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A cylindrical wire of length L and radius r has a resistance R. The resistance of another wire of the same material but of half its length and twice its radius is given by:

A cylindrical wire of length L and radius r has a resistance R. The resistance of another wire of the same material but of half its length and twice its radius is given by: Correct Answer R/8

  • Given, Length of second wire (L') = Half of length of first wire (L)
  • Also, Radius of second wire (r') = Twice radius of radius of first wire (r)
  • So, L' = L/2 and r' = 2r
  • Let ρ be Resistivity of material.
    • R = ρL / A
    • R = ρL / (πr2); where πr2 = cross section Area of cylindrical wire
  • For second wire,
    • R' = ρL'/(πr'2)
    • R' = ρ(L/2)/(4πr2)
    • R' = ρL/(8πr2)
    • R' = R/8
  • Resistance is directly proportional to length and inversely proportional to area.
  • Its unit is Ohm.

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