What is the difference between resistance and resistivity in Physics?

Resistance is a measure of how much a material opposes the flow of electric current, expressed in ohms (Ω). It depends on the material's properties, length, and cross-sectional area. Resistivity, on the other hand, is an intrinsic property of a material that quantifies how strongly it resists current flow, independent of its shape or size. It is expressed in ohm-meters (Ω·m). In the context of Cambridge International A Levels Physics, understanding these concepts is crucial for analyzing electrical circuits.

How does temperature affect the resistance of a conductor?

In most conductors, resistance increases with temperature. This is because, as temperature rises, the atoms in the conductor vibrate more vigorously, causing more frequent collisions with the electrons flowing through the material. This increased collision rate results in higher resistance. This concept is important in Cambridge International A Levels Physics as it helps explain the behavior of materials in different thermal conditions.

How is resistivity used to determine the resistance of a wire?

The resistance of a wire can be calculated using the formula R = ρ(L/A), where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is its cross-sectional area. This formula shows that resistance is directly proportional to the length and resistivity, and inversely proportional to the cross-sectional area. Understanding this relationship is essential for solving problems related to electricity in the Cambridge International A Levels Physics curriculum.

Why is resistivity considered an intrinsic property of a material?

Resistivity is considered an intrinsic property because it is inherent to the material itself, independent of its shape or size. It reflects how strongly a material opposes the flow of electric current due to its atomic structure. This concept is crucial in Cambridge International A Levels Physics as it helps students understand material properties and their impact on electrical conductivity.

What factors influence the resistivity of a material?

The resistivity of a material is influenced by its atomic structure, temperature, and the presence of impurities. For instance, in metals, increased temperature typically leads to higher resistivity due to increased atomic vibrations. Impurities can also affect resistivity by disrupting the regular atomic structure, either increasing or decreasing it. Understanding these factors is important for students studying electricity in the Cambridge International A Levels Physics syllabus.

Why is "Saying any device with $R = V/I$ is ohmic" a common mistake in Resistance and resistivity?

Why it happens: Confusing definition with law. How to avoid it: R = V/I is a DEFINITION of resistance (always works). Ohm's LAW requires I V at constant T — a relationship that holds for ohmic devices only. Source: 9702 Examiner Reports 2022-2024

Cambridge International A Levels Physics (9702)

Resistance and resistivity

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Short Notes - Resistance and resistivity

Detailed Study Notes

Detailed notes on Electricity for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Resistance and Resistivity Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Ohm's law, I-V curves, resistivity. Distinguish definition from law.

At a glance

$R = V/I$ (always).
Ohm's law: $I \propto V$ at constant $T$ .
$R = \rho L/A$ .
Filament: $R$ rises with $T$ .
Diode: threshold then steep rise.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

9.3.1 — Use Ohm's law.
9.3.2 — Distinguish ohmic and non-ohmic.
9.3.3 — Compute resistivity.

Ohm's law and I-V characteristics

Distinguish ohmic and non-ohmic.

Ohm's law. Current proportional to PD at constant temperature, for a conductor. $V = IR$

Definition. $R = V/I$ always. (Even non-ohmic.)

I-V curves.

Ohmic resistor. Straight line through origin. $R$ constant.
Filament lamp. Current heats filament → $T$ rises → $R$ rises. Curve flattens at high $V$ .
Diode. Zero current until ~0.7 V threshold (silicon); then steep. Reverse direction: ~zero current.
Thermistor (NTC). Resistance DECREASES with increasing $T$ .

Cambridge tip. Sketch and label thresholds, asymptotes, directions.

Figure 1 — I-V characteristics for resistor, filament and diode

An ohmic resistor gives a straight line through the origin; a filament lamp curves as it heats; a diode only conducts above its forward threshold.

Figure 2 — How resistance varies with temperature

The two behaviours have opposite causes, which is why a thermistor makes a useful temperature sensor while a metal wire barely changes.

Figure 3 — R = V/I always, even when the graph is curved

On a curved characteristic the resistance changes from point to point, so a question must say which voltage it wants the resistance at.

$R = V/I$ always.
Ohm's law: linear at constant $T$ .
I-V graphs distinguish devices.

