A wire of resistance R has a circular cross-sectional area.
A second wire has the same length and is made of the same material. The diameter of the second wire is double the diameter of the first wire.
Which of the following is the resistance of the second wire?
Fuse wire is made of a metal that has a low melting point. The wire melts when the current exceeds a maximum value.
A student investigated how the cross‑sectional area affected the current at which a wire melted. She used wires of the same length and metal, but different diameters.
The student steadily increased the current through each wire and recorded the maximum current through the wire before it melted.
Describe how the student could determine an accurate value for the cross‑sectional area of a wire.
Explain why a current in a wire causes the resistance of the wire to change.
The length of a wire does not affect the value of current at which the wire melts.
Explain why. Assume the wire behaves as a black body.
Electrical power is transmitted from Norway to Britain using a cable laid under the North Sea.
The following information is published on a website.
Deduce, by calculation, whether the claim for efficiency is correct.
An electrical conductor XY carries a current I as shown.
The current density j is defined as j = 
where A is the cross‑sectional area of the conductor.
Current density is a vector quantity.
State what is meant by a vector quantity.
I is constant but A decreases towards end Y.
Explain how this affects the drift velocity of the free electrons in the conductor.
The resistivity ρ of the conducting material is given by ρ = 
where E is the electric field strength.
Show that the units are the same on both sides of this equation.
A potential divider circuit may contain a component known as a potentiometer. One type of potentiometer consists of a track with terminals X and Y at either end. There is a sliding contact that can move along the track connected to a terminal Z as shown.
The length of the track is 115 mm and the width is 5.0 mm.
The resistance of the track between terminal X and terminal Y is 12.0 kΩ.
Calculate the thickness t of the track.
resistivity of track material = 0.49 Ω m
The potentiometer is used to monitor the displacement of a moving tool on a machine in a production line. The tool is attached to the sliding contact. The potentiometer is connected to a resistor of resistance R and a potential difference is applied as shown. The tool moves through a maximum displacement of 60 mm from end X, producing a maximum potential difference of 5.0 V between Z and X.
Show that the potential difference between X and Y is about 10 V.
Calculate the value of R.
When the circuit is assembled, using the correctly calculated resistance value and a battery of e.m.f. 12 V, it is found that the maximum output from the potentiometer is slightly less than 5.0 V.
Explain why the maximum output is slightly less than predicted.
The tool on the machine should not travel with a speed any larger than 0.8 m s−1.
The graph shows how the displacement varies with time for the downward stroke of the moving tool.
Deduce whether this speed is exceeded by the moving tool.
A student carried out an experiment to calibrate a thermistor. She connected the thermistor in series with a resistor and a power supply as shown. Then she placed the thermistor in a beaker of hot water and used a thermometer to record the temperature θ of the water.
The student recorded θ and corresponding values of the reading V on the voltmeter as the water cooled.
Explain, making reference to charge carriers, why V increased as the water cooled.
Over a limited temperature range V varies with θ according to the expression
where b and V0 are constants.
Explain why a graph of lnV against θ would give a straight line.
The student’s data is shown in the table below.
Plot a graph of lnV against θ on the grid opposite. Use the column provided to show any processed data.
Determine values for b and V0.
The diagram shows two parallel metal plates with a potential difference (p.d.) of 100 V across them. Three equipotential lines are shown.
Draw lines to represent the electric field in the shaded area.
A parallel plate capacitor consists of a thin layer of insulator of thickness d between two plates of conducting material of area A.
The capacitor has a capacitance 0.1 μF and is charged to a p.d. of 100 V by connecting it to an electrical supply.
The capacitor is then disconnected from the supply and the p.d. between the two plates slowly decreases. This is because the insulator is not perfect and a small charge can flow through it.
The graph shows how the p.d. varies with time.
The insulator is a type of plastic and should have a resistivity greater than 1014Ω m.
Deduce whether the plastic used in this capacitor has a resistivity greater than this value.
A = 5.6 
10−3m2
d = 0.6 
10−6m
Show that the shunt would need to have a resistance of about 0.01 Ω to adapt this ammeter to read up to a maximum current of 2.0 A.
A shunt of this resistance was usually made from Manganin wire.
