The figure below shows three cylindrical copper conductors along with their face areas and lengths. Compare the
resistance and the resistivity of the three conductors. Justify your answer.

The figure below shows three cylindrical copper conductors along with their face areas and lengths. Compare the resistance and the resistivity of the three conductors. Justify your answer. 3L

Dear Student,

Here,

Case 1 

Length of the wire (L) = L


Resistance (R) = R1

Area of cross section (A) = A

We have by the formula for resistivity


R1 = ρ(L/A)


Case 2,

Length of the wire (L) = L


Resistance (R) = R2

Area of cross section (A) = A

R2 = ρ(3L/A/3)
 = ρ(3L/A) x 3
9ρ(L/A)

= 9R1



Case 3,

Length of the wire (L) = L/3


Resistance (R) = R3

Area of cross section (A) = 3A

R3 = ρ(L/3/3A)
 = ρ(L/3) x 1/3A
= 1/9ρ(L/A)
= 1/9 R1


So, in all these cases the Resistance will change as R1, R(9R1) and R(1/9 R1)

R> R1 > R3

Also as it is of same material the resistivity remains same.




Hope this information will clear your doubts about the topic.

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Regards

 

  • 3
Ra = ρ l/a
Rb = ρ (3L/A/3) = 9  ρL/A = 9 Ra
Rc = ρ (L/3/3A) = 1/9 ρL/A = 1/9 Ra
Hence Rb>Ra>Rc
ρ a = ρ b = ρ c because all the three conductors are of same material.


Hope this answers the question :)
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