(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.

 

 

Answers (1)
S safeer

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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