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Pavel
3 months ago
6

Suppose an electrical wire is replaced with one having every linear dimension doubled (i.e., the length and radius have twice th

eir original values). How is the resistance of the wire affected?
Physics
1 answer:
Softa [3K]3 months ago
4 0

Response:

The new resistance is half of the original resistance.

Explanation:

Resistance in a wire is represented by:

R=\dfrac{\rho L}{A}

\rho = resistivity of the material

L and A are the physical dimensions

If a wire is exchanged for one where all linear dimensions are doubled, i.e. l' = 2l and r' = 2r

The updated resistance of the wire can be calculated as follows:

R'=\dfrac{\rho L'}{A'}

R'=\dfrac{\rho (2L)}{\pi (2r)^2}

R'=\dfrac{1}{2}\dfrac{\rho L}{A}

R'=\dfrac{1}{2}R

The new resistance equals half of the original resistance. Thus, this provides the solution needed.

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