Question

the resistance, r, to electricity of a cylindrical - shaped wire is given by the equation $r=\frac{
ho l}{pi d^{2}}$, where $
ho$ represents the resistivity of the wires 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.

Explanation:

Step1: Analyze the given formula

The resistance formula is $R=\frac{
ho L}{\pi d^2}$, where $
ho$, $L$ are positive constants.

Step2: Evaluate limit as $d\to0^+$

As $d$ approaches 0, $d^2$ approaches 0 from the positive side. For a fraction with a positive numerator and a denominator approaching 0, the value grows without bound.

$$\lim_{d \to 0^+} \frac{ ho L}{\pi d^2} = \infty$$

Answer:

The resistance approaches infinity.