Transformers

(Higher Tier only) (Separate Physics only)

The whole of this lesson is Higher Tier and Separate Physics content, and is not part of the Combined Science course.

A transformer changes the size of an alternating potential difference (pd). It is built from two coils of wire wound on a shared iron core:

• the primary coil is connected to the alternating input supply;
• the secondary coil provides the output.

The core is made of iron because iron is easily magnetised, which lets the magnetic field pass efficiently from one coil to the other. The two coils are not electrically connected: energy passes between them only through the changing magnetic field in the core.

(Higher Tier only) (Separate Physics only)

A transformer works by combining electromagnetism with the generator effect:

1. An alternating current in the primary coil produces a changing magnetic field in the iron core.
2. The iron core carries this changing field round to the secondary coil.
3. The changing field through the secondary coil induces an alternating pd across it (the generator effect).

A transformer only works with alternating current. A steady direct current would make a constant field, and a constant field does not induce a pd in the secondary coil.

Because the field must keep changing to induce a pd, this is why mains electricity, and the National Grid, uses ac. If the primary were fed with dc, the secondary would give an output only at the instants the current was switched on or off, not a continuous supply.

(Higher Tier only) (Separate Physics only)

The size of the output pd depends on the number of turns on each coil. The ratio of pds equals the ratio of turns:

$\frac{V_p}{V_s}=\frac{n_p}{n_s}$

where $V_p$ and $V_s$ are the primary and secondary pds (V), and $n_p$ and $n_s$ are the numbers of turns on the primary and secondary coils.

This equation is given on the Physics equation sheet. You do not need to memorise it, but you must be able to use and rearrange it.

This gives two types of transformer:

Type	Turns	Effect on pd
Step-up	$n_s>n_p$	Increases the pd ($V_s>V_p$)
Step-down	$n_s<n_p$	Decreases the pd ($V_s<V_p$)

Worked example — a transformer has 200 turns on the primary and 1000 turns on the secondary. The primary pd is 230 V. Find the secondary pd.

Rearrange for $V_s$:

$V_s=V_p\times \frac{n_s}{n_p}=230\times \frac{1000}{200}=230\times 5=1150\text{V}$

The secondary pd is 1150 V. Since $n_s>n_p$, this is a step-up transformer, and the pd has increased as expected.

(Higher Tier only) (Separate Physics only)

A transformer cannot create energy. If a transformer is 100% efficient, the power delivered by the secondary equals the power supplied to the primary. Since power = pd × current:

$V_s{I}_s=V_p{I}_p$

where $I_p$ and $I_s$ are the primary and secondary currents (A).

This equation is given on the Physics equation sheet. Use and rearrange it; you do not need to memorise it.

The consequence is important: if a transformer steps the pd up, it must step the current down by the same factor, and vice versa. High pd goes hand in hand with low current.

Worked example — a 100% efficient transformer supplies a device with an output of 12 V at 2.0 A. The input pd is 230 V. Find the current drawn from the input supply.

First find the power output:

$V_s{I}_s=12\times 2.0=24\text{W}$

Because the transformer is 100% efficient, the input power is also 24 W. Rearrange $V_p{I}_p=24$ for $I_p$:

$I_p=\frac{V_s{I}_s}{V_p}=\frac{24}{230}=0.104\text{A}(3\text{s.f.})$

The current drawn from the supply is about 0.10 A. The low-pd side (12 V) carries the larger current (2.0 A), and the high-pd side (230 V) carries the smaller current, exactly as the power equation predicts.

(Higher Tier only) (Separate Physics only)

Transformers are what make the National Grid efficient. Power stations generate electricity, which must travel long distances through cables that have resistance. Some energy is always wasted heating those cables.

The power wasted in a cable depends on the current, not the pd (it rises with the square of the current). So to cut losses, the grid transmits power at a very high pd and a low current:

• Step-up transformers at the power station raise the pd (to around 400,000 V) and lower the current for transmission, so far less energy is wasted as heat.
• Step-down transformers near homes and factories reduce the pd back to safe, usable levels (230 V for homes).

Transmitting at high pd keeps the current low, which minimises heating losses in the cables. This is the whole reason the grid relies on transformers.

Because the power is (near enough) unchanged by an efficient transformer, raising the pd is the practical way to reduce the current, and so the wasted heat, without reducing the power delivered.

1. Trying to use a transformer with dc

A transformer needs a changing magnetic field to induce a pd, so it only works with alternating current. Steady dc gives a constant field and no continuous output.

2. Flipping the turns ratio

Line up the equation carefully: $\frac{V_p}{V_s}=\frac{n_p}{n_s}$. Primary quantities go together on the top-left, secondary on the bottom-right. Getting the fraction upside down turns a step-up answer into a step-down one.

3. Forgetting current steps the opposite way to pd

If the pd is stepped up, the current is stepped down (for an efficient transformer). Do not assume both rise together; the power $V_s{I}_s=V_p{I}_p$ stays the same.

4. Confusing which transformer the grid uses where

Step-up at the power station for transmission; step-down near the user for safety. Swapping these is a common slip.

5. Saying high pd itself reduces the losses

Losses fall because the high pd allows a low current, and heating in the cables depends on the current. Link the high pd to the low current, then to the reduced heating.