Physics

3.15 - Transformer Calculation

6 min

Recap and the equations

Output voltage exampleOutside your course

Output current example

note 1 of 2

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 2 of 2

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.

end of notes

Key points to remember

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.

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.

3.15 - Transformer Calculation

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

Key points to remember

3.15 - Transformer Calculation

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

Key points to remember

Step 2 - Rearrange to make V_p the subject

Step 2 - Rearrange to make V_p the subject