Q.A carbon resistor is coloured with four different bands — red, green, orange and silver respectively. Find the range of its probable resistance. OR E.M.F. of an electrical cell is 2 volt. A 10 Ω resistance is joined at its two ends then potential difference is measured 1.6 volt. Find out the internal resistance and lost volt.

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

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