Electricity; Calculating Resistance.

[FlyingSpartan]

Homework Statement

Calculate the resistance of a strand of aluminium wire of diameter 4.0mm and length 1.0m, given its resistivity is 2.5*10^-8 Ωm. What would be the resistance per meter of 50 strands of this wire, using the strands in parallel as a cable?

Homework Equations

∏d^2/4 for area
ρ=RA/L,
Where ρ = Given resistivity
R= Resistance
A= Cross sectional Area
L= Length

The Attempt at a Solution

4.00mm Diameter → 4*10^-3 Converted to Meters
Length = 1m
Resistivity = 2.5*10^-8 Ωm

So I found out the Area using ∏d^2/4;∏*(4*10^-3)/4 which = 1.26*10^-5 m^2

Then I used the formula
ρ=RA/L,
rearranging for R,
ρL/A = R

and subbing in the values;

2.5*10^-8 * 1 /1.26*10^-5

which gives an answer of 1.989*10^-3 Ωm^-1

thus i multiplied it by 50 which gives a final answer of 0.09945

However my answer differs from the answer of the book which is given as 4.99Ωm^-1

Thanks for any help!

 

[BruceW]

which gives an answer of 1.989*10^-3 Ωm^-1

You've got it right up to here, so this is effectively resistance per length of one strand. And the question says that there are 50 of these strands in parallel, so now you've got to work out the total resistance of the cable due to parallel strands.

 

[technician]

The answer in the book looks wrong... are you certain you read it correctly.
I also got the resistance/m of 1 strand to be 1.98 x 10^-3
50 of these in PARALLEL will not have a resistance of 4.99 Ωm^-1
Is there a power of 10 missing somewhere?

 

[FlyingSpartan]

I've tried to calculate the resistors in paralell;

1/r = 50 * 1/1.989*10^-3

R= 3.97*10^-5

which is still far from the answer, maybe the book is wrong?

 

[BruceW]

I got 3.97*10^-5 as well, so maybe the book is wrong...

 

[technician]

I get the same as you (your original textbook answer did not have a 10^-5 in it !)
The textbook is wrong but I can't see an obvious error.
One thing you can be sure of, when resistors are in parallel the combined resistance must be less than any of the single resistors.
Cheers

 

[tiny-tim]

Welcome to PF!

Hi FlyingSpartan! Welcome to PF!

(try using the X² icon just above the Reply box )

Calculate the resistance of a strand of aluminium wire of diameter 4.0mm and length 1.0m, given its resistivity is 2.5*10^-8 Ωm.
…
However my answer differs from the answer of the book which is given as 4.99Ωm^-1

I've tried to calculate the resistors in paralell;

1/r = 50 * 1/1.989*10^-3

R= 3.97*10^-5

hmm … 4.99/3.97*10^-5 = 1.26*10⁴ …

that's the area! (times 10-to-the-something) …

clearly something's gone very wrong here! ​