# (a) Obtain the expression for the current flowing through a conductor having number density of electrons n, area of cross-section A in terms of the drift velecity $v_{d}$.(b) How does the resistivity of a semiconductor change with rise of temperature? Explain.

Let n be the number density of free electrons.

Let l be the length  of the conductor

Let A be the area of cross-section

Total charge in the conductor

Q = (nAl)e

The current flowing across the conductor is given by,

$I= \frac{Q}{t}= \frac{(nAl)e}{\frac{l}{v_{d}}}= nAev_{d}$

$\therefore I= nAev_{d}$

(b)

The resistivity of a semiconductor decreases with increasing temperature.

The resistivity of a material is given by

$\rho = \frac{m}{ne^{2}\tau }$

$\rho$ inversely depends on both numbers of free electrons per unit volume and on the relaxation time. The relaxation decreases with rising in temperature.

In the case of semiconductor, n increases with temperature. This increase is more than the decreases in $\tau$.

So, resistivity $\rho$ decreases with increase in temperature for a semiconductor.

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