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Three wires each of length L , cross-sectional area A and resistivity are connected as shown in the figure. These are to be replaced by another wire of same resistivity such that the resistance between points X and Z does not change. If L₁ is the length and A₁ is the cross-sectional area of the new wire, then which one among the following is correct?

Options

  1. AL₁ = 3L and A₁ = 2A
  2. BL₁ = L and A₁ = A
  3. CL₁ = 2L and A₁ = 3A
  4. DL₁ = 2L and A₁ = 2A

Correct answer

A. L₁ = 3L and A₁ = 2A

Step-by-step solution

The resistance of a single wire of length L , cross-sectional area A , and resistivity is given by R = L A . Between points X and Y , there are two such wires connected in parallel. The equivalent resistance R_ XY is: 1 R_ XY = 1 R + 1 R = 2 R R_ XY = R 2 = L 2A Between points Y and Z , there is one such wire. Its resistance is R_ YZ = R = L A . The total resistance between X and Z is the series combination of R_ XY and R_ YZ : R_ XZ = R_ XY + R_ YZ = L 2A + L A = 3 L 2A The new wire has length L₁ , area A₁ , and t

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