current and hence power loss in the cables

High-Voltage Transmission