Copper Winding Wire
April 3rd, 2008 | 
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please help calculate the final temperature,resistance windings 250ohm?
the resistance of the field winding of a generator is 220ohm at 20degree celsius.After the generator has worked for a period,the resistance of the windings is 250ohm.The windings are wound with copper wire.Calculate the final temperature of the winding.
t2 =- final temperature
t1 = initial temperature
The relationship which connects temperature and resistance is
Rt = R0{1 + at} where R0 is the resistance at 0 deg C, Rt is the resistance at t deg C, 'a' is the temperature coefficient which for copper is 0.00428
We must derive the expression to solve our question {unless you know the result in advance that is}
R1 = R0{1 + at1}..............(i)
R2 = R0{1 + at2}..............(ii)
R2/R1 = {1 + at2}/{1 + at1}...........(iii) = (ii)/(i)
Let r = R2 - R1 = increase in temperature
Therefore R2 = r + R1
also since r = 1 + at2 - 1 - at1 = a{t2 -t1}
from (iii) above we can say that
{r + R1}/R1 = {1 + at2}/{1 + at1} =
1 + r/R1 = 1 + a{t2 - t1}/{1 + at1} and therefore
r = [R1]*a{t2 - t1}/{1 + at1}
Rearranging we can say:-
Increase in Temperature = t2 - t1 = r{1 + at1}/{R1*a}
= [250 - 220]*{1 + 0.00428*20}/{220*0.00428} = 30*{1.0856}/{0.9416} = 34.6 deg C
Final temperature = 20 + 34.6 = 54.6 deg C
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