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
  • a)
    σ + σ2
  • b)
    σ + σ2 / 2
  • c)
    √σ1σ2
  • d)
    1σ/ σ + σ2
Correct answer is option 'D'. Can you explain this answer?

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Jan 30, 2022
Resistance of a wire in terms of connectivity (σ) is given by

where l is the length and A is area of cross section of wire respectively.
∴ Rs = R1 + R2
⇒ 
where σs is the effective conductivity 

σs = 1σ/ σ + σ2

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
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