A motor draws an apparent power of 35 kVA and operates at a power factor c 0.92. Determine the real power and the reactive power drawn by the motor. Formula: Power factor $$ = $$ Real / Apparent power App Power $$ { }^{2}= $$ Real Power $$ { }^{2}+ $$ Reactive Power [4 marks] O1PEE (DEBF1)

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To determine the real power and reactive power drawn by the motor, we can use the formulas provided.

1. **Calculate the Real Power (P)**:
   The power factor (PF) is defined as the ratio of the real power (P) to the apparent power (S):

$$
   \text{Power Factor} = \frac{P}{S}
   $$

Rearranging this formula gives us:

$$
   P = \text{Power Factor} \times S
   $$

Given:
   - Apparent Power $$ S = 35 \, \text{kVA} = 35,000 \, \text{VA} $$
   - Power Factor $$ PF = 0.92 $$

Now, substituting the values:

$$
   P = 0.92 \times 35,000 \, \text{VA} = 32,200 \, \text{W} = 32.2 \, \text{kW}
   $$

2. **Calculate the Reactive Power (Q)**:
   We can use the relationship between apparent power, real power, and reactive power:

$$
   S^2 = P^2 + Q^2
   $$

Rearranging this gives us:

$$
   Q^2 = S^2 - P^2
   $$

Now, substituting the values we have:

$$
   S^2 = (35,000)^2 = 1,225,000,000 \, \text{VA}^2
   $$
   $$
   P^2 = (32,200)^2 = 1,038,080,000 \, \text{W}^2
   $$

Now, substituting these into the equation for $$ Q^2 $$:

$$
   Q^2 = 1,225,000,000 - 1,038,080,000 = 186,920,000
   $$

Taking the square root to find $$ Q $$:

$$
   Q = \sqrt{186,920,000} \approx 432.5 \, \text{VAR}
   $$

3. **Summary of Results**:
   - Real Power $$ P \approx 32.2 \, \text{kW} $$
   - Reactive Power $$ Q \approx 432.5 \, \text{VAR} $$

Thus, the real power drawn by the motor is approximately **32.2 kW**, and the reactive power is approximately **432.5 VAR**.
The real power is approximately 32.2 kW, and the reactive power is approximately 432.5 VAR.

A motor draws an apparent power of 35 kVA and operates at a power factor c 0.92. Determine the real power and the reactive power drawn by the motor. Formula: Power factor \( = \) Real / Apparent power App Power \( { }^{2}= \) Real Power \( { }^{2}+ \) Reactive Power [4 marks] O1PEE (DEBF1)

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