Physics, 28.07.2019 18:00 JoshuaXYP9978

The length of a certain wire is kept same while its radius is doubled. what is the change in the resistance of this wire?

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Answer from: JOEREACH

The resistance of a wire is given by
$R= \frac{\rho L}{A}$
where $\rho$ is the resistivity of the material, L the length of the wire and A its cross-sectional area.

In the problem, $\rho$ and L remain the same, while A changes because the radius changes. The area is given by:
$A=\pi r^2$
This means that if we double the radius (2r), the area becomes
$A_{new}= \pi (2r)^2 = 4 \pi r^2 =4A$
And therefore, the new value of the resistance is
$R_{new} = \frac{\rho L}{4 A}= \frac{1}{4}R$

So, when the radius is doubled, the resistance becomes $\frac{1}{4}$ of its original value.

Answer from: Quest

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c.arachnids

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Answer from: Quest

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The length of a certain wire is kept same while its radius is doubled. what is the change in the res...