Superconductivity as a property of certain materials which have zero resistivity at and below a critical temperature which depends on the material. Applications (e.g. very strong electromagnets power cables).
Breithaupt chapter 4.3 pages 50 to 52
resistance p.d. across a component current through the component
R V / I
also V I R and I V / R
resistance in measured in ohms (O)
potential difference in volts (V)
electric current in amperes (A)
Resistance is a measure of the difficulty of making a current pass through a substance. It is caused by the repeated collisions between the charge carriers and the positive ions of the substance.
Resistance simulation at Phet Resistance equation demo at Phet
1. Calculate the resistance of a device if a current of 250mA flows when a potential difference of 6V is applied
R V / I
6V / 0.250A
2. Calculate the current that flows through a resistance of 4MO when 60V is applied across it
I V / R
60 V / 4 000 000 O
0.000 015 A 15 µA
5 Complete 6 Answers 7 Measuring resistance
Set up the circuit opposite.
Measure the current through the resistor with the ammeter.
Measure the potential difference across the resistor with the voltmeter.
Calculate resistance using R V / I .
Further sets of values of I and V can be obtained by changing the setting of the variable resistor. From these an average value for resistance can be obtained.
Note The resistance of the voltmeter should be as high as possible so that the ammeter only measures the current through the resistor.
Fendt Ohms law simulation
8 Ohms law
Ohms law states that the potential difference across an ohmic conductor is proportional to the current through it provided the physical conditions do not change.
A graph of p.d. against current for a conductor obeying ohms law will be a straight line through the origin.
The gradient of such a graph is equal to the resistance of the conductor.
Physical conditions remaining constant include temperature and the dimensions of the conductor
9 Resistivity ()
Experiments show the the resistance of a conductor is
1. proportional to its length L
2. inversely proportional to its cross-section area A
and so R a L /A
the constant of proportionality is the resistivity of the conductor
Therefore R L A
Reisistivity equation demo at Phet
KT resistivity simulation
10 Variation in resistivity
Resistivity is measured in ohm-metre Om.
Metals (e.g. copper) and other good conductors have very low resistivities.
Good insulators (e.g. PVC) have very high resistivities.
Semiconductors (e.g. silicon) have intermediate resistivities
Resistivity table on Wikipedia
Superconductivity is a state where certain materials have zero resistivity.
This occurs at and below a critical temperature (Tc) which depends on the material. Tc is usually below 200oC.
very strong electromagnets (e.g. in MRI scanners)
power cables to prevent wastage of electrical energy (e.g. to supply the LHC)
12 Questions on resistivity
1. Calculate the resistance of a 0.30m length of copper wire of cross-section area 5 x 10-6 m2 resistivity of copper 1.7 x 10-8 Om
R L A
(1.7 x 10-8 Om) x (0.30m) / (5 x 10-6 mm2)
0.00102 O 1.02 mO
2. Repeat the above question this time with silicon resistivity of silicon 2300 Om
(2300 Om) x (0.30m) / (5 x 10-6 mm2)
1.38 x 106 O 138 MO
13 3. Calculate the resistivity of a metal wire of cross-section diameter 0.4mm if a 25cm length of this wire has a resistance of 6O.
p x (4 x 10-4 m)2 / 4
p x (1.6 x 10-7 m2) / 4
cross-section area 1.2566 x 10-7 m2
(6 O) x (1.2566 x 10 -7 m2 ) / (0.25 m)
resistivity 3.02 x 10 -6 Om
14 Notes from Breithaupt pages 50 to 52
What is resistance Give the equation defining resistance and a sample resistance calculation.
Draw a circuit diagram and explain how resistance can be measured.
What is Ohms law How can Ohms law be verified graphically
Give the equation for resistivity. Calculate the resistance of a copper wire of diameter 1mm and length 3m.
Compare the resistivities of copper silicon and PVC.
What is superconductivity When does it occur Give two applications.
Try the summary questions on page 52
15 Answers to the summary questions
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