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:-

\[R = \frac{\rho l}{A}\]

\[ \Rightarrow l = \frac{RA}{\rho_{cu}}\]

\[ \Rightarrow l = \frac{{10}^3 \times 0 . 01 \times {10}^{- 6}}{1 . 7 \times {10}^{- 8}}\]

\[ \therefore l = 0 . 58 \times  {10}^3   m = 0 . 6  km\]