Resistivity — AQA A-Level Physics

Resistivity is a fundamental property of materials that quantifies how strongly they oppose the flow of electric current. It is defined by the equation rho = RA/L, where rho is resistivity, R is resistance, A is cross-sectional area, and L is length. Unlike resistance, resistivity is independent of the shape and size of the conductor and depends only on the material and its temperature. This makes it essential for comparing materials and selecting appropriate conductors and insulators in electrical engineering.

In the AQA A-Level Physics specification, resistivity is a key topic within the Electricity module. It builds on prior knowledge of current, potential difference, and resistance, and it leads to understanding of superconductivity and temperature dependence. Students must be able to use the resistivity equation, describe experimental methods to determine resistivity, and explain how resistivity changes with temperature for different materials. Mastery of this topic is crucial for tackling exam questions on practical skills and material properties.

• →Resistivity (rho) is a material property defined by rho = RA/L, with units ohm metres (ohm m). It is independent of the dimensions of the sample.
• →Resistance (R) depends on both the material and its dimensions: R = rho L / A. For a given material, resistance is directly proportional to length and inversely proportional to cross-sectional area.
• →The resistivity of a metal increases with temperature because lattice vibrations increase, causing more frequent collisions between charge carriers and ions. In semiconductors, resistivity decreases with temperature as more charge carriers are released.
• →Superconductors have zero resistivity below a critical temperature, allowing current to flow without energy dissipation. This is used in applications like MRI scanners and maglev trains.
• →In experimental determinations of resistivity, precise measurement of diameter (using a micrometer) and length (using a metre rule) is crucial, and systematic errors such as zero error must be accounted for.

• States and rearranges ρ = RA/L, using consistent SI units of Ω m for resistivity, m² for area and m for length.
• Explains that increasing temperature in a metal increases lattice vibrations, increasing electron scattering and so increasing resistance.
• Explains that increasing temperature in an NTC thermistor increases the number of charge carriers, decreasing resistance.
• Describes a practical use of a thermistor, such as in a potential divider circuit for temperature sensing or control.
• Distinguishes between the small, roughly linear change in a metal and the large, non-linear change in a thermistor.
• States that an ntc thermistor is a semiconductor device whose resistance decreases as its temperature increases.
• Explains that increasing temperature releases more charge carriers, increasing the number density of charge carriers and so increasing current for a given potential difference.
• Uses the relationship R = V / I to show that a larger current at the same potential difference corresponds to lower resistance.
• Describes the shape of the resistance–temperature graph for an ntc thermistor: resistance falls steeply at low temperatures and more gradually at higher temperatures.
• Recognises and uses the correct circuit symbol for a thermistor in diagrams and circuit descriptions.
• Applies ntc behaviour in a potential divider, explaining how the output potential difference changes as temperature changes.
• Describes how a thermistor in a potential divider produces an output potential difference that depends on temperature.
• Explains that as temperature rises, the resistance of an ntc thermistor falls, changing the share of the supply potential difference across each component.
• Interprets a resistance–temperature graph by reading resistance values at given temperatures and describing the curve as non-linear.
• Explains a practical use, such as a thermostat or temperature sensor, where the thermistor controls a heater, fan or alarm.
• Compares the sensitivity of the thermistor at different temperatures using the gradient of the resistance–temperature graph.
• Defines superconductivity as zero resistivity at and below a critical temperature, not merely very low resistivity.
• States that the critical temperature is a fixed property of each material and differs between materials.
• Links zero resistivity to zero resistance, so no potential difference is needed to maintain a steady current.
• Explains that above the critical temperature the material reverts to normal resistive behaviour.
• Uses ρ = 0 with R = ρL/A to show a sample of any length or area has zero resistance.
• Applies V = IR to show zero volts across a superconductor carrying a steady current.
• Explains that zero resistance allows large currents without resistive heating, enabling strong electromagnets.
• Names a context such as MRI scanners, maglev or particle accelerators where strong fields are needed.
• Explains that zero-resistance transmission cables would eliminate I²R heating losses in the grid.
• Recognises practical limits: critical temperature, critical current, critical field and cryogenic cooling costs.
• Compares superconductor cables with copper cables in terms of energy loss and cooling demand.
• States that exceeding a critical value destroys superconductivity and restores resistance.
• Connect the ammeter in series with the wire and the voltmeter in parallel across the measured length of wire.
• Measure the diameter with a micrometer at several positions and orientations, then average the readings to reduce random error.
• Calculate cross-sectional area using A = πr², converting the diameter from mm to m before halving it to find r.
• Plot a graph of resistance R against length L and use the gradient, since gradient = ρ/A, to determine ρ.
• Keep the current small and switch off between readings so that the wire's temperature, and therefore its resistivity, stays approximately constant.

