NCERT · Class 10 · Science · ElectricityState Ohm's Law. Define electric resistance and resistivity. Explain the factors on which the resistance of a conductor depends, along with their mathematical expressions and SI units.

Statement of Ohm's Law\nOhm's Law states that the electric current ($I$) flowing through a metallic wire is directly proportional to the potential difference ($V$) applied across its ends, provided that the physical conditions such as temperature remain constant.

$$\mathbf{V \propto I} \quad \text{or} \quad \mathbf{V = IR}$$\nWhere $R$ is a constant called resistance.

Electric Resistance\nResistance is the property of a conductor to resist the flow of charges through it. Its SI unit is Ohm ($\Omega$). According to Ohm's law, $R = \frac{V}{I}$.

Factors Affecting Resistance\nThe resistance $R$ of a uniform metallic conductor depends on the following factors:

1. Length ($l$): The resistance of a conductor is directly proportional to its length ($l$). Longer wires have higher resistance. $$R \propto l$$
2. Area of Cross-section ($A$): The resistance is inversely proportional to the cross-sectional area of the conductor. Thicker wires offer less resistance. $$R \propto \frac{1}{A}$|
3. Nature of Material: Different materials have different free electron densities, leading to different resistance values.
4. Temperature: For metallic conductors, resistance increases with an increase in temperature.

Combining Factors\nCombining the above factors:

$$R \propto \frac{l}{A} \quad \text{or} \quad R = \rho \frac{l}{A}$$\nWhere $\rho$ (rho) is a constant of proportionality known as electrical resistivity or specific resistance of the material.

Resistivity\nResistivity is defined as the resistance offered by a cube of a material of side $1 \text{ m}$ when current flows perpendicularly to opposite faces. The SI unit of resistivity is ohm-meter ($\Omega \cdot \text{m}$). Resistivity is a characteristic property of the material and does not depend on the length or thickness of the conductor, though it depends on temperature.