Q.A carbon resistor is coloured with four different rings having colours brown, orange, green and silver respectively. Find the range of its probable resistance. OR What is the value of shunt connected parallel to a galvanometer having resistance G, such that current flowing through the shunt will be 1/n times of total current?

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

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