Question

Two wires with the same dimensions and resistivities 1 and 2 are connected in series. The equivalent resistivity of the combination is?

Answer 1

The equivalent resistivity of the wires will be 3

Explanation :

Let L be the length and A be the area of cross section of the wires.

Resistance of wire 1 = R₁ = ρ₁L/A

=> R₁ = 1 x L/A = L/A

Resistance of wire 2 = R₂ = ρ₂L/A

=> R₁ = 2 x L/A = 2L/A

we know that in series the resistance of the wires are added,

R = R₁+R₂

=> R = L/A + 2L/A

=> R = 3L/A

=> R/(L/A) = 3

=> ρ = 3

hence the equivalent resistivity of the wires will be 3