Superconductivity and Applications Revision Notes | A Level AQA Physics

1. The Problem That Superconductivity Solves

Every time current flows through a wire, some energy is lost as heat. That is not a minor inconvenience — it costs billions of pounds in wasted electricity every year across national power grids. Now imagine a material where that loss drops to exactly zero. That is the promise of superconductivity, and it is one of the most striking phenomena in A-level physics.

To appreciate why superconductivity matters, recall what you already know about resistance. In a normal metal, electrons collide with vibrating lattice ions as they drift through the material. Those collisions convert electrical energy into thermal energy — that is resistance at work. The higher the temperature, the more the ions vibrate, and the greater the resistance.

Superconductivity turns that picture completely on its head. Below a certain temperature, some materials lose all resistance — not nearly zero, but precisely, measurably zero. Understanding when and why this happens, and what we can do with it, is exactly what the AQA specification requires.

2. Defining Superconductivity and Critical Temperature

The phrase 'at and below' is precise and examinable. Resistivity does not gradually fade away — it drops sharply to zero at the critical temperature. Picture a graph of resistivity against temperature: the line decreases as the material cools (as it does for any normal metal), then at the critical temperature it drops sharply and vertically to zero and stays there. That abrupt transition — not a smooth, perfectly linear decline — is the hallmark of a superconducting material.

The critical temperature depends entirely on the material — it is not a universal constant. Mercury, the first material found to be superconducting (discovered by Heike Kamerlingh Onnes in 1911), has a critical temperature of about 4.2 K. Some ceramic compounds called high-temperature superconductors have critical temperatures above 77 K, which is significant because liquid nitrogen (cheap and widely available) boils at 77 K and can therefore be used as a coolant.

The AQA specification states clearly that the critical field — the magnetic field strength above which superconductivity is destroyed — will not be assessed. You do not need to know about that. Focus on critical temperature and zero resistivity.

3. Zero Resistivity — What It Really Means

Zero resistivity is not the same as very low resistivity. In a normal conductor cooled to near absolute zero, resistance approaches a small but non-zero residual value caused by impurities and lattice defects. In a true superconductor below its critical temperature, resistivity is identically zero — no collisions, no energy loss, no heating of the wire.

A striking consequence: if you set up a current in a superconducting loop and remove the power supply, the current continues to circulate indefinitely. There is no resistance to dissipate it. Experiments have sustained persistent currents in superconducting rings for years without measurable decay. That is not a theoretical prediction — it has been observed in the laboratory.

Now connect this back to the formula for power dissipation. The power lost as heat in a resistor is given by $P = I^2 R$. If $R = 0$, then $P = 0$ regardless of how large the current is. A superconducting cable carrying thousands of amperes loses no energy to heating at all — provided the current remains below the material's critical current, beyond which superconductivity breaks down (this is not assessed by AQA, but worth knowing exists). That single consequence of zero resistance drives both major applications you need to know.

4. Application 1 — Production of Strong Magnetic Fields

A magnetic field is produced whenever current flows through a coil of wire. The stronger the current, the stronger the field. In a normal conducting coil, pushing very large currents through the wire generates enormous amounts of heat — the wire would melt before the field reached a useful strength. Superconducting coils remove that constraint entirely.

Because a superconducting coil has zero resistance, it dissipates no power as heat. You can drive extremely large currents through it and sustain a very strong, stable magnetic field without any continuous energy input to compensate for resistive losses. Once the current is established, it persists on its own.

This is why superconducting electromagnets are used in magnetic resonance imaging (MRI) scanners in hospitals. The coils are cooled with liquid helium to around 4 K, well below the critical temperature of the niobium-titanium alloy used. The resulting magnetic fields — typically 1.5 T to 3 T — would be impossible to sustain with conventional copper coils without catastrophic overheating. The Large Hadron Collider at CERN uses superconducting magnets for the same reason: to steer particle beams with fields that no resistive magnet could maintain.

5. Application 2 — Reducing Energy Loss in Power Transmission

National electricity grids transmit power over hundreds of kilometres. Even though transmission lines are made from low-resistivity materials such as aluminium, they still have non-zero resistance. The power lost in a transmission cable is $P_{\text{loss}} = I^2 R$, so any resistance at all causes continuous energy dissipation. Across an entire grid, this adds up to a significant fraction of the total power generated.

If transmission cables were made from superconducting materials, $R = 0$ and therefore $P_{\text{loss}} = 0$. Every joule generated at the power station would reach the consumer. In practice, the challenge is that current superconductors require cooling to very low temperatures, which itself costs energy and money. High-temperature superconductors — those with critical temperatures above 77 K — are the focus of intense research because liquid nitrogen cooling is far cheaper than liquid helium.

Several pilot projects around the world have already demonstrated superconducting power cables operating in real grid conditions. The economic and environmental case is strong: eliminating transmission losses would reduce the total amount of electricity that needs to be generated, cutting both fuel costs and carbon emissions. Whether the cooling infrastructure becomes cost-effective at scale is an ongoing engineering challenge, not a physics one.

Worked example: Calculating Power Loss Reduction with a Superconducting Cable

A transmission cable of resistance 4.0 Ω carries a current of 500 A. Calculate the power lost in the cable. State what happens to this power loss if the cable is replaced by a superconducting cable below its critical temperature.

1. $P_{\text{loss}} = I^2 R$ — This is the standard expression for power dissipated in a resistor. [M1] for selecting the correct formula.
2. $I = 500 \text{ A}, \quad R = 4.0 \text{ Ω}$ — Both values are given directly. No unit conversion is needed here.
3. $I^2 = 500 \times 500 = 250\,000 \text{ A}^2$ — Always expand the square explicitly. A common error is to write 500² = 5000 — that is wrong. 500 × 500 = 250,000. [M1] for correct substitution.
4. $P_{\text{loss}} = 250\,000 \times 4.0 = 1\,000\,000 \text{ W} = 1.0 \times 10^6 \text{ W}$ — 250,000 × 4 = 1,000,000. Express in standard form for clarity. [A1] for correct answer with units.
5. If $R = 0$: $P_{\text{loss}} = I^2 \times 0 = 0 \text{ W}$ — Zero resistance means zero power loss, regardless of current magnitude. This is the key advantage of superconducting transmission cables. [B1] for this statement.

Answer: Power lost in the normal cable: $1.0 \times 10^6$ W (1.0 MW). With a superconducting cable below its critical temperature, power loss = 0 W exactly.

6. Comparing Normal Conductors and Superconductors

Exam questions often ask you to compare the two types of material. The key is to be precise about what changes and what does not. Both carry current; both can produce magnetic fields; both obey $V = IR$ — but for a superconductor below its critical temperature, $R = 0$ so $V = 0$ across the conductor even when current flows.

Notice the distinction in the resistivity column. A very cold normal metal has low resistance — but not zero. A superconductor has identically zero resistance. That difference is not a matter of degree; it is a qualitative change in the physics of the material.

7. Exam Technique and Common Mistakes

AQA questions on superconductivity tend to cluster around three command words: 'state', 'explain', and 'evaluate'. Each demands a different level of response. Getting the command word right is the difference between a full mark and a partial one.

For 'state' questions — such as 'State what is meant by the critical temperature of a superconductor' — give a single precise sentence. Do not explain or justify; the mark is for the correct factual statement. For 'explain' questions — such as 'Explain why a superconducting cable reduces energy loss in power transmission' — you must link cause to effect using scientific principles: zero resistance leads to zero power dissipation via $P = I^2R$.