Question

The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation R = StartFraction p L Over pi d squared EndFraction, where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire. What happens to the resistance of the wire as the diameter approaches 0?
The resistance approaches 0.
The resistance approaches Pi.
The resistance approaches L.
The resistance approaches infinity.

Answer 1

R = (ρL) / (π d^2) and ρ,L > 0. As d → 0 the denominator → 0, so R → ∞. Thus the resistance approaches infinity.