Question

Prove what happens to resistance when length is doubled

Answer 1

As a wire gets longer its resistanceincreases, and as it gets thinner itsresistance also increases because its cross sectional area decreases.Doubling the length will double theresistance, but the wire also must get thinner as it is stretched, because it will contain the same amount of metal in twice the length.


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Answer 2

Explanation:

Resistance of a conductor is given by :

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

l is length of wire

A is area of cross section.

When the length of wire is doubled, its area of cross section gets reduced to half. i.e. l' = 2l and A'=A/2

New resistance is :

$R'=\rho\dfrac{l'}{A'}\\\\R'=\rho\dfrac{(2l)}{(A/2)}\\\\R'=4\rho\dfrac{l}{A}\\\\R'=4R$

So, new resistance becomes 4 times of the initial resistance.

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