The turns ratio determines whether voltage goes up or down

Transformers — AQA A-Level Physics

The ratio of the output voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. to the input voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. equals the ratio of the number of turns on the secondary coil to the number of turns on the primary coil.

\frac{V_s}{V_p} = \frac{N_s}{N_p}

$V_s$: secondary (output) voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. (V)
$V_p$: primary (input) voltage (V)
$N_s$: number of turns on the secondary coil
$N_p$: number of turns on the primary coil

Step-up transformer: Ns > Np. More turns on the secondary than the primary. The output voltage is higher than the input voltage.
Step-down transformer: Ns < Np. Fewer turns on the secondary. The output voltage is lower than the input voltage.
This equation assumes an ideal transformer with no energy losses. All the flux produced by the primary links the secondary, and none is wasted.
The ratio Ns/Np is called the turns ratio. A turns ratio of 10:1 means the secondary has 10 times as many turns, so the voltage is multiplied by 10.
You can rearrange this any way you like. $VsNp = VpNs$ is a useful form when solving for an unknown.

Worked Example

A transformer has 200 turns on the primary coil and 4500 turns on the secondary coil. The primary voltage is 12 V. Calculate the secondary voltage.

Show Solution

List known values

Primary turns: $N_p = 200$
Secondary turns: $N_s = 4500$
Primary voltage: $V_p = 12 \text{ V}$

Write the transformer equation

$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$

Rearrange for Vs

$$V_s = V_p \times \frac{N_s}{N_p}$$

Substitute and evaluate

$$V_s = 12 \times \frac{4500}{200} = 12 \times 22.5 = 270 \text{ V}$$

Since $N_s > N_p$, this is a step-up transformer, and the secondary voltage is indeed larger than the primary. This confirms the answer makes physical sense.

Answer

$V_s = 270$ V

Examiner Tips and Tricks

Always do a quick sense check.
If Ns > Np, Vs must be greater than Vp (step-up).
If your answer gives a lower voltage, you have the ratio upside down.