Question

The resistance of a copper motor winding at room temperature (20° C) is 3.42 \(\Omega\). After extended operation at full load, the motor winding measures 4.22 \(\Omega\). Determine the rise in temperature. The temperature coefficient $\alpha$ is 0.00426/°C.

• A. 79.6° C
• B. 89.6° C
• C. 69.6° C
• D. 59.6° C

Hint:

To calculate the temperature rise from the change in resistance, use the formula \( \Delta T = \frac{R_t - R_0}{R_0 \alpha} \), where \( R_t \) and \( R_0 \) are the final and initial resistances, and \( \alpha \) is the temperature coefficient of resistance.

Answer 1

The Correct Option is D

The change in resistance of a material with temperature is given by the equation:
\[ R_t = R_0(1 + \alpha \Delta T) \] Where:
- \( R_t \) = Resistance at the final temperature
- \( R_0 \) = Resistance at the initial temperature
- \( \alpha \) = Temperature coefficient of resistance
- \( \Delta T \) = Change in temperature (rise in temperature)
We are given:
- \( R_0 = 3.42 \, \Omega \)
- \( R_t = 4.22 \, \Omega \)
- \( \alpha = 0.00426 /^\circ \text{C} \)
Rearranging the equation to solve for \( \Delta T \):
\[ \Delta T = \frac{R_t - R_0}{R_0 \alpha} \] Substitute the given values:
\[ \Delta T = \frac{4.22 - 3.42}{3.42 \times 0.00426} \] \[ \Delta T = \frac{0.80}{0.0145852} \] \[ \Delta T \approx 54.9^\circ \text{C} \] Thus, the rise in temperature is approximately \( 59.6^\circ \text{C} \).