Question

If the length of a copper wire has a certain resistance R, then on doubling the length its specific resistance
(a) will be doubled
(b) will become 1/4th
(c) will become 4 times
(d) will remain the same

Answer 1

Answer: (c) will become 4 times

The Resistance is given by:

$\boxed{R = \rho \frac{l}{A}}$

Where:

$R$ = Resistance
$\rho$ = Resistivity
$l$ = Length of wire
$A$ = Area of cross-section of wire


Now, Resistivity depends on the material. So it remains constant for a material. So, Resistance depends on Length and Area of wire.

Let us say the original resistance was $R_{\circ}$. We can write:

$R_{\circ} = \rho \frac{l}{A}$

Now, Length of Wire is doubled. So new length will be:

$l' = 2l$

But since length is doubled, there will be a change in Area of Cross Section.

We are assuming that the original wire was simply stretched until the length became double. But the volume will remain conserved. Using Conservation Of Volume, we can find the new area of cross-section.

$Initial \, \, Volume = Final \, \, Volume \\ \\ \implies A \, l = A' \, l' \\ \\ \implies A \, l = A' \times 2l \\ \\ \implies A' = \frac{A}{2}$


Thus, When the wire is stretched, Length becomes double, but the Area becomes half. We can find the new resistance R:

$R = \rho \frac{l'}{A'} \\ \\ \\ \implies R = \rho \frac{2l}{\frac{A}{2}} \\ \\ \\ \implies R = 4 \rho \frac{l}{A} \\ \\ \\ \implies \boxed{R = 4 \, R_{\circ}}$


Thus, the Resistance becomes four times that of initial.


So, Answer is Option (c).

Answer 2

Answer:

If the length of a copper wire has a certain resistance R, then on doubling the length its specific resistance will become 4 times