The National Grid and Transformers

The electricity generated in a power station may have to travel a hundred miles or more through cables before it reaches a home or a factory, and along the way some of the energy is inevitably wasted as the cables warm up. The clever engineering that keeps these losses small is the reason the wires slung between pylons carry electricity at the astonishing voltage of $400\,000 \text{ V}$400000 V rather than the safe $230 \text{ V}$230 V of a household socket. The system of cables, pylons and transformers that carries electricity from power stations to consumers is called the National Grid. This lesson, part of Topic P6 (Global challenges) of OCR Gateway Combined Science A, explains why the grid transmits power at high voltage and low current, how transformers step the voltage up and down, and how this keeps transmission efficient.

By the end of this lesson you should be able to describe the structure of the National Grid, explain how a transformer changes an alternating voltage, describe the roles of step-up and step-down transformers, use the transformer equations, and explain why transmitting at high voltage and low current reduces the power wasted in the cables.

This lesson is calculation-heavy AO2 (applying the transformer voltage and power-transfer ratios) built on AO1 (describing the grid and the roles of step-up and step-down transformers).

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What Is the National Grid?

The National Grid is the nationwide network of cables and transformers that connects power stations to homes, schools, shops and factories. Its job is to move electrical energy from where it is generated to where it is needed, reliably and with as little waste as possible.

The problem the grid must solve is that carrying a large amount of power over long cables makes the cables heat up, wasting energy. The amount of energy wasted depends on the current flowing in the cables — and, as we shall see, keeping the current low is the key to keeping the losses small. To do this, the grid transmits electricity at a very high voltage and a correspondingly low current, using transformers to change the voltage at each end.

Exam Tip: The National Grid is a system of cables and transformers. Two transformers matter: a step-up transformer at the power station raises the voltage for transmission, and a step-down transformer near the consumer lowers it to a safe, usable value.

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What a Transformer Does

A transformer changes the size of an alternating potential difference (voltage). It has two coils of insulated wire wound onto a soft-iron core:

• the primary coil, connected to the input a.c. supply;
• the secondary coil, connected to the output.

The two coils are not electrically connected to each other — the only link between them is the soft-iron core. Here is how it works, step by step:

1. The alternating current in the primary coil produces a constantly changing magnetic field.
2. The soft-iron core carries (concentrates) this changing magnetic field round to the secondary coil.
3. The changing magnetic field through the secondary coil induces an alternating potential difference across it.

Because the whole process relies on a changing magnetic field, a transformer only works with alternating current (a.c.). If you connected a d.c. supply, the magnetic field would be steady (not changing), nothing would be induced in the secondary, and the output would be zero. This is one of the main reasons mains electricity is a.c.

The number of turns on each coil decides whether the voltage goes up or down:

• a step-up transformer has more turns on the secondary than the primary, and increases the voltage — used at the power station, ready for transmission;
• a step-down transformer has fewer turns on the secondary than the primary, and decreases the voltage — used near the consumer, so electricity can be used safely. The $400\,000 \text{ V}$400000 V of the transmission lines would be far too dangerous to bring into a building.

Exam Tip: A transformer works only on a.c. because it needs a changing magnetic field to induce a voltage in the secondary. More turns on the secondary → step-up (voltage up); fewer turns on the secondary → step-down (voltage down). The two coils are linked only by the soft-iron core — a common misconception is that a wire joins them.

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The Transformer Equations

The output voltage of a transformer depends on the ratio of the number of turns on the two coils. The potential differences are in the same ratio as the numbers of turns:

$\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$Vs​Vp​​=Ns​Np​​

where $V_p$Vp​ and $V_s$Vs​ are the primary and secondary potential differences (in volts, $\text{V}$V), and $N_p$Np​ and $N_s$Ns​ are the numbers of turns on the primary and secondary coils.

A transformer cannot create energy. In an ideal transformer — one that is 100% efficient — the power put into the primary equals the power taken from the secondary. Since power is $P = VI$P=VI, this gives:

$V_p I_p = V_s I_s$Vp​Ip​=Vs​Is​

where $I_p$Ip​ and $I_s$Is​ are the currents (in amperes) in the primary and secondary coils. An important consequence follows: if a transformer steps the voltage up, it must step the current down by the same factor (and vice versa), so that the product $VI$VI — the power — stays the same.

Worked Example 1 — A step-up transformer

A transformer has $100$100 turns on its primary coil and $500$500 turns on its secondary coil. The primary is connected to a $230 \text{ V}$230 V a.c. supply. Calculate the output (secondary) voltage.

Step 1 — write the equation: $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$Vs​Vp​​=Ns​Np​​.

Step 2 — rearrange to make $V_s$Vs​ the subject: $V_s = V_p \times \dfrac{N_s}{N_p}$Vs​=Vp​×Np​Ns​​.

Step 3 — substitute: $V_s = 230 \times \dfrac{500}{100}$Vs​=230×100500​.

Step 4 — calculate: $V_s = 230 \times 5 = 1150 \text{ V}$Vs​=230×5=1150 V.

Answer: the output is $1150 \text{ V}$1150 V. Since the secondary has more turns, this is a step-up transformer.

Worked Example 2 — Voltage up means current down

An ideal step-up transformer raises $230 \text{ V}$230 V to $11\,500 \text{ V}$11500 V. The current in the primary is $8.0 \text{ A}$8.0 A. Calculate the current in the secondary.

Step 1 — write the power equation for an ideal transformer: $V_p I_p = V_s I_s$Vp​Ip​=Vs​Is​.

Step 2 — rearrange to make $I_s$Is​ the subject: $I_s = \dfrac{V_p I_p}{V_s}$Is​=Vs​Vp​Ip​​.

Step 3 — substitute: $I_s = \dfrac{230 \times 8.0}{11\,500}$Is​=11500230×8.0​.

Step 4 — calculate: $I_s = \dfrac{1840}{11\,500} = 0.16 \text{ A}$Is​=115001840​=0.16 A.

Answer: the secondary current is $0.16 \text{ A}$0.16 A. The voltage was stepped up ($\times 50$×50), so the current was stepped down ($\times 50$×50) — the power ($1840 \text{ W}$1840 W) is unchanged.

Exam Tip: In $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$Vs​Vp​​=Ns​Np​​, keep the primary quantities together on top and the secondary together on the bottom. For an ideal transformer, power in = power out, so $V_p I_p = V_s I_s$Vp​Ip​=Vs​Is​: step the voltage up and the current goes down by the same factor.

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Why Transmit at High Voltage and Low Current?

This is the central idea of the lesson. When electricity travels along the long cables of the grid, the cables have resistance, so some energy is wasted heating them up. The power wasted heating a cable is given by:

$P = I^2R$P=I2R