Question

The field coil of a DC shunt-connected motor has a resistance of 108ohm at 22°C. Calculate the resistance of the winding if the temperature of the winding increases to 80°C. Take the temperature coefficient of the resistance of copper to be 4,28×10-3/°C.

Answer 1

To calculate the resistance of the winding at a higher temperature, we can use the formula for resistance considering the temperature coefficient:

\[
R_t = R_0 (1 + \alpha (T_t - T_0))
\]

Where:
- \( R_t \) = resistance at temperature \( T_t \)
- \( R_0 \) = initial resistance at temperature \( T_0 \)
- \( \alpha \) = temperature coefficient of resistance (per °C)
- \( T_t \) = final temperature (in °C)
- \( T_0 \) = initial temperature (in °C)

Given:
- \( R_0 = 108 \, \Omega \)
- \( T_0 = 22 \, °C \)
- \( T_t = 80 \, °C \)
- \( \alpha = 4.28 \times 10^{-3} \, °C^{-1} \)

Now, substituting the known values into the equation:

\[
R_t = 108 \, \Omega \times \left(1 + (4.28 \times 10^{-3} \, °C^{-1}) \times (80 - 22)\right)
\]

Calculating the temperature difference:

\[
80 - 22 = 58 \, °C
\]

Now, we can calculate the term involving \( \alpha \):

\[
\alpha \times (T_t - T_0) = 4.28 \times 10^{-3} \times 58
\]

Calculating this gives:

\[
4.28 \times 10^{-3} \times 58 = 0.24824
\]

Now substituting this back into our expression for \( R_t \):

\[
R_t = 108 \, \Omega \times (1 + 0.24824)
\]

\[
R_t = 108 \, \Omega \times 1.24824
\]

Calculating \( R_t \):

\[
R_t \approx 134.73 \, \Omega
\]

Thus, the resistance of the winding at 80°C is approximately **134.73 ohms**.