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In the figure, two metal wires of identical dimension are connected in series. Find the equivalent resistance.

  1. Req = l / σ1A + l / σ2A
  2. Req = 2l / σeqA
  3. σeq = 2σ1σ2 / σ1 + σ2
  4. σeq = σ1σ2 / σ1 + σ2

Correct answer: Req = 2l / σeqA

Solution

When two resistors are connected in series, their resistances add up. The resistance of a wire is given by R = l / (σA). For two wires in series, the equivalent resistance is Req = l / σ1A + l / σ2A, which simplifies to Req = 2l / σeqA.

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