Correct Answer - Option 3 : 5 m
Concept:
The resistance of a material is given by:
\(R = \frac{{ρ ~l}}{A}\)
R = Resistance of the wire
ρ = resistivity of the material
l = length of wire
A = cross-sectional area of the wire = πr2
\(A=\pi(\frac{d}{2})^2\)
\(R = \frac{ρ l}{\pi(\frac{d}{2})^2}=\frac{4ρ l}{\pi d^2}\)
Calculation:
Given: ρ = 100 × 10-8 Ωm
d = 0.4 mm = 0.4 × 10-3 m
R = 40 Ω, i.e.
\(40=\frac{4\times 100\times 10^{-8}\times l}{\pi (0.4 \times 10^{-3})^2}\)
l = 5.024 m
