Question

Two metal wires of identical dimensions are connected in parallel. If σ₁ and σ₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

Options

• σ₁ + σ₂

• `(σ_1 + σ_2)/2`

• 2(σ₁ + σ₂)

• `(σ_1σ_2)/(σ_1 + σ_2)`

Answer 1

σ₁ + σ₂

Explanation:

`1/"R"_"eq" = 1/"R"_1 + 1/"R"2`

⇒ `"A"/(σ"l") = "A"/(σ_1"l") + "A"/(σ_2"l")`

⇒ `1/σ = 1/σ_1 + 1/σ_2`

σ = σ₁ + σ₂