7.3.4a Transformer construction and the turns ratio

Transformer construction

1. The primary coil is connected to the input alternating potential difference.
2. The secondary coil is connected to the output circuit.
3. Both coils are wound on an iron core.
4. The two coils are separate, with no direct electrical connection; energy passes between them through a changing magnetic field in the core.
5. Iron is used because it is easily magnetised, so the changing field from the primary coil passes effectively through the secondary coil.

How a transformer works

1. A transformer needs an alternating current in the primary coil, because it continually changes direction and size.
2. The alternating current in the primary coil produces a changing magnetic field.
3. The iron core becomes magnetised and carries the changing field through the secondary coil.
4. The changing field induces an alternating potential difference across the secondary coil.
5. If the secondary circuit is complete, this drives an alternating current in it.
6. A steady direct current gives no continuous transformer action, because a constant current's field is not changing.

The transformer turns ratio

1. The potential difference across each coil depends on its number of turns, given by $\frac{V_p}{V_s}=\frac{n_p}{n_s}$.
2. $V_p$ is the potential difference across the primary coil, in volts, $V$.
3. $V_s$ is the potential difference across the secondary coil, in volts, $V$.
4. $n_p$ is the number of turns on the primary coil.
5. $n_s$ is the number of turns on the secondary coil.
6. Write both ratios in the same order: if primary is on top for the potential differences, primary must be on top for the turns.
7. A coil with more turns has the greater potential difference, so a secondary coil with five times as many turns has five times the potential difference.

Step-up and step-down transformers

1. A step-up transformer increases the potential difference, so $V_s>V_p$ and it has more secondary turns, $n_s>n_p$.
2. A step-down transformer decreases the potential difference, so $V_s<V_p$ and it has fewer secondary turns, $n_s<n_p$.

7.3.4b Transformers and power transmission

Power input and power output

1. For an ideal transformer, $P_{input}=P_{output}$.
2. Electrical power is $P=VI$, so for a transformer $V_p{I}_p=V_s{I}_s$.
3. $V_p$ and $I_p$ are the potential difference and current in the primary coil, in $V$ and $A$.
4. $V_s$ and $I_s$ are the potential difference and current in the secondary coil, in $V$ and $A$.
5. The primary coil takes the input power and the secondary coil gives the output power; if the transformer is $100\%$ efficient, no power is wasted and the two are equal.
6. To find the current drawn from the input supply for a given output, use $I_p=\frac{P_{output}}{V_p}$, assuming the transformer is ideal.

Linking potential difference, turns and current

1. The potential differences depend on the turns, $\frac{V_s}{V_p}=\frac{n_s}{n_p}$.
2. For an ideal transformer the power stays constant, so increasing the potential difference decreases the current, from $V_p{I}_p=V_s{I}_s$.
3. Combining the relationships gives $\frac{I_s}{I_p}=\frac{V_p}{V_s}=\frac{n_p}{n_s}$, so the current ratio is the inverse of the potential difference and turns ratios.
4. In a step-up transformer, $V_s>V_p$, so $I_s<I_p$.
5. In a step-down transformer, $V_s<V_p$, so $I_s>I_p$.

High-potential-difference power transmission

1. The National Grid uses step-up transformers to raise the potential difference before power is sent through the transmission cables.
2. For a fixed power, $I=\frac{P}{V}$, so a higher potential difference gives a lower current.
3. A lower current causes less heating in the cables, which have resistance, so less energy is transferred to the thermal energy stores of the cables and surroundings.
4. Near consumers, step-down transformers reduce the potential difference again to safer, usable levels.
5. The reasoning chain is: step-up transformer raises the potential difference, the current falls for the same power, less heating in the cables, so less energy is wasted and transmission is more efficient.