Which formula expresses resistivity?

• A. R = p / l
• B. R = p x l
• C. R = p + l
• D. R = p - l

Answer: (B)

Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current. It is represented by the symbol p (rho) and is measured in ohm-meters (Ω·m).

The correct relationship expressing resistivity is derived from the formula for resistance, which is given by R (resistance) = p (resistivity) x l (length) / A (cross-sectional area). When we isolate resistivity from this equation, we see that resistivity can be expressed as R multiplied by the cross-sectional area divided by the length:

p = R × (A / l).

Therefore, when considering resistivity, the formula relates resistance to the dimensions and properties of the conductor, clearly indicating that resistivity increases with the resistance and is influenced by the length of the conductor and its cross-sectional area.

The other options do not effectively represent the relationship between resistance and resistivity. They incorrectly combine the variables with addition, subtraction, or incorrect multiplication that does not reflect the physics of electrical resistance in the context of resistivity. Thus, only the proper mathematical formulation that includes multiplication is applicable in expressing the relationship as defined in electrical science.