Question regarding Electrical conduction(Resistance)

[Sanosuke Sagara]

The cross section of a bare wire is a square of area 1.00 mm^2 .A 10.0 m, 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 ohm meter.estimate the effective resistance of the arrangement .


First of all, i don't really quite understand with the phrase 'cross section of a bare wire is a square' and I want to know whether the 200 coils involved in calculating the resistance.Does the term 'effective resistance' mean using the formulae of parallel resistor as the wire is wounded one after another side by side,(This is my assumption) ?

Thanks for anybody that spend some time on this question and I really hope that somebody will explain to me the doubt I written above.

 

[OlderDan]

Most wires have a circular cross section. If you cut the wire perpendicular to its length and look at the end it is a circle. The end of this wire would be a square. The wire is wound in one continuous length onto the cylinder, and since it is a bare wire that makes contact with itself there is an electrical path between adjacent coils. This is neither a series nor parallel arrangement of the coils. This is more like a hollow cylinder of conducting material with a wire attached at both ends of the cylinder. I assume they use the word "estimate" because the resistance will depend on exactly where the wire ends contact the cylinder. I would expect there to be some difference if the end wires were on a line parallelel to the cylinder axis as compared to being on opposite sides of the axis. I think you are supposed to neglect that effect, but you need to relate this to similar problems you have done to make that decision.

 

[Dr.Brain]

The phrase "cross section of a bare were is a square of cross-section ..." means that the wire is not circular in shape just like the ordinary ropes, but it has a 'square-shaped' cross section . Here the wire has been wounded around the cylinder just like a solenoid.The number of turns are 200 and the wire length is 10m.
So, we need to calculate the effective resistance.As far as my experience goes, there has to be no direct method to this problem.

Ok because all the loops are joined, consider the whole 'solenoid' as one thick wire hollow from inside with thickness =cross sectional area of single wire.Now this new wire will have dimensions as follows:

Length : (200 x 1) mm


Take s small ring inside this thick wire , integrate it for the whole thickness , that is integrate it for radius1 to radius2 such that radius2-radius1 = thickness of waire

 

[Sanosuke Sagara]

Solution and some suggestion to solve the question

I have try to solve this question for a long time and I really can't find the correct answer.I have my doubt,solution to the question in the attachment that followed.Thanks for anybody that spend some time on this qustion.

 

[Dr.Brain]

I have try to solve this question for a long time and I really can't find the correct answer.I have my doubt,solution to the question in the attachment that followed.Thanks for anybody that spend some time on this qustion.

did u follow my approach?.., I think there's no other way than to integrate.

 

[OlderDan]

I have try to solve this question for a long time and I really can't find the correct answer.I have my doubt,solution to the question in the attachment that followed.Thanks for anybody that spend some time on this qustion.

The simplest model is to treat this as a cylindrical conductor and assume the ends of the cylinder are each at uniform potential. This is not exactly a valid assumption since the wire contacts the end of the cylinder at a point, but it is not bad if the cylinder is long compared to its diameter, and the problem did say to estimate the resistance. If you just had an ordinary wire, you would multiply the resistivity by the length and divide by the cross sectional area. The length is 200 times the thickness of the wire. The cross-sectional area is pi times the difference between the outer radius squared and the inner radius squared, which is approximately the circumference of the circle times the thickness of the wire.

Looks to me like this approach will result in the given answer.

 

[Sanosuke Sagara]

Thanks for your help OlderDan and I really appreciate it because I have really understand with the question and thanks for your explanation.