Question

The resistance in a fixed length of a wire of circular cross-section is 10.0 Ω. What will be the resistance of a wire of the same length made with the same material but with only half radius? Ans: 40 Ω

Answer 1

$R_1=\rho l/A_1=\rho l/(\pi r^2)$

$R_2=\rho l/A_2=\rho l/(\pi (r/2)^2)=4\rho l/(\pi r^2)=4R_1=4\cdot10=40\ (\Omega)$