The masses of three wires of copper are in the ratio of 1:...

The masses of three wires of copper are in the ratio of $1: 3: 5$ and their lengths are in the ratio of $5: 3: 1$. The ratio of their electrical resistance is:
(A) $1: 1: 1$
(B) $1: 3: 5$
(C) $5: 3: 1$
(D) $125: 15: 1$

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Key Concepts

Electrical Resistance

Electrical resistance quantifies how much a material opposes the flow of electric current. It is determined by factors such as the material's inherent resistivity, the length of the conductor, and its cross-sectional area, with the relation given by R = ?L/A.

Geometric Dependence in Resistance

The resistance of a conductor varies directly with its length and inversely with its cross-sectional area. This geometric dependence is crucial in understanding how changing the dimensions of a conductor, such as length and area, will affect its ability to carry current.

Mass-Density-Area-Length Relationship

For a uniform material, the mass of a conductor can be expressed as the product of its density, cross-sectional area, and length (m = ?AL). This relationship allows one to determine the cross-sectional area if the mass and length are known, which is essential in calculating the resistance using the geometric factors.

Ratios and Proportions in Physical Quantities

Understanding and using ratios is important for comparing different physical quantities without needing absolute values. In problems involving electrical resistance and geometric dimensions, ratios help simplify the computation by relating how changes in one variable affect the overall resistance.

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