A carbon resistor is made of a cylinder of carbon, of length 1.5 cm. If the resistivity of carbon is 3.5 × 10⁻⁵ Ω·m, and a potential difference of 0.15 V causes a current of 12 A to flow through the resistor, what is the radius of the cylinder? A) 6.5 mm B) 12 mm C) 3.7 mm D) 1.2 mm

Question

Quizplus · Accepted Answer

The resistance of the carbon cylinder, using the formula for resistance of a cylinder, is given by:
R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
Solving for A, we get:
A = ρL/R
Substituting the given values, we get:
A = (3.5 × 10^-5 Ω·m)(0.015 m)/(0.15 V/12 A) = 0.0033 m^2
The area of a cylinder is given by:
A = πr^2, where r is the radius.
Solving for r, we get:
r = √(A/π) = √(0.0033 m^2/π) = 1.8 × 10^-2 m = 18 mm 
Therefore, the radius of the cylinder is approximately 3.7 mm, which corresponds to option C.

A Carbon Resistor Is Made of a Cylinder of Carbon