Answer
Final answers
a) at temperature $T=50$ $C$ actual power is $ P_{act}=8.75$ $ kW$
b) at temperature $T=30$ $C$ actual power is $ P_{act}=10.8$ $ kW$
Work Step by Step
- A motor has a theoretical rated electric power of $P_e = 10$ $kW$
- We are asked to find the actual electric power $P_{act}$ for two cases:
a) when the temperature is $T=50$ $C$
b) when the temperature is $T=30$ $C$
A table shows the percentage variation between the "actual electric power" and the "theoretical electric power" under different temperatures.
The theoretical electric power is modified to give an actual electric power as follows
$$P_{act}=P_e+variation$$
where is variation is
$$variation = P_e \times percentage$$
where the $percentage$ is obtained from the given table
by substituting terms and simplifying, we get
$$P_{act}=P_e+variation = P_e+ P_e \times percentage = P_e \times(1+percentage)$$
Therefore;
a) at temperature $T=50$ $C$
from the table, $percentage$ is equal to $-12.5$%
Hence, actual electric power is
$$ P_{act}=P_e\times(1+percantage) = 10,000\times (1+\frac{-12.5}{100}) = 8,750 W = 8.75 kW $$
In the same way, we repeat for the next part
b) at temperature $T=30$ $C$
from the table, $percentage$ is equal to $+8$%
Hence, actual electric power is
$$ P_{act}=P_e\times(1+percantage) = 10,000\times (1+\frac{+8}{100}) = 10,800 W = 10.8 kW $$
