Question

A cylindrical conductor of length l, diameter D and resistivity ρ has resistance R. A different cylindrical conductor of resistivity 2ρ, length 2l and diameter 2D, find its resistance.

Answer 1

Resistance of the first conductor is $R_1 = \frac{\rho l}{S} = \frac{\rho l}{\pi \left(\frac{D}{2}\right)^2} = \frac{4 \rho l}{\pi D^2}$.

Resistance of the second conductor is $R_2 = \frac{2 \rho \cdot 2 l}{\pi \left(\frac{2 D}{2}\right)^2} = \frac{ 4 \rho l}{\pi D^2} = R_1$.

Hence, resistances are the same.