Q.A wire of resistance $10\ \Omega$, length $2\ \text{m}$ and uniform cross-sectional area $0.5\ \text{mm}^2$ is given. Calculate the resistivity of the material of the wire.

Ohm's Law, Resistance and Resistivity

Ohm's law states that, at constant temperature, the current through a conductor is proportional to the potential difference across it, $V = IR$; the $V–I$ graph is a straight line whose slope is the resistance $R$.

The resistance of a uniform conductor depends on its material and geometry:

where $\rho$ is the resistivity (and $\sigma = 1/\rho$ the conductivity), $L$ the length and $A$ the area of cross‑section. Resistivity is an intrinsic property of the material and is independent of the sample's dimensions; only $R$ changes when a wire is reshaped.

When a wire is stretched or drawn, its volume $V = AL$ stays constant, so $A = V/L$ and

$R = \rho\frac{L^2}{V}\ \Rightarrow\ R \propto L^{2}\ \ (\text{or } R\propto 1/A^{2}).$ …