Answer :
To determine the percent efficiency of the motor, we use the efficiency formula provided:
[tex]\eta = \frac{P_{\text{out}}}{P_{\text{out}} + P_{\text{loss}}}[/tex]
Where:
- [tex]P_{\text{out}}[/tex] is the output power of the motor in watts.
- [tex]P_{\text{loss}}[/tex] is the power loss in watts.
First, we need to convert the motor's horsepower (hp) into watts because horsepower is a common unit used for engines and motors, while watts are a standard unit of power in the International System of Units (SI). The conversion factor is:
[tex]1 \text{ hp} = 746 \text{ W}[/tex]
Therefore, a 15 hp motor is equivalent to:
[tex]15 \text{ hp} \times 746 \text{ W/hp} = 11,190 \text{ W}[/tex]
Now, we'll plug the values into the formula:
[tex]\eta = \frac{11,190}{11,190 + 1,130}[/tex]
Calculate the denominator:
[tex]11,190 + 1,130 = 12,320[/tex]
Calculate the efficiency:
[tex]\eta = \frac{11,190}{12,320} \approx 0.908[/tex]
To convert this to a percentage, multiply by 100:
[tex]0.908 \times 100 = 90.8\%[/tex]
Given the options:
- A. 89.5
- B. 96.5
- C. 97.8
- D. 88.5
None of the options exactly match our computed result of 90.8%, but the closest option is A. 89.5%.
Therefore, based on the closest match, the chosen option is A. 89.5%.