A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors?
A) R
B) 2 R
C) 4 R
D) (ln2)R
E) R/(ln2)

Question

Quizplus · Accepted Answer

The resistance of a cylindrical shell (like the insulator in a coaxial cable) is inversely proportional to the logarithm of the ratio of the outer radius to the inner radius. When both the inner and outer radii are doubled, the ratio of the outer radius to the inner radius remains the same, meaning the resistance provided by the insulator does not change.

A High-Resistance Material Is Used as an Insulator Between the Conductors