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.