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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
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
also can someone tell me how to type fractions with out the / and how to get supperscipt for the power of symbol
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)
Read all about formatting here: http://www.mathsisfun.com/forum/viewtopic.php?id=2892
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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Thank you
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