OCR.4.1.2
resistivity
Energy, Power & Resistance - OCR A-Level Physics
Key Definition
resistivity
The resistance of a 1 m length of a material with a cross-sectional area of 1 \(m^{2}\). It is a property of the material, not the shape.
The resistance of a 1 m length of a material with a cross-sectional area of 1 \(m^{2}\). It is a property of the material, not the shape.
$$\rho = \frac{RA}{L}$$
- The unit of 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). is the ohm metre (ohm m).
- 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). is a material property. 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 current. Measured in ohms (Ω). depends on shape AND material.
- Longer $wire = more resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω).. Thicker wire = less resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω).$.
- ResistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m). depends on temperature and (for some materials) light intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..
- Metals: resistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m). \(\sim 10^{-8}\) to \(10^{-6}\) ohm m. Insulators: \(\sim 10^{10}\) ohm m.
Examiner Tips and Tricks
- Always convert diameter to radius, then to area in \(m^{2}\), before using the resistivity equation.
- A common error is forgetting to halve the diameter or to square it.
Common Mistake
MEDIUM
Confusing resistance and resistivity. Resistance depends on the dimensions (length, area) of the sample. Resistivity depends only on the material and temperature.
Worked Example
A constantan wire has diameter 0.22 mm and length 0.80 m. The PD across it is 1.46 V and the current is 0.14 A. Calculate its resistivity.
Show Solution
1
Calculate resistance
$R =\;\text{V}/I = 1.46 / 0.14 = 10.43 \;\Omega$
2
Convert diameter to radius in metres
$r = 0.22 / 2 = 0.11 mm = 1.1 x 10^{-4} m$
3
Calculate cross-sectional area
$A = pi r^2 = pi x (1.1 x 10^{-4})^2 = 3.80 x 10^{-8} m^2$
4
Apply resistivity equation
$rho = RA/L = 10.43 x 3.80 x 10^{-8} / 0.80$
5
$rho = 4.95 x 10^{-7} ohm m$
Answer
rho = \(5.0 \times 10^{-7}\) ohm m (2 s.f.)
Related:Current Electricity