Two wires have the same length L and the same conductivity σ & the same resistance.The cross section of one wire is circle with Diameter D.The other is rectangular with dimensions (2d) x (2d/2). If D=2mm, find d. If the second wire has dimensions D X D, which of the wires has larger resistance?? Please help

Question

theeric · Answer

Alright!

What all information can you pull from the first part?
"Two wires have the same length L and the same conductivity σ & the same resistance.The cross section of one wire is circle with Diameter D.The other is rectangular with dimensions (2d) x (2d/2). If D=2mm, find d."

theeric · Answer

Are you here, @poulaki ?

theeric · Answer

Well, for starters, you need to understand resistance. One way that resistance is calculated uses information that you have.

Resistance is linearly proportional to length.
   More length -> more resistance.
      A little more length, proportionally more resistance.

Resistance is inversely proportional to the cross-sectional area.
   More area -> less resistance.
      A little more area, proportionally less resistance.

And the proportion that I've been mentioning is captured in the "resistivity" constant. That makes sense, huh?
And the conductivity constant that you have is actually just the inverse of the resisitivity.

Overall, the formula is
$R=\dfrac1\sigma\dfrac LA$

theeric · Answer

Now, for the first part, you need to consider where the resistance for one equals the other.
I would start with the general formula, and then get more specific with the information you're given.

It might help to define $\large R_\text{round}$ and $\large R_\text{rectangular}$.

Good luck! Feel free to ask questions!

anonymous · Answer

thank you eric i just saw your answer