Question

In all metallic conductors, electric conduction is due to drifting of free electrons. But the resistivity of different metals are different.

1. Write the expression for resistivity of a conductor in terms of its dimensions.

2. Name the factors on which resistivity of a metal depends.

3. Arrive at an expression for electrical resistivity of a metal in terms of relaxation time.

4. Using the above expression explain the variation of resistivity with temperature.

Answer 1

1. ρ = \(\frac{RA}{l}\)

2. Temperature and Nature of metal 

3. We know current density

J = nv_de

But V_d = \(\frac{eE}{m}\tau\)

∴ \(\bar J=n.\frac{e\overrightarrow E}{m}\tau e\)

\(\bar J=\frac{ne^2}{m}\tau \overrightarrow E\)

\(\bar{J}=\sigma\overrightarrow E\)      where \(\sigma = \frac{ne^2}{m}\tau\)

But ρ = \(\frac{1}{\sigma}=\frac{m}{ne^2\tau}\)

4. When temperature increases, the amplitude of oscillation of atom increases. This will decrease . the relaxation time and hence resistivity increases.