Two carbon cylinders have radii r and 2r, and they both have length L. What is the resistance of the first if the resistance of the second is 12Ω?
A) 48 Ω
B) 12 Ω
C) 24 Ω
D) 3 Ω
E) 6 Ω

Question

Quizplus · Accepted Answer

The resistance $R$ of a cylinder is given by $R = \frac{\rho L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area. The cross-sectional area $A$ is proportional to the square of the radius $r$, so if the radius of the second cylinder is double that of the first, its area is four times larger. Since resistance is inversely proportional to the area, the resistance of the first cylinder, with a smaller area, will be four times greater than that of the second. Therefore, if the second has a resistance of 12Ω, the first will have a resistance of $12Ω \times 4 = 48Ω$.

Two Carbon Cylinders Have Radii R and 2r, and They