https://file.aiquickdraw.com/mathbot/file/1730119151061pm7ltdjq.jpg

To find the load current, we can follow these steps:

### Step 1: Convert Horsepower to Watts
Given:
- Power (\( P \)) in HP = 7.5 HP
- Conversion factor: \( 1 \, \text{HP} = 746 \, \text{W} \)

\[
P = 7.5 \times 746 = 5595 \, \text{W}
\]

### Step 2: Account for Motor Efficiency
Given the efficiency (\( \eta \)) is 80% (or 0.8), we can calculate the input power (\( P_{\text{input}} \)):

\[
P_{\text{input}} = \frac{P}{\eta} = \frac{5595}{0.8} = 6993.75 \, \text{W}
\]

### Step 3: Calculate Apparent Power (S)
The apparent power (\( S \)) in a three-phase system is given by:

\[
S = \frac{P_{\text{input}}}{\text{power factor}} = \frac{6993.75}{0.8} = 8742.19 \, \text{VA}
\]

### Step 4: Calculate Line Current (I)
In a three-phase system, the current \( I \) can be found using:

\[
I = \frac{S}{\sqrt{3} \cdot V}
\]

Where:
- \( V = 220 \, \text{V} \) (line voltage)
- \( \sqrt{3} \approx 1.732 \)

Substituting the values:

\[
I = \frac{8742.19}{1.732 \times 220} = \frac{8742.19}{380.64} \approx 22.96 \, \text{A}
\]

### Answer
The closest option is:

**c. 23.0 A**

Would you like further details or have any questions?

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Here are five related questions:
1. How is the efficiency of a motor related to its power consumption?
2. Why do we use apparent power in three-phase calculations?
3. How do we convert between different units of power, like HP and watts?
4. What impact does the power factor have on the current in three-phase systems?
5. How can power factor correction improve efficiency in electrical systems?

**Tip:** In three-phase systems, knowing the line voltage and apparent power helps simplify current calculations.

Uma tensão trifásica de 60HZ, 220V, alimenta o motor elétrico de uma bomba d' água que possui as seguintes características: potência nominal de 7,5 HP, fator de potência de 0,8 e rendimento de 80%. Sabendo-se que 1HP = 746W e que uma rede elétrica de tensão trifásica de 60 Hz, 220V, alimenta esta bomba. O valor da corrente de carga é:

Learn how to calculate the load current for a 7.5 HP motor operating at 220V, 60Hz with three-phase power. This problem involves understanding electrical concepts such as efficiency, power factor, and current calculations in three-phase systems, suitable for undergraduate engineering students.

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