Question

What would be new resistance if length of conductor is doubled and thickness is halved?

Answer 1

Hint
Resistance of a conductor can be explained as the resistance to the circulation of electrical current through a conductor. It is foremost to detail out that the conductivity of the material and resistivity are inversely proportional to each other.

Complete step by step answer
The resistance of the conductor is directly proportional to the length of the conductor, and indirectly proportional to the cross-sectional sector of the conductor. The formula for the resistance of the conductor of the cross-sectional sector is given by;
$\Rightarrow R = \dfrac{{\rho l}}{A}$
Where, $R$ denotes the resistance of the conductor, $\rho $ denotes the material's resistance in ohms, $l$ denotes the length of the conductor, and $A$ denotes the cross-sectional area of the conductor in ${m^2}$.
As the length of the conductor gets doubled, the resistance of the conductor also increases. Doubling the length of the conductor will double the resistance of the conductor, but the thickness of the conductor also must get halved as it is stretched, because it will contain the same amount of metal in twice the length. The volume of a cylinder is length multiplied by the cross-sectional area of the conductor. But in order to find the new cross section, we have to take into account what the wire is made of. Most of the materials withstand a change in volume of the area more than they withstand a change in shape, and due to that, they lose very few volumes.
Therefore, the new resistance is $8$ times than that of the old resistance. If the length of the conductor is doubled then the resistance would increase by $8$ times. Since length becomes $2l$ and the cross-sectional area becomes ${\dfrac{1}{4}^{th}}$.
Hence, almost the new resistance of the conductor increases by $4$ times.

Note
Doubling the length of a conductor will double the overall resistance of the conductor and double the overall inductance of the conductor. Since conductance is the inverse of the resistance, doubling the length of the conductor will cut the overall conductance in half.