A wire of length 100 cm has a resistance of 10$\Omega$. If its cross-sectional area is 0.005cm2, determine its resistivity

Analyze the question: We are given a wire's length, resistance and cross-sectional area, and we must find its resistivity.

Concept: Resistance depends on the material and the wire's dimensions:

R = ρL / A, so ρ = RA / L

Solution:

• R = 10 Ω
• A = 0.005 cm²
• L = 100 cm

ρ = (10 × 0.005) / 100 ρ = 0.05 / 100 ρ = 0.0005 Ω cm

Check on units: Ω × cm² ÷ cm = Ω cm, which matches the options, so there is no need to convert to metres.

Answer: The resistivity is 0.0005 Ω cm.

Tip: Keep length and area in the same unit system (all cm, or all m). Then the unit of resistivity follows directly (Ω cm or Ω m). Also remember ρ = RA/L by thinking "Resistance Area over Length".