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.