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## #1 2007-04-12 18:29:42

Insanic
Guest

### how do i find l

i have an engineering problem and well its more maths than engineering, i got stuck at the last step but ill submit all the steps i took incase i got it wrong

A heater is made with a power rating of 1000W and runs on 240V. If the heating element is made of wire wound onto a former and the wire is a nickel-chromium alloy with a resistivity of 103x10power of -8Ωm, with a diameter of 1mm, what will the length of the wire be to give the heater required power rating?

erh. i wasnt sure what to do so i wrote all the data done first
Power(P)=1000,           Potential difference(E)=240,             resistivity(p)= 103x10power-8                diameter=1mm
length(L)= un known,

heres the formula that i got given
R=p times L/a

i found a with the other formula they gave me a= (pie times d^2)/4, so pie times 0.001^2/4 which i got 7.85x10power of -7

and now to get R i did ohms law R=E/I but we dont have I (current), so i did electric power formula P=EI so I=P/E and 1000/240=4.17, so now R= 240/4.17 and i got 57.6

now we have R, p and a so R=p times L/a, 57.6=103x10power-8 times L/ 7.85x10power of -7

this is were i got up to i need L but im not sure if ive done the whole thing wrong or how to get L by its self on one side
thanks for helping

## #2 2007-04-12 18:39:52

Insanic1
Guest

### Re: how do i find l

i read over it, alot of grammar issues but i wasnt thinking straight.

a is the cross sectional area (m squared)

im new to this sorry

## #3 2007-04-12 19:02:30

insanic
Guest

### Re: how do i find l

also can someone tell me how to type fractions with out the / and how to get supperscipt for the power of symbol

## #4 2007-04-12 22:18:48

MathsIsFun
Registered: 2005-01-21
Posts: 7,685

### Re: how do i find l

R = pL/a, and you want "L"?

Divide both sides by "p" (which I think is  really "rho" ρ, right?): R/p = L/a
Multiply both sides by a: Ra/p = L

And that is your formula, L = Ra/p

IF a = 7.85x10power of -7, R = 57.6, and p=103x10power-8 (assuming you got the right numbers here!):

L = Ra/p = 57.6 * 7.85E-7 / 103E-8 = 43.9

(Note: I use "E" to mean ×10 to the power, like on calculators)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #5 2007-04-13 01:15:12

insanic
Guest

### Re: how do i find l

Thank you

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