Question

A wire of resistance 4 ohm is
(1) doubled its original length
(2) tripled its original length
Calculate the new resistance in each case?????????????

Answer 1

Hey there !!!!

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Resistance = resistivity*length/area

                  =ρ*l/A--------Equation 1


           Volume = Area *length

            Area=Volume/length

 Equation 1  becomes 

resistance = ρ*l/volume/length = ρ*l*l/volume= ρ*l²/volume

At constant resistivity(ρ) and volume resistance is directly proportional to l²


                 R∞l²
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a)A wire of resistance 4 ohm is drawn  to twice its original length 

     l₂=2l₁  R₁=4    R₂=??

   R₁/R₂=l₁²/(2l₂)²

   4/R₂=1/4

   R₂=16Ω

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b) A wire of resistance 4Ω is drawn to thrice its original length:

  l₂=3l₁  R₁=4    R₂=?? 

   R₁/R₂=l₁²/(3l₂)²

   4/R₂=1/9

   R₂=36Ω

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Hope this helped you.....................