Physics

The key is understanding how resistance depends on both length and cross-sectional area through $R = \rho L/A$. When volume stays constant but diameter shrinks, the wire must get longer to compensate—and that length increase drives up resistance. Calculate how diameter and area scale together, then use the constraint that $V = AL$ remains fixed to find the new length, and finally track how both $L$ and $A$ change the resistance ratio.

The key is understanding how resistance depends on both length and cross-sectional area through $R = \rho L/A$. When volume stays constant but diameter shrinks, the wire must get longer to compensate—and that length increase drives up resistance. Calculate how diameter and area scale together, then use the constraint that $V = AL$ remains fixed to find the new length, and finally track how both $L$ and $A$ change the resistance ratio.