A rod (length = 80 cm) with a rectangular cross section (1.5 mm × 2.0 mm) has a resistance of 0.20 Ω. What is the resistivity of the material used to make the rod? A) 6.0 × 10−⁷ Ω ⋅ m B) 3.8 × 10−⁷ Ω ⋅ m C) 7.5 × 10−⁷ Ω ⋅ m D) 3.0 × 10−⁷ Ω ⋅ m E) 4.8 × 10−⁷ Ω ⋅ m

Question

Quizplus · Accepted Answer

We can use the formula for resistance of a conductor in terms of resistivity, length, and cross-sectional area:
$R = \frac{ho L}{A}$
where $R$ is resistance, $ho$ is resistivity, $L$ is length, and $A$ is cross-sectional area.
We can rearrange this equation to solve for resistivity:
$ho = \frac{RA}{L}$
Plugging in the given values, we have:
$ho = \frac{(0.20\ \Omega)(1.5	imes10^{-3}\ m)(2.0	imes10^{-3}\ m)}{0.80\ m} = 7.5	imes10^{-8}\ \Omega\cdot m$
Therefore, the answer is (C).

A Rod (Length = 80 Cm) with a Rectangular Cross