To calculate the increase in the resistance of the shunt field coil of the DC generator due to temperature rise, we can use the formula for the change in resistance due to temperature change:
\[ R_T = R_0(1 + \alpha \Delta T) \]
Where:
- \( R_T \) is the resistance at the new temperature.
- \( R_0 \) is the original resistance at the initial temperature.
- \( \alpha \) is the temperature coefficient of resistance.
- \( \Delta T \) is the change in temperature.
Given:
- \( R_0 = 140 , \Omega \)
- \( \alpha = 4.25 \times 10^{-3} /°C \)
- \( \Delta T = 65°C \)
Now, substituting these values into the formula:
\[ R_T = 140 \times (1 + 4.25 \times 10^{-3} \times 65) \]
First, calculate \( \alpha \Delta T \):
\[ \alpha \Delta T = 4.25 \times 10^{-3} \times 65 = 0.27625 \]
Now substitute back into the equation for \( R_T \):
\[ R_T = 140 \times (1 + 0.27625) = 140 \times 1.27625 \]
Calculating \( R_T \):
\[ R_T = 140 \times 1.27625 \approx 178.65 , \Omega \]
To find the increase in resistance (\( \Delta R \)), we subtract the original resistance from the new resistance:
\[ \Delta R = R_T - R_0 = 178.65 , \Omega - 140 , \Omega \approx 38.65 , \Omega \]
Thus, the increase in resistance of the coil when the temperature increases by 65°C is approximately 38.65 ohms.
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