If we have data on the variation of current with the length of a wire, we can use Ohm's law to determine the resistance of the wire at different lengths. Ohm's law states that the current through a wire is proportional to the voltage across it, and that the proportionality constant is the resistance of the wire. Mathematically, Ohm's law can be expressed as:
V = IR
where V is the voltage across the wire, I is the current flowing through the wire, and R is the resistance of the wire.
If we rearrange this equation to solve for resistance, we get:
R = V/I
where R is the resistance of the wire, V is the voltage across the wire, and I is the current flowing through the wire.
If we have data on the variation of current with the length of the wire, we can measure the voltage across the wire at different lengths and use Ohm's law to determine the resistance of the wire at each length. Once we have this data, we can plot a graph of resistance versus length of the wire. The slope of this graph will give us the resistivity of the wire.
The resistivity of a material is defined as its resistance per unit length and per unit cross-sectional area. Mathematically, resistivity can be expressed as:
ρ = RA/L
where ρ is the resistivity of the material, R is the resistance of the wire, A is the cross-sectional area of the wire, and L is the length of the wire.
If we know the cross-sectional area of the wire, we can use the slope of the graph of resistance versus length to determine the resistivity of the wire. The resistivity of the wire can then be compared with the resistivity of known materials to identify the material of the wire.