Question

The resistance of a conductor increases for a given material at constant temperature when:
A. Its thickness increases
B. Its length increases
C. Its length decreases and thickness increases
D. Its length increases and thickness decreases

Answer 1

Hint: The resistance is defined as the opposition offered to the flow of current in a conductor. Resistance is mainly directly proportional to the length of the conductor and inversely proportional to the cross-section area or thickness of the conductor. Here, we will use the formula of resistance which is given below.

Formula used:
The formula of resistance of the conductor is given by
$$R = \rho \dfrac{L}{A}$$
Here, $R$ is the resistance, $\rho $ is the specific resistance, also known as resistivity, $L$ is the length of the conductor and $A$ is the area of cross-section or thickness of the conductor.

Complete step by step answer:
We can say that the resistance is the hindrance offered to the flow of current in a conductor.
We know that every conductor has a resistance, that is why the conductor gives out heat when current passes through them. The formula of resistance of the conductor is given by
$R = \rho \dfrac{L}{A}$
Therefore, we can say that the resistance of a conductor depends upon the following terms:
-The area of cross-section of the conductor.
-The length of the conductor.
-The resistivity of the conductor.

As we can see that the resistance of a conductor will be directly proportional to the length of the conductor and inversely proportional to the area of cross-section. Therefore, the resistance of the conductor increases with increase in length of the conductor and decrease in thickness or area of cross section of the conductor.

Hence, option D is the correct.

Note:Here, the resistance of the conductor also depends on the temperature and the material of a conductor. This is because the resistivity depends on the temperature and material of the conductor and resistance depends on the resistivity of the conductor.