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Q.

The conductivity of a semiconductor increases with temperature because

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a

Number density of free current charge carriers increases.

b

Relaxation time increases.

c

Both number density of carriers and  relaxation time increases  but effect of increase in relaxation time  is much less than increase in number density.

d

Number density of carriers increases, relaxation time decreases  but effect of decrease in relaxation time  is much less than increase in number density.

answer is D.

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Detailed Solution

i = eA (n1V1+n2 V2) with increase in temperature the both V1 and V2 the drift velocities for both the charge carriers  decreases and relaxation time decreases due to frequent collision but generation of free charge carriers increases more due to increase in temperature.
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The conductivity of a semiconductor increases with temperature because