Determine the current flow in a 480-volt, 3-phase, 10-horsepower motor circuit after the circuit has been corrected to 100% power factor.
The Correct Answer and Explanation is:
To determine the current flow in a 480-volt, 3-phase, 10-horsepower (hp) motor circuit after correcting the circuit to 100% power factor, follow these steps:
Step 1: Convert horsepower to watts
The power rating of the motor is 10 horsepower. To convert horsepower to watts, use the conversion factor:
[
1 \, \text{hp} = 746 \, \text{W}
]
[
\text{Power in watts} = 10 \, \text{hp} \times 746 \, \text{W/hp} = 7460 \, \text{W}
]
Step 2: Calculate the total power in a 3-phase system
For a 3-phase system, the total power (P) is related to the voltage (V), current (I), and power factor (pf) by the following equation:
[
P = \sqrt{3} \times V \times I \times \text{pf}
]
Given that the power factor is corrected to 100%, ( \text{pf} = 1 ). Now, solve for the current (I):
[
I = \frac{P}{\sqrt{3} \times V \times \text{pf}}
]
Substitute the known values:
[
I = \frac{7460 \, \text{W}}{\sqrt{3} \times 480 \, \text{V} \times 1}
]
[
I = \frac{7460}{480 \times 1.732} = \frac{7460}{831.36} \approx 8.97 \, \text{A}
]
Step 3: Conclusion
The current flow in the motor circuit is approximately 8.97 amps.
Explanation
The current calculation for a 3-phase motor circuit depends on the power supplied, the voltage of the system, and the power factor. The motor’s power rating was first converted to watts to ensure that we were working with the appropriate units. In a 3-phase system, the power is given by the formula involving the square root of 3, the voltage, and the current, and it also considers the power factor. By correcting the power factor to 100%, the current calculation is straightforward since the power factor is now equal to 1, simplifying the formula. Thus, the current drawn by the motor in a 480-volt, 3-phase system at 10 horsepower is approximately 8.97 amps.