A copper wire is in the form of a cylinder and has resistance R. It is stretched till its thickness is reduced by half of its initial size. Find the new resistance in terms of R.
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Given:
Shape of copper wire = Cylinder
Resistance = R
New size = 1/2 of initial size
To Find:
New resistance
Solution:
Initial volume = LA = Lπr²
Thickness is reduced by half = r = r/2
If we stretch wire till it is 1/2 of the initial size then it's length will increase four times.
New volume = LA = L'πr²
= Lπ(r/2)²
= Lπr²/4
= LA/4
As, volume should be constant, thus = LA = LA/4 = LA
So L = 4L
Where, L is the length and A is the area.
New resistance -
R = ρL/A
= ρ(4L)/(A/4)
= 16ρL/A
Answer: The new resistance is 16r
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