What is the resistance of $1.0 \mathrm {~m}$ of a solid cylindrical metal cable having a diameter of $0.40$ inches and a resistivity of $1.68 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }$ ?
A) $0.00021 \Omega$
B) $0.0012 \Omega$
C) $0.0021 \Omega$
D) $0.00012 \Omega$

Question

Quizplus · Accepted Answer

The resistance $R$ of a conductor can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. The diameter of the cable is $0.40$ inches, which needs to be converted to meters ($1$ inch = $0.0254$ meters), so the diameter in meters is $0.40 \times 0.0254 = 0.01016$ meters. The radius $r$ is half of the diameter, $r = 0.01016 / 2 = 0.00508$ meters. The cross-sectional area $A$ of the cable is $\pi r^2 = \pi \times (0.00508)^2$ square meters. Plugging in the values, $R = 1.68 \times 10^{-8} \Omega \cdot m \times \frac{1.0}{\pi \times (0.00508)^2}$. Calculating this gives a resistance close to $0.00021 \Omega$.

What Is the Resistance Of 1.0 m1.0 \mathrm {~m}1.0 m Of a Solid Cylindrical Metal Cable Having a Diameter Of Solid

What Is the Resistance Of $1.0 \mathrm {~m}$ Of a Solid Cylindrical Metal Cable Having a Diameter Of Solid