1. Resistivity

2. Learning objectives Candidates should be able to: (a) define resistivity of a material; (b) select and use the equation (c) describe how the resistivities of metals and semiconductors are affected by temperature; (d) describe how the resistance of a pure metal wire and of a negative temperature coefficient (NTC) thermistor is affected by temperature

3. Resistivity or Resistance They’re different things. Resistivity is a property of a material so copper will have a different resistivity to iron for example

4. definition The resistivity ρ of a wire of length l, resistance R and area of cross-section A is given by Ρ=RA l

5. How do we know? Resistance is proportional to length Resistance is inversely proportional to cross- sectional area

6. Can you work out the units

7. Units Ωm

8. The effect of temperature on resistivity If we heat up a metal the internal energy of the atoms also increases. This could be down to either potential energy or kinetic energy

9. Potential or kinetic When you heat up a metal it will expand (before it eventually melts) but only a comparatively small amount. Therefore the atoms have gained very little extra space so it isn’t a gain in potential energy. So it must be that heating a metal causes an increase in kinetic energy

10. Kinetic energy As we heat a metal the atoms within it start to vibrate more. Conduction electrons moving through this are more likely to bang into one of these moving atoms. This means that the increase in temperature increases the resistance. In fact the resistance is directly proportional to the temperature in Kelvin

11. How does this affect resistivity Well expansion will slightly increase both length and cross-sectional area. This means that with the minimal effect of temperature the resistivity must be also increasing (proportionally) with temperature.

12. Semiconductors - Thermistors These are made from silicon to which a small impurity of other atoms. This means that when temperature is increased it has a much greater affect on the resistance.

13. NTC These impurity atoms help with conduction The resistance actually reduces as temperature increases. It is therefore said to have a negative temperature coefficient. (This is because the increase in temperature releases more conduction electrons to transmit the electricity). An NTC can have a resistance of 9000Ω at 0⁰C and of 240 Ω at 100 ⁰C

14. Candidates should be able to: (a) describe power as the rate of energy transfer; (b) select and use power equations P = VI, P=I 2R and V 2 = P R (c) explain how a fuse works as a safety device (d) determine the correct fuse for an electrical device; (e) select and use the equation W = IVt; (f) define the kilowatt-hour (kW h) as a unit of energy; (g) calculate energy in kW h and the cost of this energy when solving problems.

15. Power We have already seen that V=IR And P=IV Provided that we are applying this to one part of a circuit we can do some combining so

16. P=IV, V=IR So P = I (IV) = I 2 R Also I= V/R So P = (V/R) V = V 2 /R

17. These are all work outable in an exam but why waste the time. LEARN THEM

18. We can also work out energy By multiplying power by time So W = Vit W = I 2 Rt W=tV 2 /R

19. Fuses Made from thin copper wire. Low resistivity Because the wire is thin it’s resistance causes the wire to melt if the current passing through it is too high This breaks the circuit if the current is too high

20. From GCSE The fuse needs to be one which is rated just over the normal maximum current used by the device. This maximum normal current is calculated by P=IV

21. Circuit breakers Electromagnetic switches which are triggered when the system is overloaded Cables deliver 60A at 230V. So what is the power?

22. The kilowatt hour If we worked out how many joules of energy was used in a home the number would be massive. A 60W bulb uses 60J every second. Instead we use a bigger value of power (the kilowatt) and time (the hour) Therefore Energy = Power x time So kilowatt x hour = the kilowatt hour