Problem Sheet Resistivity and Resistance 1

See if you can work out these questions on resistivity. Hint, they all use the formula =RA/l in some form or another. You will receive 3 marks for each question. These relate to your working, units and the correct answer!

( = resistivity in m, R = resistance in , A = area in m2, l = length in m; 1 cm = 0.01m, 1cm2=1x10-4m2, A = r2)

1.  A section of copper power cable for the Eurostar train is 800 metres long. It has a radius of 10 cm. We know that  = 1.7x10-8 m for copper. What is the resistance of this section?

2.  A Hi-Fi Buff buys herself a new Arcam 8 Amplifier. She sees some new banana connectors which, the salesman says will improve the sound quality. She wants to check this but unfortunately she failed her GCSE physics exam and cannot work out the resistance. However, she knows that the radius of the connector is 0.25 cm, the length is 2 cm and the resistivity of gold is 2.4 x 10-8 m. Can you work out the resistance?

3.  It is winter and an owner of a BMW M3 has fallen on hard times. Instead of taking her car to the BMW garage she decides to service it herself. Her car needs a new resistor for the heater system. She decides to make her own but does not know which wire to make it out of. She measures the old piece of wire; it is 8 cm long, has a radius of 0.2cm. She uses an ohm meter and measures the resistance as 1.08x10-4. What type of wire should she use?

4.  A computer nerd has decided to upgrade his Celeron CPU to the new Pentium 4 Chip. He looks up all the technical features on Intel's website. However, typically they have missed off how long the chip is! He measures the space of the Celeron CPU in the socket on his motherboard. It is 2 cm long. Amazed he sees that the P4 chip is made out of pure germanium! He has the other technical data and can therefore work out the length of the chip.  = 0.6m, R = 7200 , A = 0.05 cm2. Will he have to splash out on a new motherboard?


Problem Sheet Resistivity and Resistance 2

See if you can work out these questions on resistivity. Hint, they all use the formula =RA/l in some form or another. You will receive 3 marks for each question. These relate to your working, units and the correct answer!

( = resistivity in m, R = resistance in , A = area in m2, l = length in m; 1 cm = 0.01m, 1cm2=1x10-4m2, A = r2)

Material / Resistivity (m)
Copper / 1·7×10-8
Graphite / 800×10-8
Resistance putty / 4·2×10-2
Silicon / 2·3×103
Pyrex / 1012
Carbon / 3 x 10-5

1.  Calculate the resistance of 25cm of copper wire which is 2mm in diameter.

2.  Find the resistance of 1 cubic centimetre of graphite.

3.  An unknown substance, 1mm cube, has a resistance of 2.2 x 106 when measured across opposite faces. Identify the substance.

4.  Calculate the length of carbon required to make a 3.9 resistor of cross sectional area 1.26 x 10-5 m2.

5.  An electrical heating element is to be made from nichrome wire. The current in the heating element is to 5.00A when the voltage across it 12.0V. Calculate the resistance of the heating element. The resistivity of nichrome is 1.10 x 10-6 m. The cross sectional area of the wire used is 7.85 x 10-7 m2. Calculate the length of wire required.