Question

What length of a copper wire of cross-sectional area 0.01 mm² will be needed to prepare a resistance of 1 kΩ? Resistivity of copper = 1.7 × 10^–8 Ωm

Answer 1

Given:
Resistivity of copper, ρ_cu = 1.7 × 10^–8 Ωm
Area of cross-section, A = 0.01 mm² = 0.01 × 10^–6 m²
Required resistance, R = 1 kΩ = 10³ Ω
Let l be the required length of the copper wire.
We know:
$$\begin{gathered} R=\frac{\rho l}{A} \\ \Rightarrow l=\frac{RA}{{\rho }_{\mathrm{cu}}} \\ \Rightarrow l=\frac{{10}^3\times 0.01\times {10}^{-6}}{1.7\times {10}^{-8}} \\ \therefore l=0.58\times {10}^3\mathrm{m}=0.6\mathrm{km} \end{gathered}$$