Resistance and How It Varies With Diameter

[Bashyboy]

So, the relationship of resistance is R= \rho \frac{l}{A}; assuming the resistor is cylindrical, the cross-sectional area of the resistor is A = \pi r^2. The relationship between the radius and diameter is r = \frac{d}{2}. Substituting in this relationship, A = \pi (\frac{d}{2})^2

So, if I were to double the diameter, the cross sectional area would become A = \pi \frac{(2d)^2}{4} \rightarrow A = \pi d^2 Does this mean that the cross sectional area quadruples? further implying that the resistance decreases by 1/4?

 

[TSny]

Yes. That's correct.