Question

A wire of length L is drawn to a length 2l then it's resistance will be

Answer 1

Explanation:

then resistance will be two times increase .....

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Answer 2

Answer:

The resistance of the wire will increase 4 times.

Explanation:

The volume of the cross-section of the wire will remain the same i.e. given as,

$V_1=V_2$

$A\times l=A_2\times 2l$

$A_2=\frac{A}{2}$            (1)

Where,

V₁, V₂=volume of the cross-section

A₁=area of the cross-section

A₂=area after the increase of length

l₁=length of the wire

l₂=new length

The resistance of the wire is given as,

$R=\rho\frac{l}{A}$           (2)

R=resistance of the wire

ρ=resistivity of the wire

The original resistance of the wire is R and its new resistance will be R' i.e.

$R'=\rho\frac{l_2}{A_2}=\rho\frac{2l}{\frac{A}{2}}=\rho\frac{4l}{A}=4R$

Hence, the resistance of the wire will increase 4 times.