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Resistivity
Electricity Lesson 5
Learning Objectives

To define resistivity.

To know what causes resistance.

To know how to measure resistance.
Practice Conversion

If a wire has a cross sectional area of 1.23
square millimetres

What is its area in square metres.
What does resistance depend on?




The resistance of a wire depends on three
factors:
the length; double the length, the resistance
doubles.
the area; double the area, the resistance halves.
the material that the wire is made of.
Resistivity

For a conductor of length L and uniform crosssectional area, A, its resistance R is proportional
to L but inversely proportional to A.

So the resistance is given by:-
R

L
A
Where ρ is the resistivity of the conductor.
Resistivity

Rearranging gives an equation for resistivity:-
RA

L


The unit of resistivity is the ohm metre (Ωm)
In words:-
area (metre 2 )  resistance (ohms)
Resistivit y (ohm metres) 
length (metre)
Resistivity

Resistivity is a property of the material. It is
defined as the resistance of a wire of the
material of unit area and unit length.

It has the symbol ρ, don’t mix this up with
density!
Cross Sectional Area

For a circular conductor with a radius r,
diameter d, the cross sectional area is given by:-
 d  d
A  r     
4
2
2
2
2
Question

Constantan has a resistivity of 47 × 10-8
Ωm. How much of this wire is needed to make
a 10 ohm resistor, if the diameter is 0.5 mm?
Answer




Work out the radius in metres: r = 0.25 × 10-3
m
Now work out the area: A = πr2 = π × (0.25 ×
10-3)2 = π × 6.25 × 10-8 m2 = 1.96 × 10-7 m2
Now work out R: R = ρL/A . 10 = (47 × 10-8
Wm × L ) / 1.96 × 10-7 m2
L = 10 × 1.96 × 10-7 m2 ¸ 47 × 10-8 = 4.17 m
Superconductivity

-
-
-
Normally materials have some resistance.
When current flows through them they heat up.
But superconductors can be cooled below a
transition temperature below which the
resistivity disappears.
This means no energy is lost as heat energy.
For metals the transition temp is about 10 K
(-263 °C)
Uses of superconductors...

Power cables that can transmit electricity with
no loss of energy.

Really strong electromagnets that don’t need a
constant power source (e.g. Maglev trains).

Electronic circuits that work really fast.