Resistivity — OCR A-Level Physics
Test yourself on Resistivity with OCR A-Level practice questions.
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Resistivity explained
This row is a guided-reading item for section 4.2.4 Resistivity.
Read the full explanation
The statement is only '(a)', so it is a placeholder for the first learning point of the section rather than a full assessed statement. Use the official OCR A Level Physics A specification to read the complete wording of 4.2.4(a) before revising. In guided reading you should locate the exact clause, identify the quantities and equations it names, and note how it connects to resistance, length and cross-sectional area. Do not invent content for '(a)'; treat it as a pointer to the specification text and check the current specification for the full statement.
(i) resistivity of a material; the equation R = ρL/A
Resistivity ρ is a property of the material itself, not of a particular specimen, so it lets you compare copper with nichrome regardless of shape. The defining equation R = ρL/A rearranges to ρ = RA/L. Here R is resistance in ohms (Ω), L is the length in metres (m) and A is the cross-sectional area in square metres (m²). Because ρ = RA/L, its unit is Ω m. A long thin wire has more resistance than a short thick one of the same material. Doubling L doubles R; doubling A halves R. Typical values: copper about 1.7 × 10⁻⁸ Ω m, nichrome about 1.1 × 10⁻⁶ Ω m. In a multiple-choice question you may be asked to identify the unit, to predict how R changes when L or A changes, or to calculate ρ from R, L and A.
(ii) techniques and procedures used to determine the resistivity of a metal.
To find the resistivity of a metal you measure R, L and A for a wire and use ρ = RA/L. Measure the diameter d with a micrometer at several places and orientations, then average; A = πd²/4. Measure L with a metre rule between the contact points. Measure R by passing a current and finding V and I, using R = V/I; a voltmeter in parallel with the wire and an ammeter in series avoids contact resistance. Take several readings of V and I, plot V against I and use the gradient to reduce random error. Then ρ = RA/L. A typical metal gives ρ of order 10⁻⁸ to 10⁻⁶ Ω m. In multiple-choice questions you may be asked which instrument suits which quantity, or how to reduce uncertainty.
(b) the variation of resistivity of metals and semiconductors with temperature
In a metal, increasing temperature makes the lattice ions vibrate more, so conduction electrons collide more often and resistivity increases. Over a limited range near room temperature the rise is roughly linear, so ρ ≈ ρ₀(1 + αΔT). In a semiconductor, increasing temperature releases more charge carriers (electrons and holes) across the small energy gap, so the number density n rises sharply and resistivity falls. This is a negative temperature coefficient of resistivity. So the same temperature change has opposite effects: metals become worse conductors, semiconductors become better conductors. In multiple-choice questions you may be asked to identify a graph shape or to explain the microscopic reason.
(c) negative temperature coefficient (NTC) thermistor; variation of resistance with temperature.
An NTC thermistor is a semiconductor device whose resistance falls as temperature rises. This is a negative temperature coefficient of resistance. The effect is strong: resistance may drop by a factor of several over a modest temperature range, and the R–T graph is a steep curve, not a straight line. The microscopic reason is that heating releases many more charge carriers, so the number density n increases and resistance falls. Because the change is large and reproducible, NTC thermistors are used as temperature sensors and in potential-divider circuits. In multiple-choice questions you may be asked to read an R–T graph, to choose a circuit, or to explain the shape using carrier number density.
Your focus
- Locate and read the full specification statement for 4.2.4(a).
- Identify the quantities and equation associated with resistivity.
- Explain how resistivity differs from resistance.
Show all 15 objectives
- State the equation R = ρL/A and rearrange it to find ρ, R, L or A.
- Explain why resistivity is independent of the dimensions of a specimen.
- Use the equation to predict or calculate how resistance changes with length and cross-sectional area.
- Describe a procedure to measure the resistivity of a metal wire.
- Select appropriate instruments for measuring diameter, length, current and potential difference.
- Explain how repeat readings and a V–I graph improve the reliability of the result.
- Describe how the resistivity of a metal changes with temperature and explain why.
- Describe how the resistivity of a semiconductor changes with temperature and explain why.
- Compare the two behaviours using the ideas of collision rate and charge-carrier number density.
- Describe how the resistance of an NTC thermistor varies with temperature.
- Explain the variation using the increase in the number density of charge carriers.
- Interpret an R–T graph and relate the thermistor to its use in a potential-divider circuit.
Resistivity exam tips
Marking Points
- Resistivity is defined by R = ρL/A, rearranged as ρ = RA/L.
- ρ is a property of the material; R also depends on the dimensions L and A.
- The unit of ρ is the ohm metre (Ω m), obtained from Ω × m² / m.
- Doubling the length L doubles the resistance R for a fixed material and area.
- Doubling the cross-sectional area A halves the resistance R for a fixed material and length.
- A larger ρ means a poorer conductor; copper has a much smaller ρ than nichrome.
- Measure the diameter d with a micrometer screw gauge at several positions and orientations, then average.
- Calculate the cross-sectional area from A = πd²/4, converting d to metres.
