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If the length of a wire is increased by 5% then it's resistance reduces or decreases and by what percentage?
Answers
Resistance is directly proportional to the length of the wire, and inversely proportional to the cross sectional area of the wire.
R = pl/A, where R is resistance, p is the material's resistance in ohms, l is the length, and A is the cross sectional area in m^2.
As a wire gets longer its resistance increases, and as it gets thinner its resistance also increases because its cross sectional area decreases.
Doubling the length will double the resistance, but the wire also must get thinner as it is stretched, because it will contain the same amount of metal in twice the length. The volume of a cylinder is length * cross sectional area, but in order to find the new cross section, you need to consider what the wire is made of. Most materials resist a change in volume more than they resist a change in shape, and because of that, they lose less volume than otherwise would be expected when stress is applied.
In the case of the stretched wire, its density will be less after stretching than it was before. This means that the volume of space occupied by the metal in the wire expands, due to the cross sectional area not shrinking in proportion to the stretch of its length. The amount of reduction in cross section is determined according to Poisson's ratio ....
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When the length of a wire is increased by 5% then its resistance reduces because the resistance is directly proportional to the length of cross section.
It reduces by 25%
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