I need some explanation on this

[flyingpig]

Homework Statement

[PLAIN]http://img23.imageshack.us/img23/949/unledto.png

Go to problem b)

[PLAIN]http://img850.imageshack.us/img850/5388/unledzb.png

The Attempt at a Solution

Now my question is why L + 2x? L is the height and x is the width, why are they adding them? I know $$\lambda$$ is the resistance per unit length, but I don't understand they are adding them. It would make sense if they added the entire arclength (perimeter) of the rectangle

 

[cepheid]

The problem says the rod has negligible resistance, which means that you only need to add up the lengths of the three sides of the rectangle that are formed by nichrome wire. This is one height (L) and two widths (2x).

 

[flyingpig]

The problem says the rod has negligible resistance, which means that you only need to add up the lengths of the three sides of the rectangle that are formed by nichrome wire. This is one height (L) and two widths (2x).

What about the distance PQ?

 

[OnlyMe]

What about the distance PQ?

The distance between P & Q is L.

 

[SammyS]

OK!

Resistance is: R = λ(2x + L) + 0(L), because, as cepheid pointed out, the rod has negligible resistance.

 

[cepheid]

  P--------------------
   |            x
   |  
   |
   | L
   |
   |
   |            x
  Q--------------------

Just to be clear, these are the three sides of the rectangle I was referring to. (The fourth side, made by the rod, is not shown). Adding their lengths up, we get:

L + x + x = L + 2x

 

[flyingpig]

OK!

Resistance is: R = λ(2x + L) + 0(L), because, as cepheid pointed out, the rod has negligible resistance.

It's okay, OnlyMe explained it to me pretty well lol.

Also, the rod isn't length L, look closely...

 

[cepheid]

Also, the rod isn't length L, look closely...

Maybe not, but the portion of it that conducts current and is part of the loop has length L...not that it matters since it has no resistance and hence you multiply it by 0 anyway.