A 3.0\ m wire has resistance 4.5\. Find the resistance of a 1.0\ m length of the same wire. [2 marks]

WJEC Eduqas Eduqas 2018-style practice: A wire of length 1.5\ m and diameter 0.40\ mm has a resistance of 2.2\. Calculate the resistivity of the metal.

Cross-sectional area: A = π r^2 = π (0.20 × 10^-3)^2 = π × 4.0 × 10^-8 = 1.26 × 10^-7\ m^2 (radius is half the diameter). Resistivity from R = LA: = RAL = 2.2 × 1.26 × 10^-71.5 = 2.77 × 10^-71.5 = 1.85 × 10^-7\ \,m. Markers reward using the radius (not diameter) in the area, = (RA)/(L), and the resistivity about 1.8 × 10^-7\ \,m.

EnglandPhysicsSyllabus dot point

What determines a component's resistance, and how do resistivity and temperature affect it?

Resistance: Ohm's law and resistance, the I-V characteristics of an ohmic conductor, a filament lamp and a diode, resistivity and its temperature dependence, and the behaviour of thermistors.

A focused answer to the Eduqas A-Level Physics Component 2 resistance content, covering Ohm's law and the definition of resistance, the I-V characteristics of an ohmic conductor, a filament lamp and a diode, resistivity and its temperature dependence, and the behaviour of thermistors.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

Resistance is the ratio of potential difference to current, $R = \frac{V}{I}$ , measured in ohms. Ohm's law states that for an ohmic conductor at constant temperature the current is proportional to the voltage, so $R$ is constant and the I-V graph is a straight line through the origin. A filament lamp's I-V curve is S-shaped because the resistance rises as the filament heats; a diode conducts only one way, with a sharp turn-on around $0.6\ \text{V}$ in forward bias. Resistivity $\rho$ is a property of the material, linked to resistance by $R = \frac{\rho L}{A}$ . For a metal, resistance rises with temperature (more lattice vibration scatters the electrons); for a thermistor (a semiconductor), resistance falls sharply with temperature as more charge carriers are freed.

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What this dot point is asking

Eduqas wants you to define resistance and state Ohm's law, sketch and explain the I-V characteristics of an ohmic conductor, a filament lamp and a diode, define resistivity and use $R = \frac{\rho L}{A}$ , and describe how the resistance of a metal and of a thermistor change with temperature.

The answer

Resistance and Ohm's law

I-V characteristics

Resistivity

Temperature dependence and thermistors

Resistance of a series combination of wires

A wire is made of two equal-length sections of the same metal joined end to end. The first has cross-sectional area $A$ and the second has area $2A$ . The first section has resistance $6.0\ \Omega$ . Find the resistance of the second section and the total resistance.

step 1: Compare using R = rho L / A

The sections have the same material ( $\rho$ ) and length ( $L$ ), so resistance is inversely proportional to area: $R \propto \frac{1}{A}$ .

step 2: Resistance of the wider section

Doubling the area halves the resistance: $R_2 = \frac{6.0}{2} = 3.0\ \Omega$ .

step 3: Total resistance in series

$R_\text{total} = R_1 + R_2 = 6.0 + 3.0 = 9.0\ \Omega$ .

Examples in context

Resistivity sets the choice of conductor in power transmission (copper or aluminium for low loss) and the design of heating elements (high-resistivity alloys such as nichrome). Thermistors are everywhere as temperature sensors: in thermostats, fire alarms, fridges and car engines. Diodes rectify alternating current and protect circuits, and the I-V curve of a filament lamp explains why a cold bulb draws a large surge of current at switch-on.

Try this

Q1. State Ohm's law. [1 mark]

Cue. For a metallic conductor at constant temperature, the current is directly proportional to the potential difference.

Q2. A $3.0\ \text{m}$ wire has resistance $4.5\ \Omega$ . Find the resistance of a $1.0\ \text{m}$ length of the same wire. [2 marks]

Cue. Resistance is proportional to length: $\frac{4.5}{3} = 1.5\ \Omega$ .

Q3. State how the resistance of an NTC thermistor changes as its temperature rises, and why. [2 marks]

Cue. It falls, because more charge carriers are freed, increasing the carrier density.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20184 marksA wire of length

1.5\ \text{m}

and diameter

0.40\ \text{mm}

has a resistance of

2.2\ \Omega

. Calculate the resistivity of the metal.

Show worked answer →

Cross-sectional area: $A = \pi r^2 = \pi (0.20 \times 10^{-3})^2 = \pi \times 4.0 \times 10^{-8} = 1.26 \times 10^{-7}\ \text{m}^2$ (radius is half the diameter).

Resistivity from $R = \dfrac{\rho L}{A}$ : $\rho = \dfrac{RA}{L} = \dfrac{2.2 \times 1.26 \times 10^{-7}}{1.5} = \dfrac{2.77 \times 10^{-7}}{1.5} = 1.85 \times 10^{-7}\ \Omega\,\text{m}$ .

Markers reward using the radius (not diameter) in the area, $\rho = \frac{RA}{L}$ , and the resistivity about $1.8 \times 10^{-7}\ \Omega\,\text{m}$ .

Eduqas 20204 marksSketch and explain the I-V characteristic of a filament lamp, and state how its resistance changes as the current increases.

Show worked answer →

The graph is an S-shaped curve through the origin: for small voltages it is roughly linear, but as the voltage and current rise the curve bends towards the voltage axis (the gradient $\frac{I}{V}$ falls).

As the current increases, the filament heats up. The metal ions vibrate more, scattering the drifting electrons more often, so the resistance increases. The decreasing gradient of the I-V curve shows this rising resistance, since $R = \frac{V}{I}$ grows along the curve.

Markers reward the S-shaped curve through the origin, linking the rising temperature to more lattice vibration and electron scattering, and stating the resistance increases.

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Sources & how we know this

Eduqas GCE AS/A Level Physics specification (A720QS) — WJEC Eduqas (2015)