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

(a) 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 diameter? (c) Which material is the best conductor, for wires of equal length and diameter?

(a) 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 diameter?
(c) Which material is the best conductor, for wires of equal length and diameter?

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Key Concepts

Relationship Between Resistance and Resistivity

For a wire with uniform cross-sectional area and length, the resistance is given by the formula R = ?L/A, where ? is the resistivity. This means that when wires of identical length and diameter are compared, the ratio of their resistances is simply the ratio of their resistivities. This concept enables one to directly infer how materials like silver, copper, and aluminum compare in terms of electrical resistance.

Material Conductivity Ranking

The conductivity of a material is the inverse of its resistivity, meaning that materials with lower resistivity exhibit higher conductivity and are better conductors. In comparing common conductive materials, the one with the lowest resistivity (hence the highest conductivity) will allow electric current to pass most efficiently. This concept is essential for determining which wire material is the best conductor when comparing the effects of resistivity.

Electrical Resistivity

Electrical resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. In the context of wires, resistivity directly determines the resistance of a wire when its dimensions (length and cross-sectional area) are constant. Thus, comparing the resistances of different materials boils down to comparing their resistivities.

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