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Exercise 1.6.6: Temperature-dependent resistance of a winding (written test, approx. 6 % of a 60-minute written test, WS2020)
On the rotor of an asynchronous motor, the windings are designed in copper.
The length of the winding wire is $40~\rm{m}$.
The diameter is $0.4~\rm{mm}$.
When the motor is started, it is uniformly cooled down to the ambient temperature of $20~°\rm{C}$.
During operation the windings on the rotor have a temperature of $90~°\rm{C}$.
$\alpha_{Cu,20~°\rm{C}}=0.0039 ~\frac{1}{\rm{K}}$
$ \beta_{Cu,20~°\rm{C}}=0.6 \cdot 10^{-6} ~\frac{1}{\rm{K}^2}$
$ \rho_{Cu,20~°\rm{C}}=0.0178 ~\frac{\Omega \rm{mm}^2}{\rm{m}}$
Use both the linear and quadratic temperature coefficients! 1. determine the resistance of the wire for $T = 20~°\rm{C}$.
2. what is the increase in resistance $\Delta R$ between $20°C$ and $90°C$ for one winding?