CBSE 2025 · Region 2 · Set 3 · Q22 · 3 marks
(a)Define Electrical conductivity. Obtain the expression of electrical conductivity of a conductor in terms of number density and relaxation time of free electrons.(b)Explain qualitative change in resistivity of a conductor with temperature using expression obtained in (a) .
(a)
Define Electrical conductivity. Obtain the expression of electrical conductivity of a conductor in terms of number density and relaxation time of free electrons.
(b)
Explain qualitative change in resistivity of a conductor with temperature using expression obtained in (a) .
Marking-scheme solution
(a)
Electrical conductivity: It is the reciprocal of the resistivity.
$\displaystyle \sigma=1 / \rho$
$\displaystyle I t=n e A v_{d} t$
Substituting $\displaystyle v_{d}=\frac{e E}{m} \tau$:
$\displaystyle I t=\frac{e^{2} A}{m} \tau n t E$
$\displaystyle I=j A$
$\displaystyle \Rightarrow j=\frac{n e^{2}}{m} \tau E$ .........($\displaystyle 1$)
$\displaystyle j=\sigma E$ .......................($\displaystyle 2$)
Comparing eq. ($\displaystyle 1$) & ($\displaystyle 2$):
$\displaystyle \sigma=\frac{n e^{2}}{m} \tau$
(b)
On increasing the temperature, the value of $\displaystyle \tau$ decreases, as a consequence conductivity decreases and hence resistivity increases.
Current ElectricityDrift of Electrons and the Origin of ResistivityApplyshort_answermedium
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