Question

What would be the length of resistance wire of area of cross-section 3 mm² used for making a resistance of 100 Ω? The specific resistance of the wire is 0.000070 ohm cm.

Answer 1

Given: R = 100 Ω, ρ = 0.000070 Ω cm = 7 × 10⁻⁵ Ω cm

Convert area to cm² because ρ is in Ω cm:

A = 3 mm² = 3 × (0.1 cm)² = 0.03 cm²

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

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

\[= \frac{100 \times 0.03}{7 \times 10^{-5}}\]

\[= \frac{3}{7 \times 10^{-5}}\]

= 4.2857 × 10⁴ cm

= 428.57 m