Question

Resistance of a conductor increases with:
A) Increase in length.
B) Increase in temperature.
C) Decrease in cross sectional area.
D) All of these.

Answer 1

Hint: Resistance is defined as the hurdles in the flow of the current. The resistance stops the flow of current due to which the flow of current is decreased. The rheostat is a variable resistance which is used to vary the resistance according to required current.

Formula used:
The formula of the resistance is given by,
$ \Rightarrow R = {R_o}\left( {1 + \alpha \Delta T} \right)$
Where $\alpha $ is coefficient of thermal expansion and change in temperature is $\Delta T$.
The formula of the resistance is also given by,
$ \Rightarrow R = \rho \dfrac{l}{A}$
Where l is length, the resistivity is $\rho $ an area of the cross section is A.

Complete solution:
In this problem it is asked that resistance of a conductor is dependent on which of the factors. We need to find the correct answer for this problem.
The formula of the resistance is given by,
$ \Rightarrow R = {R_o}\left( {1 + \alpha \Delta T} \right)$
Where $\alpha $ is coefficient of thermal expansion and change in temperature is $\Delta T$.
So the resistance depends upon the change in the temperature.
Also the formula of the resistance is also given by,
$ \Rightarrow R = \rho \dfrac{l}{A}$
Where l is length, the resistivity is $\rho $ an area of the cross section is A.
The resistivity is the resistance of a conductor of length 1m and area of cross section of $1{m^2}$
The resistance is directly proportional to length and the resistance is inversely proportional to the area of cross section.
The resistance depends upon the increase in temperature, increase in length and decrease in area of cross section.

The correct answer for this problem is option D.

Note: The students are advised to understand and remember the formula of the resistance when there is change in temperature and also the formula of the resistance which depends upon the resistivity, length and area of cross section.