Explanation:

The specific resistance of a conductor, also known as resistivity, is the measure of its ability to resist the flow of electric current. It is denoted by the Greek letter rho (ρ) and is measured in ohm-meters (Ωm). The specific resistance of a material is an intrinsic property and depends on various factors such as temperature, composition, impurities, and crystal structure.

Effect of Temperature on Specific Resistance

When the temperature of a conductor increases, the specific resistance also increases. This is because when the temperature increases, the atoms in the conductor vibrate more vigorously, which makes it harder for the electrons to move through the lattice. This increase in resistance is a non-linear relationship and is governed by the following equation:

ρt = ρ0 [1 + α (t - t0)]

Where ρt is the specific resistance at temperature t, ρ0 is the specific resistance at reference temperature t0, and α is the temperature coefficient of resistivity.

Effect of Cross-sectional Area on Specific Resistance

The specific resistance of a conductor is inversely proportional to its cross-sectional area. This means that as the cross-sectional area of a conductor increases, its resistance decreases. This can be explained by the fact that a larger cross-sectional area provides more space for the electrons to move through, thereby reducing the resistance.

Effect of Length on Specific Resistance

The specific resistance of a conductor is directly proportional to its length. This means that as the length of a conductor increases, its resistance also increases. This can be explained by the fact that a longer conductor provides more obstacles for the electrons to move through, thereby increasing the resistance.

Effect of Cross-sectional Shape on Specific Resistance

The specific resistance of a conductor also depends on its cross-sectional shape. For example, a wire with a circular cross-section will have a lower resistance than a wire with a rectangular cross-section of the same area. This is because a circular cross-section provides a more uniform distribution of current, while a rectangular cross-section concentrates the current at the corners, increasing the resistance.

Conclusion:

In conclusion, the specific resistance of a conductor increases with an increase in temperature. The other factors that affect the specific resistance are the cross-sectional area, length, and cross-sectional shape of the conductor.