Question

Solve the following problem.

What is the resistance of one of the rails of a railway track 20 km long at 20° C? The cross-section area of the rail is 25 cm² and the rail is made of steel having resistivity at 20° C as 6 × 10^-8 Ω m.

Answer 1

Given: l = 20 km = 20 × 10³ m, A = 25 cm² = 25 × 10^-4 m², ρ = 6 × 10^-8 Ω m

To find: Resistance of rail (R)

Formula: ρ = `"RA"/"l"`

Calculation: From formula,

R = `ρ"l"/"A"`

∴ R = `(6xx10^-8xx20xx10^3)/(25xx10^-4)=(6xx4)/5xx10^-1`

= 0.48 Ω

The resistance of one of the rails of railway track is 0.48 Ω.