A nichrome wire of length $1.5\text{m}$ and cross‑sectional area $0.8{\text{mm}}^2$ has a resistivity of $1.10\times 10^{-6}\Omega \text{m}$ at $20^{\circ }\text{C}$. What is its resistance?

Step-by-step solution

1. Convert the area from ${\text{mm}}^2$ to ${\text{m}}^2$: $0.8{\text{mm}}^2=0.8\times 10^{-6}{\text{m}}^2$.
2. Use the formula $R=\rho \frac{L}{A}$ where $\rho$ is resistivity, $L$ is length and $A$ is area.
3. Substitute the values: $R=(1.10\times 10^{-6})\frac{1.5}{0.8\times 10^{-6}}$.
4. Calculate the numerator: $1.10\times 10^{-6}\times 1.5=1.65\times 10^{-6}$.
5. Divide by the area: $\frac{1.65\times 10^{-6}}{0.8\times 10^{-6}}=2.0625\Omega$.
6. Round to two decimal places: $R\approx 2.06\Omega$.

Concept tested: Resistance from resistivity

Published 8 September 2026 · How this solution was prepared and checked