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Here is the question I'm facing,

The cross sectional area of a bare wire is a square of area 1.00mm^2. A 10.0m, length of this wire is wound close together on a wooden cylinder so that neighbouring coils are completely in contact with each other. There is a total of 200 coils. The resistivity of the material of the wire is 1.0 x 10^(-6)ohmm. Estimate the effective resistance of the arrangement.

My question is what's the purpose of wounding a wire closely together and what's the words 'completely in contact with each other' trying to emphasize? Furthermore, how does the effective resistance of the arrangement changes after the wire is wounded to 200 coils ?

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  • $\begingroup$ It means that you can easily estimate the total length and cross section of the wire, which you need for the calculation of the resistance. $\endgroup$ – CuriousOne May 11 '16 at 5:56
  • $\begingroup$ You have to calculate the resistance between its ends of a hollow cylinder which is made of the material of the wire. $\endgroup$ – Farcher May 11 '16 at 6:15
  • $\begingroup$ Really appreciate it, I thought nobody would answer it ! $\endgroup$ – Acery May 11 '16 at 10:39
  • $\begingroup$ @Farcher - Hmm... I'm wondering if there's not a hollow cylinder but a cylinder made of insulator, since we know there's no current in an insulator, so what do we do to the effective resistance of the same arrangement? I mean will the current still passing through the cross sectional area of the non-hollowed insulator cylinder? $\endgroup$ – Acery May 12 '16 at 13:33
  • $\begingroup$ It is as shown in the diagram provided by user3386109. A hollow cylinder. $\endgroup$ – Farcher May 12 '16 at 13:41
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The resistance of the wire is a function of the area and the length: $$ R=\rho\frac{l}{A}$$

Before you wind the wire it has a length of $10m$ and a cross-sectional area of $1mm^2$. After winding the wire around the wooden cylinder, it looks like this:

wire cylinder

So now it has a much shorter length, and the area is the cross-sectional area of a hollow cylinder. You need to figure out the diameter of the cylinder that uses up all of the wire in 200 turns. Then you need to calculate the cross-sectional area and length of the cylinder to plug into the formula.

To answer your question: winding the wire closely together so that the coils contact each other allows the current to flow along the length of the cylinder. Otherwise (if the coils didn't contact each other) then the current would have to follow the wire round and round the cylinder (and in that case the resistance would be no different than when the wire was straight).

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  • $\begingroup$ Thank you, and I was thinking the same as you before this, maybe my calculations went wrong somewhere and I thought I was wrong, again thank you !! $\endgroup$ – Acery May 11 '16 at 10:41

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