Transformers and the national grid

The size of the induced potential difference depends on how rapidly the magnetic field through the coil changes and how many turns experience that change. Keeping other conditions the same:

• Faster movement of the magnet or conductor produces a larger potential difference because magnetic field lines are cut more rapidly.
• A stronger magnetic field produces a larger potential difference because the conductor experiences a greater magnetic change.
• More turns on the coil produce a larger potential difference because the potential differences induced in the individual turns add together.
• A larger coil area, when it experiences the same changing field across its area, produces a larger potential difference because more magnetic field passes through the coil.

Reversing the direction of movement reverses the polarity of the induced potential difference. Reversing the magnet's poles while keeping the movement the same also reverses the polarity. In a complete circuit, reversing the polarity reverses the induced current.

The induced field resists the change — Higher Tier

An induced current produces its own magnetic field. This field opposes the change that caused the induction.

For example, push a magnet north-pole first towards a coil in a complete circuit. The near end of the coil becomes a north pole, repelling the approaching magnet and resisting its movement. Pull the north pole away instead, and the near end of the coil becomes a south pole. It now attracts the departing magnet, again resisting the movement.

These two situations explain why ‘opposes the change’ matters: the coil repels an approaching magnet but attracts a departing one. Its response acts against the movement in both cases.

How a transformer transfers energy between circuits — Higher Tier

A transformer has a primary coil, connected to an alternating supply, and a secondary coil, connected to the output circuit. Both are wound around an iron core. Iron is useful because it is easily magnetised.

The alternating current in the primary coil repeatedly changes direction, producing a changing magnetic field. The iron core links this changing field to the secondary coil. The changing magnetic field through the secondary coil induces an alternating potential difference across it. If the secondary circuit is complete, an alternating current flows.

The two coils are separate circuits: current does not flow directly from one coil into the other. Energy is transferred through the changing magnetic field. A steady direct current does not maintain a changing field, so it cannot produce a continuous output voltage in this way.

Stepping alternating voltages up and down — Higher Tier

A step-up transformer increases the alternating potential difference. It has more turns on the secondary coil than on the primary coil. A step-down transformer decreases the alternating potential difference and has fewer turns on the secondary coil.

Transformers do not create extra energy. Increasing the voltage does not mean increasing the available power: for an ideal transformer, a higher output voltage is accompanied by a lower output current.

Why the National Grid uses high voltages

The National Grid transfers electrical energy over long distances. Its transmission cables have resistance, so current heats them. Energy transferred to the cables and surroundings by heating is no longer available to consumers.

Electrical power is related to current and potential difference by:

$$P = VI$$

Here, $P$ is power in watts (W), $V$ is potential difference in volts (V), and $I$ is current in amperes (A). For the same power, increasing the voltage reduces the current. A smaller current causes less heating in the transmission cables, reducing wasted energy and improving the efficiency of transmission.

A step-up transformer near the power station, before long-distance transmission, raises the voltage. Step-down transformers in local areas, before the supply reaches buildings, lower it for domestic use. Homes receive a much lower voltage than the long-distance transmission lines; the domestic mains supply is about 230 V.

The key is the combination: high voltage reduces losses during transmission, while the voltage is reduced locally to a level suitable for domestic appliances.

Calculating voltage and current in an ideal transformer — Higher Tier

For a transformer with 100% efficiency, the input power equals the output power:

$$V_P I_P = V_S I_S$$

The subscripts $P$ and $S$ mean primary and secondary. Both potential differences are measured in volts and both currents in amperes. Real transformers waste some energy, so this equality is an ideal assumption.

For example, suppose an ideal transformer has a primary potential difference of 230 V and a primary current of 0.20 A. Its secondary potential difference is 12 V. The input power is $230 \times 0.20 = 46\text{ W}$, so:

$$I_S = \frac{V_P I_P}{V_S} = \frac{230 \times 0.20}{12} \approx 3.83\text{ A}$$

The lower secondary voltage allows a larger secondary current while the power remains 46 W.

You can also rearrange the equation to find a voltage. For an ideal transformer with a primary voltage of 100 V, a primary current of 2 A and a secondary current of 0.5 A:

$$V_S = \frac{V_P I_P}{I_S} = \frac{100 \times 2}{0.5} = 400\text{ V}$$

This transformer steps the voltage up while reducing the current. Both sides transfer the same power, 200 W.

• A changing magnetic field through a coil induces a potential difference; a complete circuit allows current to flow.
• Larger induced voltage: faster movement, stronger field, more turns or larger coil area under the same changing-field conditions.
• Reverse the movement or the magnetic poles → reverse the induced polarity.
• The induced current's magnetic field opposes the original change: it resists both approach and withdrawal of a magnet.

Transformers — Higher Tier

AC in primary → changing magnetic field in iron core → alternating potential difference in secondary → AC if the secondary circuit is complete.

• Step-up: higher output voltage; more secondary turns.
• Step-down: lower output voltage; fewer secondary turns.
• Steady DC cannot maintain transformer action.

National Grid

Power station → step-up transformer → high-voltage transmission → local step-down transformers → domestic supply.

For the same power, $P = VI$: higher voltage → lower current → less cable heating → less wasted energy → greater efficiency.

Ideal transformer equation — Higher Tier

For 100% efficiency:

$$V_P I_P = V_S I_S$$

Voltages: V. Currents: A. Input power equals output power; stepping voltage up reduces current, and stepping voltage down increases current.