See the full worked example for resistance and resistivity →

Resistivity

Material constant.

Formula. $R = \rho L / A$ .

Resistivity $\rho$ is a MATERIAL property; depends on substance and temperature.

Typical values (Ωm).

Copper: $1.7 \times 10^{-8}$ .
Aluminium: $2.8 \times 10^{-8}$ .
Tungsten: $5.6 \times 10^{-8}$ .
Rubber (insulator): $\sim 10^{13}$ .

Effect of temperature. Metals: $\rho$ increases with $T$ . Semiconductors: $\rho$ DECREASES with $T$ .

Example. Cu wire 1.5 m, $A = 5 \times 10^{-7}$ m², $R = 0.051$ Ω: $\rho = RA/L = 1.7 \times 10^{-8}$ Ωm.

Cambridge tip. Mark scheme rewards SI units throughout.

Figure 4 — Resistance depends on length and cross-sectional area

Length and area are geometry; resistivity is the material. Two wires of the same metal always share ρ but rarely share R.

Figure 5 — Typical resistivity values

Copper is used for wiring because its resistivity is near the bottom of this scale — the choice of material, not the thickness, does most of the work.

$R = \rho L/A$ .
$\rho$ is material constant.
Metals: $\rho$ up with $T$ .

See the full worked example for resistance and resistivity →

Quick recap

$R = V/I$ ; Ohm's law: $I \propto V$ .
I-V curves identify device type.
$R = \rho L/A$ .

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$R = V/I$ and $R = \rho L/A$ .
I-V for ohmic, filament, diode.

How it’s examined

Resistance/resistivity on every Paper. Most-tested: Ohm's law (4-5 marks), I-V curves (6 marks), resistivity calc (6-7 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Resistance and resistivity

Step-by-step solutions to past-paper-style questions on resistance and resistivity, written exactly the way a tutor would explain them at the board.

1Ohm's law (4 marks)
Extended• Adapted from 9702/22 May/Jun 2024• Ohm's law
Question
A 12 V battery drives 0.40 A through a resistor. Find the resistance. (4 marks)
Step-by-step solution
1. Step 1
  $R = V/I$ .
  $R = 12/0.40 = 30 \text{ }\Omega$
Answer
$R = 30$ Ω.
2Resistivity calculation (6 marks)
Extended• resistivity
Question
A copper wire 1.5 m long with cross-section $5.0 \times 10^{-7}$ m² has resistance 0.051 Ω. Find the resistivity. (6 marks)
Step-by-step solution
1. Step 1
  $R = \rho L/A \Rightarrow \rho = RA/L$ .
  $\rho = \dfrac{(0.051)(5.0 \times 10^{-7})}{1.5} \approx 1.7 \times 10^{-8} \text{ }\Omega\text{m}$
Answer
$\rho \approx 1.7 \times 10^{-8}$ Ωm.
3I-V characteristics (6 marks)
Extended• I-V
Question
Describe I-V characteristics for (a) ohmic resistor, (b) filament lamp, (c) semiconductor diode. (6 marks)
Step-by-step solution
1. Step 1
  (a) Ohmic. Straight line through origin. Slope = $1/R$ .
2. Step 2
  (b) Filament lamp. Curve through origin. Resistance INCREASES with temperature (current heats filament).
3. Step 3
  (c) Semiconductor diode. Zero current until threshold (~0.7 V); then current rises rapidly. Reverse: ~zero current.
Answer
(a) Straight line. (b) Curve up — R increases. (c) Threshold then steep rise; one-way.

Key Formulae — Resistance and resistivity

The formulae you need to memorise for resistance and resistivity on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Ohm's law
$V = IR$
When to use
For ohmic devices at constant temperature.
Resistivity
$R = \dfrac{\rho L}{A}$
$\rho$
resistivity (Ωm)
$L$
length
$A$
cross-sectional area
When to use
Resistance from material property and dimensions.

Key Definitions and Keywords — Resistance and resistivity

Definitions to memorise and the exact keywords mark schemes credit for resistance and resistivity answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Resistance
Examiner keyword
Ratio of PD to current. $R = V/I$ . Units: ohm (Ω) = V/A.
Ohm's law
Examiner keyword
Current proportional to PD at constant temperature, for a conductor.
Resistivity
Examiner keyword
Material property. $\rho = RA/L$ . Units: Ω·m.

