The resistivity, $\mathit{P}$, of a material of length l, cross-sectional area A, resistance R, is given by the equation

Analyze the question: You need the formula that links resistivity (ρ, written here as P) to resistance R, length l and cross-sectional area A.

Concept: The resistance of a conductor depends on three things:

• It is directly proportional to its length: R ∝ l
• It is inversely proportional to its cross-sectional area: R ∝ 1/A
• It depends on the material, which is where resistivity comes in.

Solution:

Combining these gives

R = ρl/A

Make ρ the subject:

ρ = RA/l

Check with units: R is in ohms (Ω), A is in m², and l is in m. So ρ = Ω × m²/m = Ω·m, which is the correct SI unit of resistivity.

Now compare with the other options:

• B: l/(RA) gives units of 1/(Ω·m), which is conductivity, not resistivity.
• C: Rl/A gives Ω/m, which is the wrong unit.
• D: R/(Al) gives Ω/m³, which is also wrong.

Tip: Remember it as "R equals rho L over A", then rearrange. A quick unit check (the answer must come out in Ω·m) will save you in the exam.