Download - Resistivity
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 cross-sectional area, A, its resistance R is proportional to L but inversely proportional to A.
So the resistance is given by:-
Where ρ is the resistivity of the conductor.A
LR
Resistivity
Rearranging gives an equation for resistivity:-
The unit of resistivity is the ohm metre (Ωm)
In words:-
L
RA
(metre)length
(ohms) resistance)(metre areametres) (ohmy Resistivit
2
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:-
42
222 ddrA
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.