Answer
$l = 848.23 m$
Work Step by Step
Given:
A plain carbon steel wire 3 mm in diameter is to offer a resistance of no more than 20 Ω
Required:
maximum wire length using data in Table 18.1
Solution:
From Table 18.1, $σ = 0.6 \times 10^{7} (Ω−m)^{-1}$
Combining Equations 18.2 and 18.4:
$l = \frac{RA}{ρ} = RσA = Rσπ (\frac{d}{2})^{2}$
$l = (20 Ω)[0.6 \times 10^{7} (Ω−m)^{-1}](π) (\frac{3 \times 10^{-3} m}{2})^{2} = 848.23 m$
