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

Re=R1+R22ℓσA=ℓσ1A+ℓσ2Aσ=2σ1σ2σ1+σ2

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

Re=R1+R22ℓσA=ℓσ1A+ℓσ2Aσ=2σ1σ2σ1+σ2

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Two metal wires of identical dimensions are connected in series. If $σ$ ₁ and $σ$ ₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

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$\frac{σ_{1} + σ_{2}}{σ_{1} σ_{2}}$

$\frac{σ_{1} + σ_{2}}{2 σ_{1} σ_{2}}$

$\frac{2 σ_{1} σ_{2}}{σ_{1} + σ_{2}}$

$\frac{σ_{1} σ_{2}}{σ_{1} + σ_{2}}$

answer is B.

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$\begin{array}{l} R_{e} = R_{1} + R_{2} \\ \frac{2 ℓ}{σA} = \frac{ℓ}{σ_{1} A} + \frac{ℓ}{σ_{2} A} \\ σ = \frac{2 σ_{1} σ_{2}}{σ_{1} + σ_{2}} \end{array}$

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

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Two metal wires of identical dimensions are connected in series. If $σ$ ₁ and $σ$ ₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is