Common Mistakes and Misconceptions — Resistance and resistivity

The traps other students keep falling into on resistance and resistivity questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Saying any device with $R = V/I$ is ohmic
9702 Examiner Reports 2022-2024
Why it happens
Confusing definition with law.
How to avoid it
$R = V/I$ is a DEFINITION of resistance (always works). Ohm's LAW requires $I \propto V$ at constant $T$ — a relationship that holds for ohmic devices only.

Resistance and resistivity — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Cambridge International A Levels Physics (9702)

Resistance and resistivity

0% Complete

3 tasks remaining

Short Notes - Resistance and resistivity

Detailed Study Notes

Detailed notes on Electricity for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Resistance and Resistivity Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Ohm's law, I-V curves, resistivity. Distinguish definition from law.

At a glance

$R = V/I$ (always).
Ohm's law: $I \propto V$ at constant $T$ .
$R = \rho L/A$ .
Filament: $R$ rises with $T$ .
Diode: threshold then steep rise.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

9.3.1 — Use Ohm's law.
9.3.2 — Distinguish ohmic and non-ohmic.
9.3.3 — Compute resistivity.

Ohm's law and I-V characteristics

Distinguish ohmic and non-ohmic.

Ohm's law. Current proportional to PD at constant temperature, for a conductor. $V = IR$

Definition. $R = V/I$ always. (Even non-ohmic.)

I-V curves.

Ohmic resistor. Straight line through origin. $R$ constant.
Filament lamp. Current heats filament → $T$ rises → $R$ rises. Curve flattens at high $V$ .
Diode. Zero current until ~0.7 V threshold (silicon); then steep. Reverse direction: ~zero current.
Thermistor (NTC). Resistance DECREASES with increasing $T$ .

Cambridge tip. Sketch and label thresholds, asymptotes, directions.

Figure 1 — I-V characteristics for resistor, filament and diode

An ohmic resistor gives a straight line through the origin; a filament lamp curves as it heats; a diode only conducts above its forward threshold.

Figure 2 — How resistance varies with temperature

The two behaviours have opposite causes, which is why a thermistor makes a useful temperature sensor while a metal wire barely changes.

Figure 3 — R = V/I always, even when the graph is curved

On a curved characteristic the resistance changes from point to point, so a question must say which voltage it wants the resistance at.

$R = V/I$ always.
Ohm's law: linear at constant $T$ .
I-V graphs distinguish devices.

See the full worked example for resistance and resistivity →

Resistivity

Material constant.

Formula. $R = \rho L / A$ .

Resistivity $\rho$ is a MATERIAL property; depends on substance and temperature.

Typical values (Ωm).

Copper: $1.7 \times 10^{-8}$ .
Aluminium: $2.8 \times 10^{-8}$ .
Tungsten: $5.6 \times 10^{-8}$ .
Rubber (insulator): $\sim 10^{13}$ .

Effect of temperature. Metals: $\rho$ increases with $T$ . Semiconductors: $\rho$ DECREASES with $T$ .

Example. Cu wire 1.5 m, $A = 5 \times 10^{-7}$ m², $R = 0.051$ Ω: $\rho = RA/L = 1.7 \times 10^{-8}$ Ωm.

Cambridge tip. Mark scheme rewards SI units throughout.

Figure 4 — Resistance depends on length and cross-sectional area

Length and area are geometry; resistivity is the material. Two wires of the same metal always share ρ but rarely share R.

Figure 5 — Typical resistivity values

Copper is used for wiring because its resistivity is near the bottom of this scale — the choice of material, not the thickness, does most of the work.

$R = \rho L/A$ .
$\rho$ is material constant.
Metals: $\rho$ up with $T$ .

See the full worked example for resistance and resistivity →

Quick recap

$R = V/I$ ; Ohm's law: $I \propto V$ .
I-V curves identify device type.
$R = \rho L/A$ .

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$R = V/I$ and $R = \rho L/A$ .
I-V for ohmic, filament, diode.

