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

Question

Quizplus · Accepted Answer

The resistance $R$ of a cylinder is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area. For the first cylinder, both the radius and the length are doubled compared to the second. Doubling the radius quadruples the area ($A \propto r^2$), and doubling the length doubles the resistance, but the quadrupled area reduces the resistance by a factor of four. Thus, the changes cancel out, and the resistance remains 12 Ω, halved to 6 Ω due to the doubled cross-sectional area.

Two Carbon Cylinders Have Radii 2r and R, and the First