Question

A wire has a resistance of 16 ohm it is melted and redrawn into a wire of half its length calculate the resistance of new wire what is the percentage change in its resistance

Answer 1

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Answer 2

Explanation:

Resistance of wire, R = 16 Ω

Resistance, $R=\rho\dfrac{l}{A}$...............(1)

Where,

$\rho$ is the resistivity of the material.

It is melted and redrawn into a wire of half its length. Let R' be the new resistance.

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

Dividing (1) by (2)

$\dfrac{R'}{R}=2$

$R'=\dfrac{R}{2}$

So, the resistance of the new wire is half of the initial resistance.

The percentage change in its resistance is given by :

$R\%=\dfrac{R-R'}{R}\times 100$

$R\%=\dfrac{R-(R/2)}{R}\times 100$

$R\%=50\%$

Hence, this is the required solution.