If a copper wire is stretched to make its radius decrease by 0.1 %, then the percentage increase

step 1 Students, in this problem we have given if a copper wire is stressed to make its radius decrease

If a copper wire is stretched to make its radius decrease by...

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Key Concepts

Small Percentage Approximations

For small changes in dimensions, approximations like the binomial expansion are used to simplify calculations. These approximations allow us to estimate the percentage changes in derived quantities, such as resistance, by linearizing the relationships between the parameters involved.

Conservation of Volume

When a wire is stretched, its volume remains constant, meaning that an increase in length must be accompanied by a decrease in cross-sectional area. This relationship is crucial for analyzing how changes in dimensions such as radius affect the length and consequently the resistance of the wire.

Electrical Resistance

Resistance is a measure of how much a material opposes the flow of electric current. It is determined by both the intrinsic property of the material, its resistivity, and its geometry, specifically its length and cross-sectional area, through the relation R = ?L/A.

Geometric Dependency of Resistance

The resistance of a conductor depends directly on its length and inversely on its cross-sectional area. Any change in the physical dimensions of a wire, due to stretching for example, alters its resistance by changing these dimensions, even if the material's intrinsic resistivity remains constant.

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