Question

Two metal wires of identical dimensions are connected in series.If (sigma)¹ and (sigma)2 are the conductivities of the metals respectively ,the effective conductivity of the combination is?????

Answer 1

Hey there !!!!!

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Conductance = 1/ Resistance 

Resistance = resistivity*length of conductor/ Area

So,

Effective Conductance = 1/resistivity   as length and area are constant

According to question as two wires of length "L" are joined so resulting length = 2L

So as wires of resistances R₁ and R₂ are connected in series

Effective resistance(R) = R₁+R₂


                    =R₁+R₂

Conductivity of R₁= ρ₁L/A   R₂= ρ₂L/A

                    ρ2L/A=ρ₁L/A+ρ₂L/A 

                    2ρ=ρ₁+ρ₂

          σ= 2/ρ₁+ρ₂= 2/(1/σ₁+1/σ₂) = 2σ₁σ₂/σ₁+σ₂

So effective conductivity of combination is σ=2σ₁σ₂/σ₁+σ₂

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Hope this helped you....................