Calculate the length of Manganin wire of radius 0.95 mm required to make this shunt.
Analogue ammeters were used before digital meters became widely available. The analogue ammeter shown will measure a maximum current of 1.0 mA and has a resistance of 18 Ω.
(Source: © David J. Green/Alamy Stock Photo)
The analogue ammeter can be adapted to measure a larger current by adding a resistor, known as a shunt, in parallel with the ammeter. The arrangement is shown below. The analogue ammeter is represented by the 18 Ω resistor.
The maximum current through the 18 Ω resistor remains as 1.0 mA.
Show that the shunt would need to have a resistance of about 0.01 Ω to adapt this ammeter to read up to a maximum current of 2.0 A.
A shunt of this resistance was usually made from Manganin wire.
Calculate the length of Manganin wire of radius 0.95 mm required to make this shunt.
The photograph shows a statue of Buddha in Sri Lanka, which is protected by a lightning conductor.
During a storm, a potential difference of 2.7 MV was generated between a cloud and the top of the lightning conductor on the statue. A flash of lightning passed between the cloud and the lightning conductor, producing a current of 25 kA for a time of 7.5 ms.
Calculate the energy transferred by the lightning strike.
The lightning conductor is a length of copper wire with a diameter of 1.2 × 10–2m and a resistance of 4.3 × 10−3 Ω. It runs along the back of the statue from the base to a height of 1.5 m above the top of the statue.
A guidebook claims that the statue is over 30 m high.
Assess the validity of this claim.
resistivity of copper = 1.7 
10−8 Ω m
Give a reason why the lightning conductor should be taller than the statue.
The photograph shows a statue of Buddha in Sri Lanka, which is protected by a lightning conductor.
During a storm, a potential difference of 2.7 MV was generated between a cloud and the top of the lightning conductor on the statue. A flash of lightning passed between the cloud and the lightning conductor, producing a current of 25 kA for a time of 7.5 ms.
Calculate the energy transferred by the lightning strike.
The lightning conductor is a length of copper wire with a diameter of 1.2 × 10–2m and a resistance of 4.3 × 10−3 Ω. It runs along the back of the statue from the base to a height of 1.5 m above the top of the statue.
A guidebook claims that the statue is over 30 m high.
Assess the validity of this claim.
resistivity of copper = 1.7 10−8 Ω m
Give a reason why the lightning conductor should be taller than the statue.
Also involves Transformers
A “metre bridge” is a circuit which can be used to measure an unknown resistance accurately. The metre bridge includes a metre length of nichrome wire.
Calculate the resistance of a 1.00 m length of the nichrome wire.
resistivity of nichrome = 1.12
10–6
diameter of wire = 4.00
10–4 m
This metre length of wire, labelled AB, is connected to a 1.50 V cell of negligible internal resistance and a switch as shown.
Explain how the potential along this wire varies with distance from A when the switch is closed.
Show that the potential difference between A and a point 75.0 cm along the wire from A is about 1.1 V.
Some liquids conduct electricity. This property can be used to pump these liquids through pipes.
A short section of a rectangular pipe containing a liquid is shown in the diagram. The pipe is placed in a magnetic field of flux density B and a current I is passed through the liquid as shown.
Add an arrow to the diagram above to show the direction in which the liquid will move.
A practical demonstration of this principle used two rectangular electrodes, opposite each other on either side of the pipe, a distance of 0.60 mm apart. The dimensions of the electrodes are shown in the diagram.
The electrodes were connected to a 1.5 V cell. Salt water was pumped using a magnetic field of magnetic flux density 0.40 T.
Show that the current through the salt water is about 20 mA.
resistivity of salt water = 1.6 Ω m
Hence calculate the force on the salt water.
A student carried out an experiment to determine the resistivity of nichrome wire.
He used an ohmmeter to measure the resistance of a length of nichrome wire as shown.
The diameter of the wire was measured as 0.27 mm ± 0.01 mm. The length of the wire was measured as 1.25 m ± 0.05 m.
Determine which of the three measurements introduces the greatest uncertainty into the value for the resistivity. Your answer should include calculations.
Explain how the student could reduce the uncertainty in the measurement of the diameter.
Calculate the minimum value of resistivity possible from the student’s data.
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