1. Resistivity Electricity Lesson 5

2. Learning Objectives To define resistivity. To know what causes resistance. To know how to measure resistance.

3. Practice Conversion If a wire has a cross sectional area of 1.23 square millimetres What is its area in square metres.

4. 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.

5. 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.

6. Resistivity Rearranging gives an equation for resistivity:- The unit of resistivity is the ohm metre (Ωm) In words:-

7. 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!

8. Cross Sectional Area For a circular conductor with a radius r, diameter d, the cross sectional area is given by:-

9. 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?

10. Answer Work out the radius in metres: r = 0.25 × 10 -3 m Now work out the area: A = πr 2 = π × (0.25 × 10 -3 ) 2 = π × 6.25 × 10 -8 m 2 = 1.96 × 10 -7 m 2 Now work out R: R = ρL/A. 10 = (47 × 10 -8 Wm × L ) / 1.96 × 10 -7 m 2 L = 10 × 1.96 × 10 -7 m 2 ¸ 47 × 10 -8 = 4.17 m

11. 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)

12. 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.