Can you help me with this homework question as I cant find any formula for it. The resistance of a shunt field winding of a motor is 20 ohms at 15 degrees c. After some time of running the resistance increases to 22 ohms. Calculate the final temp of the winding given that a is 0.004 per degree celsius? Thanks.
No formula. Just basic Algebra. 20 ohms = f(15) 1 Celcius = 0.004 ohms You have 1 point and you have the slope therefor you have a line. Since you have a point and the slope, you can get the exact formula for the line and solve for any point on it. point = (15,20) slope = 0.004 Ohms/Celcius so 20 Ohms = 0.004 Ohms/Celcius * 15 Celcius + Constant From this we solve for Constant and we get 19.4 ohms Now we have the next point we need to solve for 22 ohms, 22 Ohms = 0.004 Ohms/Celcius * X + 19.4 Ohms X = 650 Celcius There ya go
The variation of the resistance of the resistor by the temperature is gave by the formula: R=R0[1+ α (T-T0)] from here: T=T0+(R/R0-1)/ α T=15+(22/20-1)/0,004 T=40°C