State the relationship between the resistance R of a wire to its length l and cross sectional area A.

Question

A. State the relationship between the resistance R of a wire to its length l and cross sectional area A. Use the mathematical symbols to arrive at the final formula.

B. Using the formula define the resistivity of a material.

Answer 1

(A) R ∝ l 

R ∝ l/A 

R = ρ l/A 

(B) R = ρ l/A 

ρ = R A/l for A =1m² and l = 1m, we have ρ = R 

Hence resistivity is the resistance offered by a wire of length 1 m having a cross sectional area of 1 m².