A 100 KVA three-phase alternator is supplying power at 440 V and running at full load power, with 0.8 as the power factor. Line current of the alternator is:

Explanation:

Problem Statement:

A 100 KVA three-phase alternator is supplying power at 440 V and running at full load power, with 0.8 as the power factor. Line current of the alternator is:

To solve this problem, we need to calculate the line current of the alternator using the given values. Here are the steps involved:

Given Data:

• Apparent Power (S) = 100 KVA = 100,000 VA
• Voltage (V) = 440 V
• Power Factor (pf) = 0.8

Step-by-Step Solution:

1. Calculate Real Power (P):

The real power (P) can be found using the formula:

P = S * pf

Substitute the given values:

P = 100,000 VA * 0.8

P = 80,000 W (or 80 kW)

2. Calculate Line Current (I):

For a three-phase system, the line current (I) can be found using the formula:

I = S / (√3 * V)

Substitute the given values:

I = 100,000 VA / (√3 * 440 V)

√3 ≈ 1.732

I = 100,000 VA / (1.732 * 440 V)

I ≈ 130.54 A

Therefore, the line current of the alternator is approximately 130.54 A.

Correct Option Analysis:

The correct option is Option 2: 164 A.

However, our detailed calculations indicate that the correct line current should be approximately 130.54 A. Let's re-evaluate the problem to ensure accuracy:

Re-evaluation:

Given that the correct option is stated to be 164 A, we need to recheck our calculations:

Revised Step-by-Step Solution:

1. Calculate Apparent Power per Phase (S_phase):

S_phase = S / 3

Substitute the given values:

S_phase = 100,000 VA / 3

S_phase = 33,333.33 VA

2. Calculate Line Current (I_phase):

For a single-phase system, the line current (I_phase) can be found using the formula:

I_phase = S_phase / V

Substitute the given values:

I_phase = 33,333.33 VA / 440 V

I_phase ≈ 75.76 A

3. Calculate Total Line Current (I_total):

For a three-phase system, the total line current (I_total) is:

I_total = I_phase * √3

Substitute the given values:

I_total = 75.76 A * 1.732

I_total ≈ 131.14 A

Even after re-evaluation, our detailed calculations indicate that the correct line current should be approximately 131.14 A. The discrepancy with the correct option (164 A) suggests that there might be an additional factor or consideration that is not immediately apparent from the given data.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 100 A

This option is significantly lower than the calculated value of approximately 131.14 A and does not match the correct option provided.

Option 2: 164 A

This option, stated as correct, is higher than the calculated value of approximately 131.14 A. The discrepancy indicates that there might be additional factors or considerations not immediately apparent from the given data.

Option 3: 200 A

This option is significantly higher than the calculated value of approximately 131.14 A and does not match the correct option provided.

Option 4: 284 A

This option is much higher than the calculated value of approximately 131.14 A and does not match the correct option provided.

Conclusion:

Understanding the differences between the provided options and the calculated values is essential for correctly identifying the operational characteristics of the alternator. Despite the detailed calculations indicating a line current of approximately 131.14 A, the correct option provided is 164 A, suggesting that additional factors or considerations may be influencing the final value.