Masses of three conductors of same material are in the...

Masses of three conductors of same material are in the proportion of $1: 2: 3$ their lengths are in the proportion of $3: 2: 1$ then their resistance will be in the proportion of...
(A) $1: 1: 1$
(B) $1: 2: 3$
(C) $9: 4: 1$
(D) 27:6:1

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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 both the material properties and its geometry, following the relation R = ?L/A, where ? is the resistivity, L is the length, and A is the cross-sectional area. This concept is fundamental in analyzing how variations in dimensions affect the resistance of conductors.

Mass-Density-Volume Relationship

For any uniform material, mass is directly related to the volume and the density of the material. Since volume is calculated as the product of cross-sectional area and length, the relationship m = ?_material × A × L connects these three variables. Understanding this relationship allows one to re-express geometrical quantities like cross-sectional area in terms of mass and length.

Proportional Reasoning in Physics

Proportional reasoning involves using known ratios to deduce the effects on physical quantities when others change. In problems where dimensions and mass vary proportionately, the resistance can often be expressed as a function of these ratios. This method is invaluable for solving problems systematically by substituting proportional relationships into fundamental equations, thereby simplifying the comparison between different cases.

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