Question

one wire has a cross-sectional area of 135 circular mils and a resistance of 18 ohms. a second piece of wire, identical except for cross-sectional area, has a resistance of 9 ohms. determine what the cross-sectional area of this second wire is. (cross-sectional area and resistance are inversely proportional.)

Explanation:

Set up the inverse proportion equation

$$ R \cdot A = k $$

$$ 18 \cdot 135 = k $$

Solve for the constant of proportionality

$$ k = 2430 $$

Calculate the cross-sectional area of the second wire

$$ 9 \cdot A_2 = 2430 $$

$$ A_2 = \frac{2430}{9} = 270 $$

Answer:

270 circular mils