Question

Draw a graph of resistivity of a conductor with temperature.

Answer 1

Hint: Resistivity of a material is the property of a material to oppose the flow of charges when a potential difference is created across it. It is given as $\rho =\dfrac{m}{n{{e}^{2}}\tau }$ and $\tau $ decreases with temperature. Hence, you can relate resistivity and temperature.

Formula used:
$\rho =\dfrac{m}{n{{e}^{2}}\tau }$

Complete step by step answer:
We know that when a charge is placed in between a potential difference, the charge accelerates. A potential difference produced an electric field. The electric field exerts a force on the charge and therefore the charge accelerates.
Every material consists of electrons. An electron has a charge of –e. Therefore, when a potential difference is created by attaching a cell across a piece of a given material, the electrons are accelerated under the influence of the electric field. Hence, there is a flow of charge in the circuit.
However, the charges (electrons) do not flow easily. They do not accelerate and a flow with a constant velocity called drift velocity. This is due to many factors such as the collisions between the electrons and some properties of the material.
Therefore, we say that the material opposes the flow of the charges. This property of the material is called the resistivity of the material. Also called specific resistance. The value of resistivity of a material given as $\rho =\dfrac{m}{n{{e}^{2}}\tau }$ … (i)
Here, m is the mass of an electron, n is the number of electrons per unit volume and $\tau $ is the relaxation time.
In a given material, at a given temperature, electrons possess some thermal and they continuously collide with each other. The time interval between two consecutive collisions is called relaxation time.
When the temperature is increased, the thermal energy of the electrons also increases. Hence, the frequency of collisions also increases which decreases the relaxation time. If we follow equation (i), we see that resistivity is inversely proportional to the relaxation time. Hence, if the relaxation time decreases, the resistivity of the material increases.
The graph of resistivity of a material versus temperature is shown below.

Note:
Do not confuse between resistance and specific resistance.
Specific resistance is equal to the resistivity of the material.
Resistance also opposes the flow of charges and is given as $R=\dfrac{\rho l}{A}$, where l and A are the length of the material across which the potential difference is created and cross sectional area respectively.
Hence, resistance of a material depends on the dimensions of the material whereas resistivity is independent of the dimensions of the material.