# Homework Help: Resistance of resistors

1. Jun 12, 2010

### Philip Wong

hi guys,
I know this sound strange but it did happen. I was working on a question asking about calculating the resistance of a resistors, using different material one is copper and another is aluminium. I got the right answer, and wrote down the formula and steps that I used. But then I only didn't put in the values that I actually used. Just formula, steps and answer. Now when I come back to look at it again, I couldn't get the same answer that I originally correct. Either could I back track how I did it, so I hope someone can point it out to me, how I did it in the first place, and did I do it right then.

1. The problem statement, all variables and given/known data
a 20mm long piece of copper wire (sigma = 5.8*10^7 (ohm.m)^-1) with a diameter of 0.01mm is used as a resistor. you want to design a resistor with the same resistance but the only wire avaiable to you is an aluminium wire (sigma = 3.4*10^7)ohm.m)^-1) with diameter 0.02 mm. calculate the length for the piece of aluminium wire for which the two resistances are the same

2. Relevant equations
R = pL/A

3. The attempt at a solution
the steps that I wrote down original listed below, and I haven't put in the fitted values then, but as I tries to put in all the values in again, I didn't get a consistence result.

Rcu = pL/A
= L/ (sigma* A)
= (L/sigma) (4/ pi d^2)
=4.39ohm

Values I used to reattempt to get answer:
L = 20mm = 0.02m
sigma = 5.8*10^7
d = (0.01*10-3) ^2

Rcu = (0.02/(5.8*10^7)) * (4/ (pi*(.01*10^-3)^2

Why......?

2. Jun 12, 2010

### rl.bhat

R = ρL/A

RCu = ρ(Cu)L1/A1 = ρ(Al)L2/A2 = R(Al)

Substitute the values and find L2

3. Jun 12, 2010

### vela

Staff Emeritus
I think you must be plugging it into your calculator incorrectly. I just got the same answer you got originally.

4. Jun 12, 2010

### Philip Wong

ohh! indeed i have made a mistake at input my values. because I recalculated it everything, this time I've got a consistent answer.

ahaha! thanks
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.908136248588562, "perplexity": 1425.8361459321363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823303.28/warc/CC-MAIN-20181210034333-20181210055833-00183.warc.gz"}