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
a)
σ_{1 } + σ_{2}
b)
σ_{1 } + σ_{2} / 2
c)
√σ_{1}σ_{2}
d)
2σ_{1}σ_{2 }/ σ_{1 } + σ_{2}
Correct answer is option 'D'. Can you explain this answer?
Resistance of a wire in terms of connectivity (σ) is given bywhere l is the length and A is area of cross section of wirerespectively.∴ Rs = R1 + R2⇒where σs is the effective conductivityσs =2σ1σ2/σ1+σ2
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Resistance of a wire in terms of connectivity (σ) is given bywhere l is the length and A is area of cross section of wirerespectively.∴ Rs = R1 + R2⇒where σs is the effective conductivityσs =2σ1σ2/σ1+σ2