Section 1 of 9Why a wire has resistance
Collisions
- Collisions electrons collide with the metal ions in the wire, which transfers energy from their kinetic store to the vibrating ions.
Heating
- Heating the ions vibrate more, so the temperature of the wire rises.
More vibration
- More vibration greater vibration of the ions means more collisions with the electrons, which means more resistance.
Section 2 of 9Factors affecting resistance
Length
- Length a longer wire gives each electron more collisions, so the resistance is greater.
Cross-sectional area
- Cross-sectional area a thicker wire gives more space for electrons to flow, so the resistance is smaller.
Material
- Material different metals have different numbers of free electrons, so copper conducts better than nichrome or steel.
- Heating elements use nichrome (high resistance) and cables use copper (low resistance).
Temperature
- Temperature for a metal, the resistance increases as the temperature rises.
Section 3 of 9Proportionality (Extended)
Length
- R is directly proportional to length (R ∝ L), so doubling the length doubles R.
Area
- R is inversely proportional to area (R ∝ 1/A), so doubling the area halves R.
- For a round wire A = πd2/4, so doubling the diameter divides R by four.
Combined
- R ∝ L / A, giving R2 / R1 = (L2 / L1) × (A1 / A2).
Graphs
- R against L is a straight line through the origin, and R against 1/A is also a straight line through the origin.
Section 4 of 9Experiment: resistance and length
1
Tape a length of resistance wire (such as constantan) to a metre rule.
2
Connect a cell, a switch and an ammeter in series with the wire, using a crocodile clip at the 0 cm mark and a sliding clip.
3
Connect a voltmeter in parallel with the section of wire between the clips.
4
Close the switch and record the current and p.d. for a length of 20 cm, then switch off.
5
Repeat for 40, 60, 80 and 100 cm, switching off between readings so the wire does not heat up.
6
Calculate R = V / I for each length and plot R against length.
Expected result
- Expected result a straight line through the origin.
To investigate area
- To investigate area use wires of the same material and length but different diameters, measured with a micrometer at several places.
Section 5 of 9Reducing errors
Heating
- Heating use a low current and switch off between readings, because heating raises the resistance.
Contact resistance
- Contact resistance poor contact at the clips gives a line that misses the origin.
Zero errors
- Zero errors check the meters read zero before starting.
Random errors
- Random errors repeat readings and draw a line of best fit.
Section 6 of 9Applications
Power lines
- Power lines made thick and from low-resistance aluminium or copper so little energy is wasted as heat.
Filament lamps
- Filament lamps use a very thin, long coiled wire so the resistance is high and the filament glows.
Fuse
- Fuse a thin wire that overheats and melts when the current is too large.
Section 7 of 9More from the specification
More from the specification
Electrostatic Charging by Friction
- Friction between insulating materials causes the transfer of mobile negative electrons;
- rubbing a polythene rod with a cloth transfers electrons onto the rod, leaving it negatively charged while the cloth acquires an equal positive charge.
Gold-Leaf Electroscope Operation
- A gold-leaf electroscope detects the presence of net electrical charge;
- bringing a charged rod near the brass cap induces charges,
- causing like charges to accumulate on the stem and gold leaf,
- which repel each other and deflect the leaf.
Resistance in an Electrical Circuit
- In an electrical circuit, the resistance of a conducting wire opposes the flow of electric charge (current);
- according to Ohm's law, resistance equals potential difference divided by current (R = V/I) and increases linearly with wire length.
Electrostatic Charging by Friction
- Friction between insulating materials causes the transfer of mobile negative electrons;
- rubbing a polythene rod with a cloth transfers electrons onto the rod, leaving it negatively charged while the cloth acquires an equal positive charge.
Gold-Leaf Electroscope Operation
- A gold-leaf electroscope detects the presence of net electrical charge;
- bringing a charged rod near the brass cap induces charges,
- causing like charges to accumulate on the stem and gold leaf,
- which repel each other and deflect the leaf.
Resistance in an Electrical Circuit
- In an electrical circuit, the resistance of a conducting wire opposes the flow of electric charge (current);
- according to Ohm's law, resistance equals potential difference divided by current (R = V/I) and increases linearly with wire length.
Electromotive force
- Energy transferred from other forms to electrical energy per unit charge.
Gold-leaf electroscope
- A device in which a charged gold leaf falls when photoelectrons discharge the plate.
Mains supply
- Domestic a.c. supply, rated 230 V rms at 50 Hz in the UK.
Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Electroscope
- Instrument with a metal cap, stem and gold leaf used to detect charge.
Terminal
- Connection point of a cell, labelled + or −.
Insulator
- Material that does not allow current to flow.
Component
- Part of a vector along one axis.
Potential difference
- Work done by a unit charge passing through a component.
Electric field
- Region of space in which a charge experiences a force.
Alternating current
- Current that continually reverses direction.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Resistance | Opposition to current, R = V / I. |
| Length | Resistance is directly proportional to the length of a wire. |
| Cross-sectional area | Resistance is inversely proportional to the area of a wire. |
| Resistance wire | Wire such as constantan with a high, steady resistance. |
| Micrometer | Instrument used to measure the diameter of a thin wire. |
Section 9 of 9Exam technique
1
Saying resistance is proportional to diameter — it depends on area, so on diameter squared.
2
Leaving the current on between readings — the wire heats up and the results are not repeatable.
3
Mixing up direct and inverse proportion — R increases with length but decreases with area.
4
Forgetting that a different material has a different resistance even with the same dimensions.