Physics

8.13 - Transformer Calculation

9 min

Recap and the equations

Output voltage example

Output current example

note 1 of 5

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 5

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.

note 3 of 5

The transformer power equation

If a transformer is assumed to be 100% efficient, the input power equals the output power:

Input power = output power

Because power is $P = V I$ , this gives the transformer power equation.

Formula for transformer power

$V_{p} I_{p} = V_{s} I_{s}$

Where:

$V_{p}$ = Potential difference across the primary coil, in volts (V)
$I_{p}$ = Current through the primary coil, in amperes (A)
$V_{s}$ = Potential difference across the secondary coil, in volts (V)
$I_{s}$ = Current through the secondary coil, in amperes (A)

What this means for current

Because total power stays the same:

A step-up transformer increases potential difference and decreases current.
A step-down transformer decreases potential difference and increases current.

note 4 of 5

Worked example - Primary potential difference from power

A transformer has a potential difference of 12 V and a current of 8 A in its secondary coil. The current in the primary coil is 2 A. Assuming the transformer is 100% efficient, calculate the potential difference across the primary coil.

Step 1 - Write the power equation

$V_{p} I_{p} = V_{s} I_{s}$

Step 2 - Rearrange to make V_p the subject

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

Step 3 - Substitute and calculate

$V_{p} = \frac{12 \times 8}{2} = 48 V$

The potential difference across the primary coil is 48 V.

note 5 of 5

Using the transformer equations for the National Grid

The National Grid transmits electrical power at a very high potential difference and low current to minimise energy loss.

How transformers are used

Step-up transformers at power stations increase the potential difference, which decreases the current ( $V_{p} I_{p} = V_{s} I_{s}$ ).
Lower current means less energy is wasted as heat in the transmission cables, because power wasted depends on current squared ( $P = I^{2} R$ ).
Step-down transformers near consumers decrease the potential difference to safe, usable levels.

A chain running left to right: power stations, step-up transformer (raises potential difference, lowers current), pylons carrying wires, step-down transformer (lowers potential difference to a safe level), then buildings labelled safe to use.

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

Physics

8.13 - Transformer Calculation

9 min

Recap and the equations

Output voltage example

Output current example

note 1 of 5

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 ( $V_{s} < V_{p}$ ).

note 2 of 5

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.

note 3 of 5

The transformer power equation

If a transformer is assumed to be 100% efficient, the input power equals the output power:

Input power = output power

Because power is $P = V I$ , this gives the transformer power equation.

Formula for transformer power

$V_{p} I_{p} = V_{s} I_{s}$

Where:

$V_{p}$ = Potential difference across the primary coil, in volts (V)
$I_{p}$ = Current through the primary coil, in amperes (A)
$V_{s}$ = Potential difference across the secondary coil, in volts (V)
$I_{s}$ = Current through the secondary coil, in amperes (A)

What this means for current

Because total power stays the same:

A step-up transformer increases potential difference and decreases current.
A step-down transformer decreases potential difference and increases current.

note 4 of 5

Worked example - Primary potential difference from power

Step 1 - Write the power equation

$V_{p} I_{p} = V_{s} I_{s}$

Step 2 - Rearrange to make V_p the subject

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

Step 3 - Substitute and calculate

$V_{p} = \frac{12 \times 8}{2} = 48 V$

The potential difference across the primary coil is 48 V.

note 5 of 5

Using the transformer equations for the National Grid

The National Grid transmits electrical power at a very high potential difference and low current to minimise energy loss.

How transformers are used

Step-up transformers at power stations increase the potential difference, which decreases the current ( $V_{p} I_{p} = V_{s} I_{s}$ ).
Lower current means less energy is wasted as heat in the transmission cables, because power wasted depends on current squared ( $P = I^{2} R$ ).
Step-down transformers near consumers decrease the potential difference to safe, usable levels.

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

8.13 - 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

The transformer power equation

Formula for transformer power

Where:

What this means for current

Worked example - Primary potential difference from power

Step 1 - Write the power equation

Step 2 - Rearrange to make Vp the subject

Step 3 - Substitute and calculate

Using the transformer equations for the National Grid

How transformers are used

Key points to remember

8.13 - 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

The transformer power equation

Formula for transformer power

Where:

What this means for current

Worked example - Primary potential difference from power

Step 1 - Write the power equation

Step 2 - Rearrange to make Vp the subject

Step 3 - Substitute and calculate

Using the transformer equations for the National Grid

How transformers are used

Key points to remember

Step 2 - Rearrange to make V_s the subject

Step 2 - Rearrange to make V_p the subject

Step 2 - Rearrange to make V_s the subject

Step 2 - Rearrange to make V_p the subject