A copper wire has length $L=7.5\text{ m}$ and cross‑sectional area $A=2.0{\text{ mm}}^2$. The resistivity of copper at $20^{\circ }\text{C}$ is $\rho =1.68\times 10^{-8},\Omega \text{m}$. Calculate the resistance of the wire.

Step-by-step solution

1. Step 1: Convert the area from mm${}^2$ to m${}^2$. $A=2.0,{\text{mm}}^2=2.0\times 10^{-6},{\text{m}}^2$.
2. Step 2: Use the formula $R=\rho ,\frac{L}{A}$.
3. Step 3: Substitute the values: $R=1.68\times 10^{-8},\Omega \text{m};\frac{7.5\text{ m}}{2.0\times 10^{-6},{\text{m}}^2}$.
4. Step 4: Calculate: $R=1.68\times 10^{-8}\times 3.75\times 10^6,\Omega =0.063,\Omega$.
5. Step 5: Hence the resistance of the wire is $0.063$ Ω.

Concept tested: Resistance of a conductor

Published 22 September 2026 · How this solution was prepared and checked