3.5.1.3
Worked example: calculating resistivity from experimental data
Resistivity & Superconductivity — AQA A-Level Physics
Worked Example
A student measures the resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω). of a constantan wire at different lengths. The wire has a mean diameter of 0.19 mm. From the graph of R against L, the gradient is 15.7 Ω m⁻¹. Calculate the resistivityA material property that quantifies how strongly it resists currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohm-metres (Ω m). of the wire.
Show Solution
1
Convert diameter to metres
$d = 0.19\;\text{mm} = 0.19 \times 10⁻^{3}\;\text{m}.$
2
Calculate cross-sectional area
$A = \\pid^{2}/4 = \\pi(0.19 \times 10⁻^{3})^{2} / 4 = 2.84 \times 10⁻⁸\;\text{m}^{2}.$
3
The gradient of the R vs L graph equals ρ/A.
4
Rearrange
$\\rho = gradient \times\;\text{A} = 15.7 \times 2.84 \times 10⁻⁸.$
5
$\\rho = 4.5 \times 10⁻⁷ \Omega\;\text{m}.$
Answer
$\\rho = 4.5 \times 10⁻⁷ \Omega\;\text{m}$
Examiner Tips and Tricks
- When reading a gradient, use two points on the line of best fit (not data points) that are far apart.
- Show your triangle on the graph.
- The larger the triangle, the more accurate the gradient.