What are the ratios of the resistances of (a) silver and (b)...

What are the ratios of the resistances of (a) silver and (b) aluminum wire to the resistance of copper wire $\left(R_{\mathrm{Ag}} / R_{\mathrm{Cu}}\right.$ and $\left.R_{\mathrm{Al}} / R_{\mathrm{Cu}}\right)$ for wires of the same length and the same mass (not the same diameter)? (c) Which material is the best conductor, for wires of equal length and equal mass? The densities are: silver $10.1 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} ;$ copper $8.9 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} ;$ aluminum $2.7 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$.

What are the ratios of the resistances of (a) silver and (b) aluminum wire to the resistance of copper wire $\left(R_{\mathrm{Ag}} / R_{\mathrm{Cu}}\right.$ and $\left.R_{\mathrm{Al}} / R_{\mathrm{Cu}}\right)$ for wires of the same length and the same mass (not the same diameter)?
(c) Which material is the best conductor, for wires of equal length and equal mass? The densities are: silver $10.1 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} ;$ copper $8.9 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} ;$ aluminum $2.7 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$.

Key Concepts

Comparative Material Conductivity

Comparative material conductivity involves analyzing the intrinsic resistivities of different materials in conjunction with their densities when wires of equal mass and length are considered. This comparison helps in determining which material will yield the lowest resistance and thus serve as the best conductor in a given scenario.

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is independent of the physical shape or size of the conductor and is used in determining the convenience or difficulty of establishing current flow in different materials.

Electrical Resistance

Electrical resistance is the measure of how much a material opposes the flow of electric current and is determined by its resistivity, length, and cross-sectional area according to the formula R = ?L/A. This formula is central to understanding how variations in material properties and conductor dimensions affect overall resistance.

Density and Wire Geometry

When wires are made from the same mass and have the same length, the density of the material directly influences their cross-sectional area, since mass is the product of density, cross-sectional area, and length. This relationship means that for a given mass and length, a material with a lower density will yield a wire with a larger cross-sectional area, which in turn lowers its resistance.

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