Question

Define resistivity of a conductor. Discuss its dependence on temperature of the conductor and draw a plot of resistivity of copper as a function of temperature.

Hint:

Resistivity increases with temperature in most metals, which is why heating a conductor increases its resistance.

Answer 1

Definition of Resistivity: Resistivity \( \rho \) of a material is a property that quantifies how strongly the material resists the flow of electric current. It is defined as: \[ \rho = R \frac{A}{L} \] Where:
\( R \) is the resistance of the conductor,
\( A \) is the cross-sectional area,
\( L \) is the length of the conductor. 

Dependence of Resistivity on Temperature: The resistivity of most conductors increases with an increase in temperature. This is because the atoms in the conductor vibrate more at higher temperatures, impeding the flow of electrons. The temperature dependence of resistivity is given by: \[ \rho(T) = \rho_0 [1 + \alpha(T - T_0)] \] Where: - \( \rho(T) \) is the resistivity at temperature \( T \), - \( \rho_0 \) is the resistivity at a reference temperature \( T_0 \), - \( \alpha \) is the temperature coefficient of resistivity. 

Plot of Resistivity of Copper: The plot of resistivity of copper with respect to temperature shows a linear increase with temperature in the range commonly encountered.