Question

The windings of a motor has a resistance of 120 ohms at 15 oC. After running for two
hours, the resistance increases to 140 ohm. Find the new temperature of the windings if
its temperature coefficient at 0 oC is 0.004.

Answer 1

After running for two hours, the resistance increases to 140 ohms. If the temperature coefficient of the windings at 0?C is 0.004

Answer 2

Given: The windings of a motor has a resistance of 120 ohms at 15° C. After running for two hours, the resistance increases to 140 ohm. Its temperature coefficient at 0° C is 0.004.

To find: The new temperature of the windings.

Solution:

• The heating effect of current on the windings of the motor can be represented using the formula,

        $R_{2} = R_{1} [1 + \alpha (T_{2} - T_{1})]$

• Here, R₁ and R₂ are the two resistances, T₁ and T₂ are the two temperatures that give the change in temperature and α is the coefficient of temperature.

        $140 = 120 [1+ 0.004(T_{2} - 15)$

• On rearranging the terms, the value of the new temperature is found to be,

        $T_{2} = 56.67$

Therefore, the new temperature of the windings is 56.67° C.