Which equation describes the relationship between resistance, resistivity, length, and cross-sectional area of a wire?

• A. R = pA/l
• B. R = pL/A
• C. R = A/pL
• D. R = L/pA

Answer: (B)

The equation that describes the relationship between resistance (R), resistivity (ρ, represented as "p" in some contexts), length (L), and cross-sectional area (A) of a wire is R = ρL/A.

In this equation, resistance (R) is directly proportional to the length (L) of the wire and the resistivity (ρ) of the material, indicating that longer wires or materials with higher resistivity will have greater resistance. Conversely, resistance is inversely proportional to the cross-sectional area (A) of the wire, meaning that a larger area allows more current to flow and thus results in lower resistance.

This relationship is fundamental in electrical engineering and physics, highlighting how physical characteristics of a conductor influence its ability to conduct electricity. Understanding this equation is crucial when analyzing circuits, as it helps in calculating changes in resistance based on material properties and geometric configuration of the wires used.