# Physics - Resistivity

## AIM

The aim of the experiment I am conducting is to find the resistivity of a 24 watt light bulb. This will be conducted through a series of experiments which will be followed by some calculations using formulas such as:

Or

ρ is the resistivity (measured in ohm metres, Ω-m)

R is the electrical resistance of the material (measured in ohms,Ω)

is the length of the piece of material (measured in metres, m)

A is the cross-sectional area of the material (measured in square metres, m²).

There are other equations that could be used to work out electrical resistivity, such as:

E is the  of the  (measured in  per , V/m);

J is the magnitude of the  (measured in  per , A/m²).

Finally, electrical resistivity is also defined as the inverse of the  σ (), of the material, or:

Electrical conductivity or is a measure of a material's ability to conduct an electric current. This is because resistivity and conductivity are reciprocals.

I aim to use the first equation to work out resistivity by re-arranging it, like so:

So if I can measure ‘R’, being resistance, ‘A’ being cross sectional area and ‘l’ being length of a light bulb, I can use the latter equation to work out the resistivity of the light bulb.

## RESISTIVITY

The resistance of a wire depends on quite a few factors; these will affect the wires in many different ways, such as temperature increasing resistance. The length of the wire will make a difference. This is because when you have a long wire, the electrons have to ‘squeeze’ together for longer to be able to pass through the wire than they do in order to be able to pass through a short wire, the electrons have to squeeze together in order for them to avoid ‘bumping’ into the other particles in the lattice of the wire.  The thickness of the wire would also affect the resistance of wire, a thick wire of the same material, length and temperature would have less of a resistance of a thinner wire, this is because there is more room for more electrons to be able squeeze together, creating more ‘lanes’ for the electrons to be able to pass through, this increases the current, which for if the voltage was the same, would lower the resistance, we can see this using the simple formula:

Where V is voltage and I is current.

In a thin wire, there are fewer ‘lanes’ for the electrons to be able to pass through, causing a lower current and therefore a higher resistance. Another cause of an increased or decreased resistance in a wire is temperature. In general, electrical resistance of metals increases with temperature; this is caused by electron-phonon interactions. Phonons being the mode of vibration which occurs in a rigid lattice, such as the lattice of the wire. Also collision theory comes to play, where at higher temperatures the particles in the wire move around more, causing more collisions between the particles and the electrons, this will generally slow down the electrons and forcing them to squeeze together. At high temperatures, the resistance of a metal increases proportionately with temperature. This can be shown in this diagram

As the temperature of a metal is reduced, the temperature dependence of resistivity follows a complex temperature rule. Mathematically the temperature dependence of the resistivity ‘ρ’ of a metal is given by a formula called the Bloch-Gruneissen formula. The Bloch-Gruneissen equation is quite complicated and is as follows.

Different materials also affect the resistance of the wire, for example copper is a better conductor than steel, steel is a better conductor than silicon, and so on.

As we can see if I was to work out the resistance of a particular wire I would need to take into account the length, temperature, area and material of the wire. The relevant property of the material is its resistivity.

## VOLTAGE AND CURRENT

### VOLTAGE

Voltage is the ‘push’ which makes a current flow through a wire. We can distinguish between two types of voltage, one being a voltage where the charge is losing energy, such as through a resistor on the wire like a light bulb, this is called a potential difference. Voltage can also be where a charge is gaining energy, such as in transformers and generators, this is called an electromotive force. Thus the voltage across the power supply is an electromotive force or e.m.f., while the voltage across a resistor in a circuit (such as a ...