Question
Pouer facter is the effleient of the mpter.
A motor draws an apparent power of 35 kVA and operates at a power factor of
0.92. Determine the eral power and the reactive power drawn by the motor.
Formula: Power factor = Real / Apparent power
App Power
A motor draws an apparent power of 35 kVA and operates at a power factor of
0.92. Determine the eral power and the reactive power drawn by the motor.
Formula: Power factor = Real / Apparent power
App Power
Ask by Weston Schmidt. in Singapore
Dec 09,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The Real Power drawn by the motor is 32.2 kW and the Reactive Power is approximately 13.717 kVAR.
Solution
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Beyond the Answer
To find the real power drawn by the motor, we can use the formula for power factor:
Real Power = Apparent Power × Power Factor.
Thus, Real Power = 35 kVA × 0.92 = 32.2 kW.
Thus, Real Power = 35 kVA × 0.92 = 32.2 kW.
Now, to find the reactive power, we can rearrange the second formula:
Apparent Power² = Real Power² + Reactive Power².
Calculating the reactive power gives us:
Reactive Power = √(App Power² - Real Power²) = √(35² - 32.2²) ≈ 18.36 kVAR.
Apparent Power² = Real Power² + Reactive Power².
Calculating the reactive power gives us:
Reactive Power = √(App Power² - Real Power²) = √(35² - 32.2²) ≈ 18.36 kVAR.
So, the motor draws approximately 32.2 kW of real power and 18.36 kVAR of reactive power; a neat little electrical puzzle solved!
Understanding power factor can be a game-changer in energy management! Higher power factors mean more efficient use of electricity, which can save on costs. Many utility companies may even offer incentives for businesses to improve their power factor, so keeping an eye on it can not only enhance efficiency but also lead to some financial perks—who doesn’t love that?
