Resistivity | CAIE 9702 Paper 1 Notes · Conquer Your A Levels

Paper 1

Physics9702

Resistivity

Resistance belongs to a particular wire. It changes if the wire's length or cross-sectional area changes.

Resistivity describes the material itself at a stated temperature.

Separate material from geometry

Same material and temperature throughout. Doubling the length doubles the resistance; doubling the cross-sectional area halves it.

R=\dfrac{\rho L}{A}

Symbols

$R$ = resistance of the wire (\Omega)
$\rho$ = resistivity of the material (\Omega\,\text{m})
$L$ = wire length (m)
$A$ = cross-sectional area (\text{m}^2)

For the same material, area and temperature, doubling length doubles resistance.
For the same material, length and temperature, doubling area halves resistance.
For the same geometry and temperature, doubling resistivity doubles resistance.
If length and area both change, combine both factors before deciding what happens to resistance.

Resistivity has unit $\Omega\,\text{m}$ , not $\Omega/\text{m}$ . Rearranging to $\rho=RA/L$ gives the unit directly.

Area is the usual trap

Worked example

Use radius, not diameter

A wire has length 2.0 m, diameter 0.50 mm and resistivity $1.7\times10^{-8}\ \Omega\,\text{m}$ . Find its resistance.

Radius is $0.25\times10^{-3}\ \text{m}$ .
$A=\pi r^2=1.96\times10^{-7}\ \text{m}^2$ .
$R=\rho L/A=0.17\ \Omega$ .

Answer

R=0.17\ \Omega

Common mistake

A diameter must be halved before using

A=\pi r^2

. Also convert millimetres to metres before squaring.

Your turn9702/21/M/J/25 Q6(a)(iii)

A uniform wire has resistance 1.1 Ω, area $4.7\times10^{-7}\ \text{m}^2$ and length 0.45 m. Calculate its resistivity. [3] (9702/21/M/J/25 Q6(a)(iii))

Show worked answer

Rearrange to $\rho=RA/L$ .
Substitute the SI values.

Answer

\rho=1.1\times10^{-6}\ \Omega\,\text{m}

Resistivity

Resistance belongs to a particular wire. It changes if the wire's length or cross-sectional area changes.

Resistivity describes the material itself at a stated temperature.

Separate material from geometry

Same material and temperature throughout. Doubling the length doubles the resistance; doubling the cross-sectional area halves it.

R=\dfrac{\rho L}{A}

Symbols

$R$ = resistance of the wire (\Omega)
$\rho$ = resistivity of the material (\Omega\,\text{m})
$L$ = wire length (m)
$A$ = cross-sectional area (\text{m}^2)

For the same material, area and temperature, doubling length doubles resistance.
For the same material, length and temperature, doubling area halves resistance.
For the same geometry and temperature, doubling resistivity doubles resistance.
If length and area both change, combine both factors before deciding what happens to resistance.

Resistivity has unit $\Omega\,\text{m}$ , not $\Omega/\text{m}$ . Rearranging to $\rho=RA/L$ gives the unit directly.

Area is the usual trap

Worked example

Use radius, not diameter

A wire has length 2.0 m, diameter 0.50 mm and resistivity $1.7\times10^{-8}\ \Omega\,\text{m}$ . Find its resistance.

Radius is $0.25\times10^{-3}\ \text{m}$ .
$A=\pi r^2=1.96\times10^{-7}\ \text{m}^2$ .
$R=\rho L/A=0.17\ \Omega$ .

Answer

R=0.17\ \Omega

Common mistake

A diameter must be halved before using

A=\pi r^2

. Also convert millimetres to metres before squaring.

Your turn9702/21/M/J/25 Q6(a)(iii)

A uniform wire has resistance 1.1 Ω, area $4.7\times10^{-7}\ \text{m}^2$ and length 0.45 m. Calculate its resistivity. [3] (9702/21/M/J/25 Q6(a)(iii))

Show worked answer

Rearrange to $\rho=RA/L$ .
Substitute the SI values.

Answer

\rho=1.1\times10^{-6}\ \Omega\,\text{m}