Question

The temperature dependence of resistances of Cu and undoped Si in the temperature range 300 – 400 K, is best described by.
A. Linear increase for Cu, linear increase for Si
B. Linear increase for Cu, exponential increase for Si
C. Linear increase for Cu, exponential decrease for Si
D. Linear decrease for Cu, linear decrease for Si

Answer 1

Hint: Resistance of a material depends upon the physical dimensions of the material and the intrinsic property of the given material called resistivity. The resistivity of materials can vary depending upon the condition. It varies with temperature and this variance also depends and changes from material to material. This variance depends upon the lattice structure and energy gap in the materials.
Formula used:
$$R=\rho {\displaystyle \frac{l}{A}}$$

Complete answer:
Resistance of a material depends upon the physical dimensions of the material and the intrinsic property of the given material. It is formulated as
$$R=\rho {\displaystyle \frac{l}{A}}$$
Here $$\rho$$is called resistivity and is an intrinsic property of the material. It is also known as specific electrical resistance, or volume resistivity. It shows how good an electrical current can flow in a material and does not depend on the physical dimensions of the material.
The resistivity of materials can vary depending upon the condition. It varies with temperature and this variance also depends and changes from material to material.
In conductors there are free and loosely bound electrons present for conduction, when temperature increases the atoms of the conductor start vibrating rapidly and the collision between atoms and electron increases. This in turn increases the resistivity of the conductor. This increase is linear in nature.
For semiconductors there is a forbidden energy gap between valence band and conduction band is present. As temperature increases more and electrons gain energy to jump to the conduction band and thus conduction increases and resistivity exponentially decreases.

So, the correct answer is “Option C”.

Note:
The resistivity of a material is taken to be constant for the most parts. But many times we come across questions where there is a change in temperature and the resistivity changes. The relation between temperature and resistivity is given as $${\rho }_t={\rho }_0[1+\alpha (T{T}_0)]$$, where quantities with subscript o are the points of reference, that is resistivity at that temperature.