Question

The resistance of a wire is r ohm . the wire is stretched to double its length . then the resistance in ohms is a) r/2 b) 4r c) 2r d) r/4

Answer 1

correct option is b)4r

We know that R=pL/A
When L is doubled,

old volume=new volume
AL=A1L1......(1) {Note that volume=area*length}
L1=2L

So, from eq.(1)
A1=A/2
So, the new resistance is
R1=pL1/A1
or
R1=p(2L)/(A/2)=4(pL/A)
Therefore, R1=4R

Answer= 4R

Hope this helps..!!

Answer 2

Answer:

The new resistance is 4r.

Explanation:

The resistance of the wire is given as

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

Here, l is the length of the wire A is the cross-sectional area and \rho is the Resistivity of the wire.

For the same type wire,

$R\propto\frac{l}{A}$

$\frac{R}{R_n} \propto\frac{\frac{l}{A}}{\frac{l_n}{A_n}}$

If the wire is stretched to double the length , the area of cross section gets reduced to half (as area = length x breadth).

so above equation becomes,

$R_n=r\times\frac{\frac{2l}{A/2} }{\frac{l}{A} }$

$R_n=4R$

Thus,the new resistance is 4r.

#Learn more: resistance.

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