Question no. 26( b)and 26 (c)

Q26. (b) How does resistivity of a semi-conductor change with the increase in temperature ?

         (c) How does (i) resistance (ii) resistivity of a wire depend on its length and radius ?

 

Dear Student,

Solution:
26(b) A semiconductor is a mixture of a conductor and an insulator.
 In a semiconductor, the conduction band and the valence are moderately separated whereas they are largely separated or energy gap is as large as possible in insulators and less or negligible energy gap in conductors. In case of semiconductors as the temperature increases the electrons in the valence band get excited and jump into the conduction band and hence the conductance increases resulting in the lowering of resistance. As resistance is directly proportional to resistivity, resistivity decreases, too.

26(c)-
Resistivity is a property of the material and is independent of the dimensions. It depends just on temperature.
Resistance is directly proportional to the length of wire and inversely proportional to the square of radius of wire.
$$\begin{gathered} in general- \\ R=\rho \frac{l}{A} \\ where \text{'}R\text{'} is resis\tan ce of wire, \text{'}l\text{'} is its length, \text{'}\rho \text{'} is the resistivity of wire and \text{'}A\text{'} is the area \\ \Rightarrow R= \rho \frac{l}{{\mathrm{\pi r}}^2} \\ \mathrm{where} \text{'}\mathrm{r}\text{'} \mathrm{is} \mathrm{the} \mathrm{radius} \mathrm{of} \mathrm{cross} \mathrm{section} \mathrm{of} \mathrm{wire}. \end{gathered}$$

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