Question

the resistance, r, to electricity of a cylindrical - shaped wire is given by the equation r = ρl/π(d/2)^2, where ρ 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 infinity. the resistance approaches l. the resistance approaches r. the resistance approaches 0.

Explanation:

Step1: Recall resistance formula

The resistance formula is $R =
ho\frac{L}{\frac{\pi d^{2}}{4}}=\frac{4
ho L}{\pi d^{2}}$, where $
ho$ is resistivity, $L$ is length and $d$ is diameter.

Step2: Analyze when diameter approaches 0

As $d
ightarrow0$, the denominator $\pi d^{2}
ightarrow0$. Since $
ho$ and $L$ are non - zero (assuming non - zero resistivity and length), and $R=\frac{4
ho L}{\pi d^{2}}$, the value of $R$ will approach infinity.

Answer:

The resistance approaches infinity.