Question

1. how do length and diameter of a material impact its resistance? length is inversely proportional to resistance, whereas diameter is directly proportional to resistance. length is directly proportional to resistance, whereas diameter is inversely proportional to resistance. length and diameter are both inversely proportional to resistance. length and diameter are both directly proportional to resistance.

Explanation:

The formula for resistance \(R\) of a material is \(R =
ho\frac{l}{A}\), where \(
ho\) is resistivity (property of the material), \(l\) is length, and \(A=\pi(\frac{d}{2})^2\) ( \(d\) is diameter) is the cross - sectional area. From \(R =
ho\frac{l}{A}\), when \(
ho\) is constant, \(R\propto l\) (length \(l\) is directly proportional to \(R\)) and \(R\propto\frac{1}{A}\propto\frac{1}{d^{2}}\) (diameter \(d\) is inversely proportional to \(R\)).

Answer:

Length is directly proportional to resistance, whereas diameter is inversely proportional to resistance.