If the length of a solid cylindrical conductor is doubled while keeping its volume constant, what ha

Question

If the length of a solid cylindrical conductor is doubled while keeping its volume constant, what happens to its resistance?

Professor PC Thomas Classes · Answer

If length $l$ becomes $2l$ and volume is constant, area $A$ must become $A/2$. Resistance $R = \rho l/A$ becomes $\rho (2l)/(A/2) = 4 (\rho l/A) = 4R$.