Resistivity
Learning objectives
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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 crosssectional 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
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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
V2=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
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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