J=a*E, where J is electric current density, E is the electric field and a is the conductivity in a specific material.
the value s=1/a is the resistivity, and indicates the capacity of the material to oppose to the pass of electric current through it.
when applied to a wire, we dont use the resistivity to mesure the opposition to the current pass, we use instead the resistance(R), and for wires it is defined as
R=s*(l/A),where l is the longitude and A is the transversal area of the wire-section where the electrons pass through
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I've read some as "Resistance per unit length" hence Ohm metre units, but revision guide says "resistance per unit length and per unit cross sectional area" which I've also read in some websites. And lastly in the edexcel specimen new spec paper 1 the first multiple choice question they defined it as "resistance of a unit cube" which to me makes no sense. Can someone please clear this up for me?
Resistivity is a way of defining the generic bulk property of a given material to resist the flow of current per unit volume of that material.
It is the ratio of electric field strength to current density of a given material. Electric field strength requires both p.d. and length, while current density requires current flowing through a surface area.
Hence to find the actual in circuit resistance of an electrically resistive material, the resistivity property is combined with length and cross sectional area.
Do a thought experiment:
Take four identical resistors made of the same material and the same dimensions. A single resistor may have a resistance of say 100 ohms. Put two in series and the combined resistance is 200 ohms - the length of the resistive material was doubled to achive this.
Put the two in parallel, the combined resistance is now 50 ohms - the cross sectional surface area was doubled to achieve this.
The last description you have for the edexcel specimen scheme is correct: Resistivity is resistance per unit volume.