Question

2. The resistance of a certain wire is 10 Ω. a) What would the resistance of the same wire be if it were twice as long? b) If it had twice the diameter?

Answer 1

a)

$$R'=\rho\frac{2l}{0.25\pi d^2}=2R=20\Omega$$

b)

$$R''=\rho\frac{l}{0.25\pi (2d)^2}=0.25R=2.5\Omega$$