LBF (102BeD)
ame: Kon Kim Hon Class: A
An air handling unit (AHU) motor in a hotel consumes 32 KW of real power
and being supplied with 35.5 kVA of apparent power, Determine;
(a) the reactive power drawn by the motor,
(Ans: 15.37 KVAn
(b) the power factor of the motor,
(Ans: 0.9014 )

Question

UpStudy AI · Accepted Answer

To solve the problem, we can use the relationships between real power (P), reactive power (Q), and apparent power (S) in an AC circuit.

1. **Given:**
   - Real Power (P) = 32 kW
   - Apparent Power (S) = 35.5 kVA

2. **Formulas:**
   - Apparent Power (S) is given by the formula:
     $$
     S = \sqrt{P^2 + Q^2}
     $$
   - The power factor (PF) is given by:
     $$
     PF = \frac{P}{S}
     $$

### (a) Determine the reactive power (Q)

We can rearrange the formula for apparent power to solve for reactive power (Q):
$$
Q = \sqrt{S^2 - P^2}
$$

Substituting the given values:
$$
Q = \sqrt{(35.5)^2 - (32)^2}
$$
$$
Q = \sqrt{1260.25 - 1024}
$$
$$
Q = \sqrt{236.25}
$$
$$
Q \approx 15.37 \text{ kVAR}
$$

### (b) Determine the power factor (PF)

Now we can calculate the power factor using the formula:
$$
PF = \frac{P}{S}
$$
Substituting the values:
$$
PF = \frac{32}{35.5}
$$
$$
PF \approx 0.9014
$$

### Summary of Results:
(a) The reactive power drawn by the motor is approximately **15.37 kVAR**.  
(b) The power factor of the motor is approximately **0.9014**.
(a) The reactive power drawn by the motor is approximately 15.37 kVAR. (b) The power factor of the motor is approximately 0.9014.

LBF (102BeD)
ame: Kon Kim Hon Class: A
An air handling unit (AHU) motor in a hotel consumes 32 KW of real power
and being supplied with 35.5 kVA of apparent power, Determine;
(a) the reactive power drawn by the motor,
(Ans: 15.37 KVAn
(b) the power factor of the motor,
(Ans: 0.9014 )

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LBF (102BeD) ame: Kon Kim Hon Class: A An air handling unit (AHU) motor in a hotel consumes 32 KW of real power and being supplied with 35.5 kVA of apparent power, Determine; (a) the reactive power drawn by the motor, (Ans: 15.37 KVAn (b) the power factor of the motor, (Ans: 0.9014 )

Solución de inteligencia artificial de Upstudy

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Latest Engineering Questions

LBF (102BeD)
ame: Kon Kim Hon Class: A
An air handling unit (AHU) motor in a hotel consumes 32 KW of real power
and being supplied with 35.5 kVA of apparent power, Determine;
(a) the reactive power drawn by the motor,
(Ans: 15.37 KVAn
(b) the power factor of the motor,
(Ans: 0.9014 )