In an aluminum (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are 2.7 × 10 - 8 Ω m and 1.0 × 10 - 7 Ω m , respectively. The electrical resistance between the two faces P and Q of the composite bar is

Step-by-step solution

Aluminium A = 7 2 - 2 2 = 45 m m 2 ρ = 2.7 × 10 - 8 Ω m l = 50 m m R 1 = 2.7 × 10 - 8 × 50 45 × 10 - 3 Ω R 1 = 30 μ Ω R n e t = R 1 R 2 R 1 + R 2 = 30 × 1250 1280 = 3 × 125 × 5 64 R n e t = 1875 64 μ Ω Ferrous A = 4 m m 2 ρ = 10 - 7 Ω m l = 50 m m R 2 = 10 - 7 × 50 4 × 10 - 3 Ω R 2 = 1250 μ Ω