Resistivity

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

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

definition

• The resistivity ρ of a wire of length l, resistance R and area of cross-section A is given by

• Ρ=RA l

How do we know?

• Resistance is proportional to length

• Resistance is inversely proportional to cross-sectional area

Can you work out the units

Units

• Ωm

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

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

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

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.

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.

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

• 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.

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

P=IV, V=IR

• So P = I (IV) = I2R

• Also I= V/R

• So P = (V/R) V = V2/R

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

We can also work out energy

• By multiplying power by time• So• W = Vit• W = I2Rt• W=tV2/R

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

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

Circuit breakers

• Electromagnetic switches which are triggered when the system is overloaded

• Cables deliver 60A at 230V. So what is the power?

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