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A cylindrical resistor has a length $L$ and radius $r$ . This piece of material is then drawn so that it is a cylinder with a new length of $2 L$ . What happens to the area of this material because of this process?

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the resistance is quartered.

the resistance is quadrupled.

the resistance is unchanged.

the resistance is doubled.

answer is D.

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Detailed Solution

The area of this material because of this process, the resistance is doubled.
The resistance of a wire is expressed as

R = \frac{ρl}{A}

where

R - Resistance of the conductor,

\Rightarrow ρ (rho) - Resistivity (constant)

⇒

l - Length of the conductor

\Rightarrow A - Area of a cross - section of the conductor .

So the length is directly proportional to the resistance

(l \propto R)

, and the area of the cross-section is inversely proportional to the resistance

A \propto \frac{1}{R}

So, when the length is doubled, i.e.,

2 L

and so the resistance will be

2 R

Thus, for the resistance to remain the same as

R

, the area of the cross-section should also be doubled as

2 A

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