The resistivity of the material of a wire is $1.76 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }$. If the diameter of the wire is $2.00 \mathrm {~mm}$ and its length is $2.00 \mathrm {~m}$, what is its resistance?

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire. The area $A$ of a wire with a diameter $d$ is given by $A = \pi (\frac{d}{2})^2$. Substituting the given values: $A = \pi (1.00 \times 10^{-3})^2 = 3.14 \times 10^{-6} \, \text{m}^2$, and $R = 1.76 \times 10^{-8} \Omega \cdot \text{m} \cdot \frac{2.00 \, \text{m}}{3.14 \times 10^{-6} \, \text{m}^2} = 0.0112 \Omega$.

The Resistivity of the Material of a Wire Is 1.76×10−8Ω⋅m1.76 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }1.76×10−8Ω⋅m

The Resistivity of the Material of a Wire Is $1.76 \times 10 ^ { - 8 } \Omega \cdot \mathrm { m }$