Problem

Calculate the resistance of a wire $10 \, \mathrm{m}$ long with a diameter of $2 \, \mathrm{mm}$ and resistivity of $2.63 \times 10^{-2} \, \Omega \mathrm{m}$.

Data

• Length: $L = 10 \, \mathrm{m}$
• Diameter: $D = 2 \, \mathrm{mm} = 2 \times 10^{-3} \, \mathrm{m}$
• Radius: $r = \frac{D}{2} = 1 \times 10^{-3} \, \mathrm{m}$
• Resistivity: $\rho = 2.63 \times 10^{-2} \, \Omega \mathrm{m}$

Prerequisite Concept

• Resistance Formula:
  $R = \rho \frac{L}{A}, \, A = \pi r^2$

Solution

1. Cross-sectional area:
   $A = \pi r^2 = \pi (1 \times 10^{-3})^2 = 3.14 \times 10^{-6} \, \mathrm{m^2}$

2. Resistance:
   $R = \frac{\rho L}{A} = \frac{2.63 \times 10^{-2} \cdot 10}{3.14 \times 10^{-6}}$
   $R = 8375.8 \, \Omega$

Answer

• Resistance: $R = 8375.8 \, \Omega$

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