Question

If the length of a wire is doubled, then its resistance becomes _____.

Answer 1

To answer this question, we have to use the relation of the resistance with its length and the cross sectional area. From there we can compare the resistance of a wire by substituting once the original length and then the double length.

Formula used:
The formula which is used in solving this question is given by
$R = \rho \dfrac{l}{A}$ , here $R$ is the resistance of a wire, $\rho$ is its resistivity, $l$ is its length, and $A$ is its area of cross section.

Complete answer:
Let the original length of the wire be $l$ and the original resistance be $R$ . Also, let $A$ be its cross sectional area.
We know that the relation of the resistance of a wire with the length and the cross sectional area is given by
$R = \rho \dfrac{l}{A}$ ………………..(1)
Mow, according to the question, the length of the wire is doubled. So, the new length becomes
$\Rightarrow l' = 2l$ ……………….(2)
So the new resistance of the wire is given by
$\Rightarrow R' = \rho \dfrac{{l'}}{A}$
From (2)
$\Rightarrow R' = \rho \dfrac{{2l}}{A}$
$\Rightarrow R' = 2\rho \dfrac{l}{A}$
From (1)
$\Rightarrow R' = 2R$
So, the new resistance, after doubling the length of the wire, becomes twice of the original resistance. Hence, if the length of a wire is doubled, then its resistance becomes doubled.

Note:
We must not get confused as to why the area of the cross section of the wire is taken to be constant. While we are observing the effect of doubling the length of the wire, then we have to take the other parameter, the area of cross section as constant. Otherwise the change in the value of resistance will occur due to the change in the cross sectional area also.