Quick questions on Resistance and resistivity: Ohm's law and I-V characteristics - Edexcel A-Level Physics

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.

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.

State Ohm's law. [1 mark]

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]

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