Question

a wire of resistance 4 ohm is drawn (a) to twice its original length (b) to thrice 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.....................








        

Answer 2

Hi there !!
Just use the formula
Resistance of new wire = n2(squared) * resistance of old wire
n = how much time its increased than original length.

Hence

(a)-----> resistance of wire = 2 square * 4
=  4 * 4
= 16 ohms.

(b)------> resistance of wire = 3 square * 4
= 9 * 4
= 36 ohms

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