Question

The cross section of the iron conductor is a square of 1.2 mm. What is the length of the conductor if its resistance is 10 Ω? ρ = 10-7 Ωm.

Answer 1

The resistance is given as follows:

$$R = \rho\dfrac{l}{S}$$

where $\rho = 10^{-7}\Omega\cdot m$ is the resestivity of the material, $l$ is the length of the conductor, and $S = 1.2^2mm^2 = 1.44mm^2 = 1.44\times 10^{-6}m^2$ is the area of its cross section. Expressing $l$ and substituting $R= 10\Omega$, obtain:

$$l = \dfrac{RS}{\rho}\\ l = \dfrac{10\cdot 1.44\times 10^{-6}}{10^{-7}} = 144m$$

Answer. 144 m.