How it’s examined

Resistance/resistivity on every Paper. Most-tested: Ohm's law (4-5 marks), I-V curves (6 marks), resistivity calc (6-7 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Resistance and resistivity

Step-by-step solutions to past-paper-style questions on resistance and resistivity, written exactly the way a tutor would explain them at the board.

1Ohm's law (4 marks)
Extended• Adapted from 9702/22 May/Jun 2024• Ohm's law
Question
A 12 V battery drives 0.40 A through a resistor. Find the resistance. (4 marks)
Step-by-step solution
1. Step 1
  $R = V/I$ .
  $R = 12/0.40 = 30 \text{ }\Omega$
Answer
$R = 30$ Ω.
2Resistivity calculation (6 marks)
Extended• resistivity
Question
A copper wire 1.5 m long with cross-section $5.0 \times 10^{-7}$ m² has resistance 0.051 Ω. Find the resistivity. (6 marks)
Step-by-step solution
1. Step 1
  $R = \rho L/A \Rightarrow \rho = RA/L$ .
  $\rho = \dfrac{(0.051)(5.0 \times 10^{-7})}{1.5} \approx 1.7 \times 10^{-8} \text{ }\Omega\text{m}$
Answer
$\rho \approx 1.7 \times 10^{-8}$ Ωm.
3I-V characteristics (6 marks)
Extended• I-V
Question
Describe I-V characteristics for (a) ohmic resistor, (b) filament lamp, (c) semiconductor diode. (6 marks)
Step-by-step solution
1. Step 1
  (a) Ohmic. Straight line through origin. Slope = $1/R$ .
2. Step 2
  (b) Filament lamp. Curve through origin. Resistance INCREASES with temperature (current heats filament).
3. Step 3
  (c) Semiconductor diode. Zero current until threshold (~0.7 V); then current rises rapidly. Reverse: ~zero current.
Answer
(a) Straight line. (b) Curve up — R increases. (c) Threshold then steep rise; one-way.

Key Formulae — Resistance and resistivity

The formulae you need to memorise for resistance and resistivity on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Ohm's law
$V = IR$
When to use
For ohmic devices at constant temperature.
Resistivity
$R = \dfrac{\rho L}{A}$
$\rho$
resistivity (Ωm)
$L$
length
$A$
cross-sectional area
When to use
Resistance from material property and dimensions.

Key Definitions and Keywords — Resistance and resistivity

Resistance
Examiner keyword
Ratio of PD to current. $R = V/I$ . Units: ohm (Ω) = V/A.
Ohm's law
Examiner keyword
Current proportional to PD at constant temperature, for a conductor.
Resistivity
Examiner keyword
Material property. $\rho = RA/L$ . Units: Ω·m.

Common Mistakes and Misconceptions — Resistance and resistivity

✕Saying any device with $R = V/I$ is ohmic
9702 Examiner Reports 2022-2024
Why it happens
Confusing definition with law.
How to avoid it
$R = V/I$ is a DEFINITION of resistance (always works). Ohm's LAW requires $I \propto V$ at constant $T$ — a relationship that holds for ohmic devices only.

Resistance and resistivity — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Resistance and resistivity

Short Notes - Resistance and resistivity

Detailed Study Notes

At a glance

What you’ll learn

Ohm's law and I-V characteristics

Resistivity

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Ohm's law (4 marks)

2Resistivity calculation (6 marks)

3I-V characteristics (6 marks)

Ohm's law

Resistivity

Resistance

Ohm's law

Resistivity

✕Saying any device with R=V/IR = V/IR=V/I is ohmic

Resistance and resistivity — frequently asked questions

Resistance and resistivity

Short Notes - Resistance and resistivity

Detailed Study Notes

At a glance

What you’ll learn

Ohm's law and I-V characteristics

Resistivity

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Ohm's law (4 marks)

2Resistivity calculation (6 marks)

3I-V characteristics (6 marks)

Ohm's law

Resistivity

Resistance

Ohm's law

Resistivity

✕Saying any device with R=V/IR = V/IR=V/I is ohmic

Resistance and resistivity — frequently asked questions

✕Saying any device with $R = V/I$ is ohmic

✕Saying any device with $R = V/I$ is ohmic