A copper wire has length $L=5.0,\text{m}$ and cross‑sectional area $A=1.0,{\text{mm}}^2$. 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. Use the formula $R=\rho L/A$ to calculate the resistance.
2. Convert the area from millimetres squared to metres squared: $1.0,{\text{mm}}^2=1.0\times 10^{-6},{\text{m}}^2$.
3. Substitute the values: $R=(1.68\times 10^{-8},\Omega \text{m})(5.0,\text{m})/(1.0\times 10^{-6},{\text{m}}^2)$.
4. Simplify the expression: $R=(8.4\times 10^{-8})/(1.0\times 10^{-6})$.
5. Divide the powers of ten: $8.4\times 10^{-2}=0.084$.
6. Therefore the resistance of the wire is $0.084,Omega$.

Concept tested: Resistivity of a wire

Published 19 September 2026 · How this solution was prepared and checked