Question

When the length of conductor is doubled then it’s resistance will be ________ (When temperature

and area of cross section remains constant).​

Answer 1

Answer is B.

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made.The resistance of a wire can be expressed as R=ρ

A

L

​

,

where,

ρ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity

L - Length of the conductor

A - Area of cross section of the conductor.

From this relation, we observe that the length is directly proportional to the resistance and the area of cross section is inversely proportional to the resistance.

That is, if L becomes 2 L, R becomes 2 R. R

′

=ρ

A

2L

​

. So, R = 2R'.

Hence, If the length of a wire is doubled, then its resistance becomes 2 times.

Answer 2

When the length of the conductor is doubled then its resistance will be double. (When temperature and area of cross-section remain constant).​

Explanation:

• Consider a conductor of length L and cross-section area A.
• Assume that voltage V is applied across it. Then the resistance R depends on A and L as:

       $\begin{gathered} R \propto \frac{1}{A} \hfill \\ R \propto L \hfill \\ \end{gathered}$

• On combining these two relations, we get,

       $\begin{gathered} R \propto \frac{L}{A} \hfill \\ R = \rho \frac{L}{A} \hfill \\ \end{gathered}$

• Here, the proportionality constant $\rho$ is called the resistivity of the conductor.
• It is fixed for a material at a fixed temperature but depends on the temperature T as:

        ${\rho _T} = \rho \left( {1 + \alpha \Delta T} \right)$

• If the temperature and area of the cross-section are fixed and the length becomes double, then,

        $\begin{gathered} R' = \rho \frac{{2L}}{A} \hfill \\ R' = 2\left( {\rho \frac{L}{A}} \right) \hfill \\ R' = 2R \hfill \\ \end{gathered}$

• Hence, if the length of the conductor is doubled while the area of cross-section and the temperature remain constant, its resistance also becomes double.

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