Transformer Equations (Edexcel IGCSE Physics)

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Ashika

Last updated

2 November 2024

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The transformer equation

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)

It can be calculated using the transformer equation below:

$\frac{potential difference across primary coil}{potential difference across secondary coil} = \frac{number of turns on primary coil}{number of turns on secondary coil}$

This equation for transformers can be written using symbols as follows:

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

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

The transformer equation above can be flipped upside down to give:

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

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

Step-up transformer

A step-up transformer increases the potential difference of a power source
A step-up transformer has more turns on the secondary coil than on the primary coil (N_s > N_p)

Step-down transformer

A step-down transformer decreases the potential difference of a power source
A step-down transformer has fewer turns on the secondary coil than on the primary coil (N_s < N_p)

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 it is

Answer:

Part (a)

Step 1: List the known quantities

Number of turns in primary coil, N_p = 20
Number of turns in secondary coil, N_s = 800
Voltage in primary coil, V_p = 500 V

Step 2: Write out the transformer equation

Use the version with the secondary coil quantities on the top to minimise the amount of rearranging

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

Step 3: Rearrange for V_s

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

Step 4: Substitute values into the equation

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

Part (b)

The transformer is a step-up transformer
This is because the transformer has:
- More secondary coils
- A greater secondary voltage

Examiner Tips and Tricks

When you are using the transformer equation make sure you have used the same letter (p or s) in the numerators (top line) of the fraction and the same letter (p or s) in the denominators (bottom line) of the fraction. There will be less rearranging to do in a calculation if the variable which you are trying to find is on the numerator (top line) of the fraction. The individual loops of wire going around each side of the transformer should be referred to as turns and not coils.

The ideal transformer equation

An ideal transformer would be 100% efficient
- Although transformers can increase the voltage of a power source, due to the law of conservation of energy, they cannot increase the power output

If a transformer is 100% efficient:

$Input power = Output power$

The equation to calculate electrical power is:

$P = V \times I$

Where:
- P = power in Watts (W)
- V = potential difference in volts (V)
- I = current in amps (A)

Therefore, if a transformer is 100% efficient then:

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

Where:
- V_p = potential difference across primary coil in volts (V)
- I_p = current through primary coil in Amps (A)
- V_s = potential difference across secondary coil in volts (V)
- I_s = current through secondary coil in Amps (A)

The equation above could also be written as:

$P_{s} = V_{p} \times I_{p}$

Where:
- P_s = output power (power produced in the secondary coil) in Watts (W)

Worked Example

A transformer in a travel adapter steps up a 115 V ac mains electricity supply to the 230 V needed for a hair dryer. A current of 5 A flows through the hairdryer. Assuming that the transformer is 100% efficient, calculate the current drawn from the mains supply.

Answer:

Step 1: List the known quantities

Voltage in primary coil, V_p = 115 V
Voltage in secondary coil, V_s = 230 V
Current in secondary coil, I_s = 5 A

Step 2: Write the equation linking the known values to the current drawn from the supply, I_p

V_p × I_p = V_s × I_s

Step 3: Substitute in the known values

115 × I_p = 230 × 5

Step 4: Rearrange the equation to find I_p

$I_{p} = \frac{230 \times 5}{115}$

Step 5: Calculate a value for I_p and include the correct unit

I_p = 10 A

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