phase, $$ 400 \mathrm{~V}, 37 \mathrm{~kW} $$ motor runs at a power factor of 0.87 . Determine: the apparent power drawn by the motor (Ans: 42.529 kVA ) 37 the reactive power generated by the motor. (Ans: 20.969 kVAr ) the current drawn by the motor. (Ans: 61.3849 A )

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Given:
- Phase voltage, $$ V = 400 \, \text{V} $$
- Power, $$ P = 37 \, \text{kW} $$
- Power factor, $$ \text{Power factor} = 0.87 $$

We need to determine:
1. The apparent power drawn by the motor
2. The reactive power generated by the motor
3. The current drawn by the motor

Let's start by calculating the apparent power drawn by the motor using the formula:
$$ S = \frac{P}{\text{Power factor}} $$

Substitute the given values:
$$ S = \frac{37 \times 10^3}{0.87} $$

Now, let's calculate the apparent power.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{37\times 10^{3}}{0.87}$$
- step1: Multiply the terms:
  $$\frac{37000}{0.87}$$
- step2: Convert the expressions:
  $$\frac{37000}{\frac{87}{100}}$$
- step3: Multiply by the reciprocal:
  $$37000\times \frac{100}{87}$$
- step4: Multiply:
  $$\frac{37000\times 100}{87}$$
- step5: Multiply:
  $$\frac{3700000}{87}$$
The apparent power drawn by the motor is approximately 42.529 kVA.

Next, let's calculate the reactive power generated by the motor using the formula:
$$ Q = S \times \sqrt{1 - \text{Power factor}^2} $$

Substitute the values:
$$ Q = 42.529 \times \sqrt{1 - 0.87^2} $$

Now, let's calculate the reactive power.
Calculate the value by following steps:
- step0: Calculate:
  $$42.529\sqrt{1-0.87^{2}}$$
- step1: Convert the expressions:
  $$42.529\sqrt{1-\left(\frac{87}{100}\right)^{2}}$$
- step2: Subtract the numbers:
  $$42.529\sqrt{\frac{2431}{10000}}$$
- step3: Simplify the root:
  $$42.529\times \frac{\sqrt{2431}}{100}$$
- step4: Convert the expressions:
  $$\frac{42529}{1000}\times \frac{\sqrt{2431}}{100}$$
- step5: Multiply the numbers:
  $$\frac{42529\sqrt{2431}}{100000}$$
The reactive power generated by the motor is approximately 20.969 kVAr.

Finally, let's calculate the current drawn by the motor using the formula:
$$ I = \frac{P}{\text{Power factor} \times V} $$

Substitute the values:
$$ I = \frac{37 \times 10^3}{0.87 \times 400} $$

Now, let's calculate the current drawn by the motor.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{37\times 10^{3}}{\left(0.87\times 400\right)}$$
- step1: Remove the parentheses:
  $$\frac{37\times 10^{3}}{0.87\times 400}$$
- step2: Multiply the numbers:
  $$\frac{37\times 10^{3}}{348}$$
- step3: Factor the expression:
  $$\frac{37\times 2^{3}\times 5^{3}}{348}$$
- step4: Factor the expression:
  $$\frac{37\times 2^{3}\times 5^{3}}{4\times 87}$$
- step5: Reduce the fraction:
  $$\frac{37\times 2\times 5^{3}}{87}$$
- step6: Simplify:
  $$\frac{9250}{87}$$
The current drawn by the motor is approximately 61.3849 A.

Therefore, the answers are:
1. The apparent power drawn by the motor is 42.529 kVA.
2. The reactive power generated by the motor is 20.969 kVAr.
3. The current drawn by the motor is 61.3849 A.
1. The apparent power drawn by the motor is 42.529 kVA. 2. The reactive power generated by the motor is 20.969 kVAr. 3. The current drawn by the motor is 61.3849 A.

phase, \( 400 \mathrm{~V}, 37 \mathrm{~kW} \) motor runs at a power factor of 0.87 . Determine: the apparent power drawn by the motor (Ans: 42.529 kVA ) 37 the reactive power generated by the motor. (Ans: 20.969 kVAr ) the current drawn by the motor. (Ans: 61.3849 A )

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