Calculating the resistance from R = pl/A

[jsmith613]

Homework Statement

A laboratory lead consists of 16 strands of fine copper wire twisted together. Each strand is 30 cm long with a diameter of 0.15 mm. Calculate the potential difference across the lead when it is carrying a current of 2.0 A.
(The resistivity of copper = 1.7 × 10^-8 Ohm*m)

Homework Equations

What I would do is R = pl/A and then multiply by 2
BUT I can't find R

The Attempt at a Solution

(the answer is. apparently, 0.036 V but I can't see how)

I said R = [(1.7*10^-8)*16*0.3)/(pi*0.15/20000)^2)

 

[ideasrule]

I said R = [(1.7*10^-8)*16*0.3)/(pi*0.15/20000)^2)

Putting strands of wire in parallel decreases the total resistance, because the electrons now have many more paths to follow. 16 strands would decrease the resistance by a factor of 16.

Also, why are you dividing 0.15 by 20,000? Why is pi being squared? The area of a circle of pi*r^2, not (pi*r)^2.

 

[jsmith613]

Putting strands of wire in parallel decreases the total resistance, because the electrons now have many more paths to follow. 16 strands would decrease the resistance by a factor of 16.

Also, why are you dividing 0.15 by 20,000? Why is pi being squared? The area of a circle of pi*r^2, not (pi*r)^2.

er, sorry abou the pi^2 bad use of brackets

it was meant to be pi * (0.15/2000)^2

again sorry,

Question: it is still ONE strand of wire, just twisted, are you sure total R decreases

 

[jsmith613]

seems you are correct - I now get the correct answer
thanks

 

[jsmith613]

http://www.edexcel.com/migrationdocuments/QP GCE Curriculum 2000/June 2009/6PH02_01_que_20090521.pdf

BUT if you look at page 19 then we multiply by 8 not divide by 8

why??

 

[jsmith613]

oh, don't worry I get it
first example 16 separate strands
second example one strand with 8 branches
its ok