Calculating voltage

The ratio between the voltages in the coils of a transformer is the same as the ratio of the number of turns in the coils.

This relationship can be shown by the following equation:

\frac{primary~voltage}{secondary~voltage} = \frac{turns~on~primary}{turns~on~secondary}

This can also be written as:

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

Step-up transformers have more turns on the secondary coil than they do on the primary coil.

Step-down transformers have fewer turns on the secondary coil than they do on the primary coil.

Worked example

A transformer has 20 turns on the primary coil and 400 on the secondary coil. What is the output voltage if the input voltage is 500V?

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

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

\frac{V_{s}}{500} = \frac{400}{20}

{V_{s}}= 500 \times \left (\frac{400}{20}  \right )

V_{s} = 10,000~volts