- Measure the length L of the wire between the contact points with a metre rule.
- Measure current I with an ammeter in series and potential difference V with a voltmeter in parallel with the wire.
- Calculate resistance from R = V/I, or better, plot V against I and use the gradient.
- Substitute into ρ = RA/L and give the unit as Ω m.
- In metals, resistivity increases as temperature rises.
- The cause is increased lattice vibration, which increases the rate of collisions between conduction electrons and ions.
- The number density of charge carriers in a metal is essentially unchanged by temperature.
- In semiconductors, resistivity decreases as temperature rises.
- The cause is the release of more charge carriers across the energy gap, increasing the number density n.
- A graph of ρ against T has a positive gradient for a metal and a negative gradient for a semiconductor.
- An NTC thermistor has a resistance that decreases as temperature increases.
- The R–T graph is a steep, non-linear curve, not a straight line.
- The cause is an increase in the number density of charge carriers as temperature rises.
- NTC thermistors are used as temperature sensors and in potential dividers.
- The percentage change in resistance per kelvin is much larger than for a metal.
- The resistance change is reversible, so the device can be used repeatedly.
Examiner Tips
- 💡Open the OCR A Level Physics A specification at section 4.2.4 and read the full text of (a).
- 💡Write down the quantities and units named in the clause, such as resistivity ρ, length L and cross-sectional area A.
- 💡Link the clause to the equation R = ρL/A and to practical measurements of resistivity.
- 💡Write the equation as ρ = RA/L before substituting any numbers, so the subject is clear.
- 💡Check units of L and A first; convert mm² to m² by multiplying by 1 × 10⁻⁶.
- 💡For proportional-reasoning options, change one variable at a time and state the effect on R.
- 💡Sanity-check the order of magnitude: metals have ρ of order 10⁻⁸ to 10⁻⁶ Ω m.
- 💡List the measurements in the order you would take them: d, L, I, V, then calculate.
- 💡State that the micrometer is used because the diameter is small and needs precision.
- 💡Mention taking repeat readings and averaging to reduce random error.
- 💡Use the gradient of a V–I graph rather than a single pair of readings for a more reliable R.
- 💡Link each trend to the microscopic cause: collision rate for metals, carrier number for semiconductors.
- 💡Sketch or read the graph carefully: positive gradient for a metal, negative for a semiconductor.
- 💡Use the phrase 'number density of charge carriers' when discussing semiconductors.
- 💡Remember that resistivity, not just resistance, is being described; keep the specimen dimensions fixed.
- 💡Read the graph at the temperature asked for, and quote the resistance with its unit.
- 💡Use the phrase 'negative temperature coefficient' to justify the direction of the change.
- 💡Link the circuit use to a potential divider, where the changing resistance changes the output voltage.
- 💡Check whether the question asks about resistance or resistivity; for a fixed specimen they change together.
Common Mistakes
- Treating '(a)' as a complete statement. Correction: it is a label; read the full specification clause for 4.2.4(a).
- Assuming the section is only about resistance. Correction: resistivity is a material property and links to R = ρL/A.
- Skipping the specification and guessing the content. Correction: always check the official OCR specification wording for the exact requirement.
- Thinking resistivity depends on the length or thickness of the wire. Correction: ρ is a material property; only R depends on L and A.
- Using the unit Ω m⁻¹ for resistivity. Correction: ρ = RA/L gives Ω × m² / m = Ω m.
- Substituting A in mm² or cm² without converting to m². Correction: convert areas to m² before calculating, since 1 mm² = 1 × 10⁻⁶ m².
- Confusing resistance R with resistivity ρ in a rearrangement. Correction: write ρ = RA/L and check each symbol before substituting.
- Measuring the diameter once only. Correction: take several readings at different places and orientations and average them, because the wire may not be uniform.
- Using A = πd² instead of A = πd²/4. Correction: d is the diameter, so the radius is d/2 and A = π(d/2)² = πd²/4.
- Connecting the voltmeter in series or the ammeter in parallel. Correction: voltmeter in parallel with the wire, ammeter in series with it.
- Forgetting to convert the diameter from mm to m before calculating A. Correction: divide mm by 1000 to get m, then square.
- Saying metals and semiconductors both increase in resistivity with temperature. Correction: metals increase, semiconductors decrease.
- Explaining the metal effect by saying more electrons are released. Correction: the number of carriers is nearly constant; it is the collision rate that rises.
- Explaining the semiconductor effect by saying ions vibrate less. Correction: the dominant effect is the increase in the number of charge carriers.
- Assuming the relationship is linear for a semiconductor. Correction: the fall is non-linear and steep, often shown as a curve.
- Saying the resistance of an NTC thermistor increases with temperature. Correction: it decreases, hence 'negative' temperature coefficient.
- Treating the R–T graph as linear. Correction: it is a curve, steep at low temperature and flattening at high temperature.
- Confusing the thermistor with a metal wire. Correction: a metal wire has a positive temperature coefficient of resistance.
- Explaining the fall in resistance by saying ions vibrate less. Correction: the dominant cause is the increase in the number of charge carriers.