Physics

20.6 - Transformer Calculation

2 min

note 1 of 2

The transformer turns-ratio equation

A transformer changes the size of an alternating potential difference.
The ratio of the potential differences across the two coils equals the ratio of the numbers of turns of wire on them.

Formula for the transformer turns ratio

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

Where:

$V_{p}$ = Potential difference across the primary coil, in volts (V)
$V_{s}$ = Potential difference across the secondary coil, in volts (V)
$N_{p}$ = Number of turns on the primary coil
$N_{s}$ = Number of turns on the secondary coil

The primary coil is the input coil; the secondary coil is the output coil.

Step-up and step-down transformers

Step-up transformer - More turns on the secondary coil than the primary ( $N_{s} > N_{p}$ ), so potential difference is increased ( $V_{s} > V_{p}$ ).
Step-down transformer - Fewer turns on the secondary coil than the primary ( $N_{s} < N_{p}$ ), so potential difference is decreased ( $V_{s} < V_{p}$ ).

Two iron rings wound with orange wire, labelled iron core, primary coil and secondary coil. The left one, headed step-down transformer, has fewer turns on the secondary; the right, step-up transformer, has more.

note 2 of 2

Worked example - Output voltage of a step-down transformer

A step-down transformer has 1,200 turns on its primary coil and 300 turns on its secondary coil. The input potential difference across the primary coil is 240 V. Calculate the output potential difference across the secondary coil.

Step 1 - Write the equation with the unknown on top

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

Step 2 - Rearrange to make V_s the subject

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

Step 3 - Substitute and calculate

$V_{s} = 240 \times \frac{300}{1,200} = 60 V$

The output potential difference is 60 V.

key terms

TermDefinition

Primary coilThe coil in a transformer that the input voltage is connected across.

Secondary coilThe coil in a transformer that provides the output voltage.

Step-up transformerA transformer that increases the potential difference (voltage) and decreases the current. It has more turns on its secondary coil than on its primary coil.

Step-down transformerA transformer that decreases the potential difference (voltage) and increases the current. It has fewer turns on its secondary coil than on its primary coil.

end of notes

Key points to remember

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20.7 - National GridNext up

The transformer turns-ratio equation

A transformer changes the size of an alternating potential difference.

The ratio of the potential differences across the two coils equals the ratio of the numbers of turns of wire on them.

Formula for the transformer turns ratio

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

Where:

V_{p}

= Potential difference across the primary coil, in volts (V)

V_{s}

= Potential difference across the secondary coil, in volts (V)

N_{p}

= Number of turns on the primary coil

N_{s}

= Number of turns on the secondary coil

The primary coil is the input coil; the secondary coil is the output coil.

Step-up and step-down transformers

Step-up transformer - More turns on the secondary coil than the primary (

N_{s} > N_{p}

), so potential difference is increased (

V_{s} > V_{p}

Step-down transformer - Fewer turns on the secondary coil than the primary (

N_{s} < N_{p}

), so potential difference is decreased (

V_{s} < V_{p}

Worked example - Output voltage of a step-down transformer

Step 1 - Write the equation with the unknown on top

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

Step 2 - Rearrange to make V_s the subject

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

Step 3 - Substitute and calculate

$V_{s} = 240 \times \frac{300}{1,200} = 60 V$

The output potential difference is 60 V.

20.6 - Transformer Calculation

The transformer turns-ratio equation

Formula for the transformer turns ratio

Where:

Step-up and step-down transformers

Worked example - Output voltage of a step-down transformer

Step 1 - Write the equation with the unknown on top

Step 2 - Rearrange to make Vs the subject

Step 3 - Substitute and calculate

Key points to remember

20.6 - Transformer Calculation

The transformer turns-ratio equation

Formula for the transformer turns ratio

Where:

Step-up and step-down transformers

Worked example - Output voltage of a step-down transformer

Step 1 - Write the equation with the unknown on top

Step 2 - Rearrange to make Vs the subject

Step 3 - Substitute and calculate

Key points to remember

Step 2 - Rearrange to make V_s the subject

Step 2 - Rearrange to make V_s the subject