• 💡Write the rearranged equation before substituting values so the examiner can follow your method.
• 💡When describing temperature effects, name the mechanism: lattice vibration and scattering for metals, charge carrier release for thermistors.
• 💡Link thermistor behaviour to a circuit context, such as the output potential difference of a potential divider changing with temperature.
• 💡Sketch the resistance–temperature curve with resistance on the vertical axis and temperature on the horizontal axis, showing a decreasing curve that is steep at first and then flattens.
• 💡When explaining the decrease in resistance, always link temperature to the release of charge carriers and then to current or resistance.
• 💡In circuit questions, identify whether the thermistor is in the upper or lower part of a potential divider before predicting how the output potential difference changes.
• 💡When describing a temperature sensor, state the variable that is measured and how the thermistor changes it, for example output potential difference.
• 💡Use the resistance–temperature graph to justify your answer rather than quoting a memorised value.
• 💡In potential divider questions, calculate the output potential difference before and after a temperature change to show the direction of change clearly.
• 💡Quote the definition with both conditions: zero resistivity and at or below the critical temperature.
• 💡When comparing materials, name each material and its own T_c rather than giving one value for all.
• 💡Use ρ = 0 and V = IR to justify statements about zero potential difference and no heating.
• 💡Link each application to zero resistivity rather than listing applications without physics.
• 💡Use I²R heating to quantify the energy saved in transmission.
• 💡Mention at least one critical limit when discussing why applications are not universal.
• 💡Record raw micrometer readings with a sensible number of decimal places and show how you averaged them.
• 💡State the equation you use before substituting values, and keep units consistent throughout.
• 💡Comment on the main sources of uncertainty, such as wire diameter and temperature change, when the question asks for an evaluation.
• 💡Always write the resistivity equation in symbols and then substitute values with units. This helps you avoid unit errors and shows the examiner your working.
• 💡In practical questions, mention specific improvements like measuring diameter at multiple points, using a longer wire, or correcting for zero error. These are often worth marks.
• 💡When explaining temperature effects, be precise: for metals, state that increased lattice vibrations lead to more collisions and thus higher resistivity; for semiconductors, state that increased temperature releases more charge carriers, decreasing resistivity.

• Using the diameter instead of the radius when calculating cross-sectional area; the correction is to halve the diameter first, then use A = πr².
• Mixing units, such as using mm² or cm in the resistivity equation; the correction is to convert all lengths to metres and areas to m² before substituting.
• Claiming that heating always increases resistance; the correction is to specify that this applies to metal conductors, whereas an NTC thermistor shows a decrease.
• Thinking that resistance increases with temperature for all thermistors; correct this by stating that only ntc thermistors show a decrease in resistance as temperature rises.
• Confusing the effect of increased lattice vibrations with the dominant carrier effect; correct this by explaining that the rise in the number of charge carriers outweighs the increased scattering in an ntc thermistor.
• Treating the thermistor as an ohmic component with constant resistance; correct this by stating that its resistance changes with temperature and its current–potential difference graph is non-linear.
• Assuming the output potential difference of a potential divider changes linearly with temperature; correct this by referring to the non-linear resistance–temperature graph.
• Placing the thermistor in the wrong part of a potential divider and predicting the opposite change; correct this by tracing how the resistance change alters the potential difference across each component.
• Reading a resistance–temperature graph as a straight line; correct this by describing the curve as steep at low temperature and flattening at higher temperature.
• Saying resistivity becomes very small rather than exactly zero; correct this by stating ρ = 0 at and below T_c.
• Treating T_c as a universal constant such as 0 K; correct this by naming a material and its own T_c.
• Confusing resistance with resistivity; correct this by noting resistivity is a material property while resistance also depends on length and cross-sectional area.
• Claiming superconductors remove all energy costs; correct this by noting refrigeration still consumes energy.
• Saying superconductors can carry unlimited current; correct this by referring to the critical current.
• Assuming any material becomes superconducting when cooled; correct this by noting only certain materials have a critical temperature.
• Connecting the voltmeter in series or the ammeter in parallel; correct this by placing the ammeter in the main series path and the voltmeter across the wire section.
• Using the diameter as the radius in A = πr²; correct this by halving the diameter first.
• Leaving the circuit switched on throughout, which heats the wire and changes its resistance; correct this by using a low current and switching off between readings.
• Students often think resistivity increases with length or decreases with area. Correction: Resistivity is independent of dimensions; it is resistance that changes with length and area.
• Students may believe that resistivity and resistance are the same thing. Correction: Resistance is a property of a specific object, while resistivity is a property of the material itself.
• Students sometimes forget to convert units, such as mm squared to m squared, leading to answers that are off by factors of 10 to the power of 6. Correction: Always convert all lengths to metres and areas to metres squared before calculation.

1. 1Day 1-2: Review the definition of resistivity and the equation rho = RA/L. Practice rearranging the equation and converting units. Complete basic calculation questions from textbooks.
2. 2Day 3-4: Study the experimental method to determine resistivity. Watch a video or simulate the experiment, noting the steps and potential errors. Write a step-by-step method including how to measure diameter and length accurately.
3. 3Day 5-6: Learn about temperature dependence of resistivity for metals, semiconductors, and superconductors. Create a table comparing their behaviour and applications.
4. 4Day 7-8: Attempt past paper questions on resistivity, focusing on both calculations and practical descriptions. Mark your answers using the mark scheme and note recurring mistakes.
5. 5Day 9-10: Review all key concepts and misconceptions. Create flashcards for active recall and test yourself on definitions, equations, and explanations. If any area is weak, revisit it.

• 📋Calculation questions: You may be asked to calculate resistivity given resistance, length, and area, or to find resistance given resistivity and dimensions. Always show your working and pay attention to significant figures and units.
• 📋Practical description questions: These ask you to describe an experiment to determine resistivity, including measurements and improvements. Be specific about using a micrometer, measuring diameter at multiple points, and correcting for zero error.
• 📋Explanation questions: You may need to explain why resistivity changes with temperature for metals or semiconductors, or why superconductors are useful. Use precise terminology like 'lattice vibrations' and 'charge carriers'.
• 📋Graph questions: You might be given a graph of resistance against length for a wire and asked to determine resistivity from the gradient. Remember that gradient = rho / A, so rho = gradient times A.