Ohm's law, I-V characteristics of ohmic and non-ohmic components, resistivity $\rho = RA/L$, and the variation of resistance with temperature for metals and semiconductors.

What this dot point is asking

Edexcel wants you to state Ohm's law and recognise when it applies, sketch and explain the current-voltage (I-V) characteristics of a metallic conductor, a filament lamp and a semiconductor diode, define and use resistivity through $R = \frac{\rho L}{A}$, and explain why the resistance of a metal rises with temperature while that of a semiconductor (and a thermistor) falls.

The answer

Ohm's law and resistance

A component that obeys Ohm's law over the range tested is ohmic and has a constant resistance, giving a straight-line I-V graph through the origin. Resistance always equals $V/I$ at any point on the graph, but only an ohmic component has a single constant value across the whole range.

I-V characteristics

The diode is strongly non-ohmic and non-symmetric: it acts almost as an open circuit in reverse bias and as a low resistance once the forward voltage exceeds the threshold. When plotting characteristics experimentally, swap the supply connections to reach negative voltages, and use a potentiometer divider so you can vary the voltage smoothly down to zero.

Resistivity

Resistivity is a property of the material itself, independent of the sample's shape, which lets you compare conductors fairly. Copper has a low resistivity (about $1.7 \times 10^{-8}$ ohm metre), which is why it is used for wiring; nichrome has a much higher resistivity and is used for heating elements.

Required practical: measuring resistivity

Measure the wire's diameter at several points with a micrometer (take the mean and halve it for the radius, then $A = \pi r^2$). Measure resistance for several lengths using an ammeter and voltmeter, plot $R$ against $L$, and use the gradient $\frac{\rho}{A}$ to find $\rho = \text{gradient} \times A$. Keep the current low so the wire does not heat up and change its resistance.

Temperature dependence

In a pure metal, raising the temperature makes the lattice ions vibrate with greater amplitude, so conduction electrons collide with them more frequently; the resistance rises roughly linearly over normal ranges. In an intrinsic semiconductor, raising the temperature liberates many more charge carriers (electrons and holes), and this huge increase in carrier number outweighs the increased scattering, so the resistance falls sharply. This is why a thermistor is used as a temperature sensor.

Examples in context

National Grid transmission cables use thick aluminium or copper to keep $\rho L / A$ and hence resistive heating losses low. A toaster element is made of high-resistivity nichrome so a short, robust wire reaches red heat. A platinum resistance thermometer exploits the near-linear rise of metallic resistance with temperature for precise measurement, while an NTC thermistor exploits the opposite semiconductor behaviour to sense overheating in electronics and engines.

Try this

Q1. State Ohm's law. [1 mark]

• Cue. At constant temperature, the current through a metallic conductor is directly proportional to the potential difference across it.

Q2. A wire of resistivity $5.0 \times 10^{-7}$ ohm metre, length $2.0$ m and area $1.0 \times 10^{-6}$ m squared. Find its resistance. [2 marks]

• Cue. $R = \frac{\rho L}{A} = \frac{5.0 \times 10^{-7} \times 2.0}{1.0 \times 10^{-6}} = 1.0$ ohm.

Q3. Explain why the resistance of a metal increases with temperature. [2 marks]

• Cue. The lattice ions vibrate more, scattering conduction electrons more frequently, so the resistance rises.