Two metal wires of identical dimensions are connected in series. If σ₁ and σ₂ are conductivities of their metals, effective conductivity of combination is:
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Two metal wires of identical dimensions are connected in series. If σ₁ and σ₂ are conductivities of their metals, effective conductivity of combination is:

G1 Physics · Accepted Answer

Step 1: For each wire length L and area A, Rᵢ=L/(σᵢA). Step 2: Series equivalent R=L/A(1/σ₁+1/σ₂). Step 3: Re-express for total length 2L: R=2L/(σ(eff)A). Step 4: 2/σ(eff)=1/σ₁+1/σ₂ ⇒ σ(eff)=2σ₁σ₂/(σ₁+σ₂).