Question

On what factors does the resistance of a conductor depend? Write S.I. unit of resistance.

Answer 1

Hint: We need to understand the phenomenon or the occurrence of the resistance in a conducting material to analyse the factors which can affect the resistance in the resistor. We can easily solve this problem using the Ohm’s law and other relations.

Complete answer:
Any conducting material when applied to an external voltage will provide a current with a notable amount of resistance within the material. The resistance is the property of a material which resists the flow of free electrons or ions under an external potential difference.
From the Ohm’s law, the voltage drop across a conductor is directly proportional to the current flow. The resistance is the proportionality constant in this relation given as –
\[\begin{align}
  & V\propto I \\
 & \therefore V=IR \\
\end{align}\]
The S.I. the unit of the resistance is Ohm \['\Omega '\].
There is another quantity known as the resistivity of the material of the conductor which is the resistance per unit length of the conductor. It is a material property and changes only with temperature.
When we measure the resistance of a conducting wire with several dimensions, we can see that the resistance value changes as we change the cross-sectional area of the wire and the length of the wire. It is given as –
\[\begin{align}
  & R\propto \dfrac{l}{A} \\
 & \therefore R=\rho \dfrac{l}{A} \\
\end{align}\]
We can understand that the resistance is directly proportional to the length of the conducting wire and inversely proportional to the area of cross-section of the wire at a constant temperature. Also, the S.I unit of resistance is Ohm \['\Omega '\].
This is the required solution.

Note:
The resistance is highly dependent on the temperature of the surrounding. The voltage drop across a resistor increases sharply with the increase in the temperature. The Joule’s heating results in the rise of temperature and therefore the resistance in the circuit with time.