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To solve this problem, we need to calculate the line current \( I_L \) for a 3-phase motor, given the following parameters:

- Power \( P = 30 \, \text{kW} = 30,000 \, \text{W} \)
- Power factor \( \text{pf} = 0.85 \, \text{(lagging)} \)
- Line voltage \( V_L = 440 \, \text{V} \)

For a 3-phase motor, the total power \( P \) is given by the formula:

\[
P = \sqrt{3} \times V_L \times I_L \times \text{pf}
\]

We can rearrange this formula to solve for the line current \( I_L \):

\[
I_L = \frac{P}{\sqrt{3} \times V_L \times \text{pf}}
\]

Now, substituting the known values into the equation:

\[
I_L = \frac{30,000}{\sqrt{3} \times 440 \times 0.85}
\]

Let me calculate this.The line current required for the 30 kW, 3-phase motor with a power factor of 0.85 and a line voltage of 440 V is approximately **46.31 A**.

Would you like further details or have any questions?

Here are 5 related questions for further understanding:
1. How does the power factor affect the efficiency of a 3-phase motor?
2. What is the difference between line current and phase current in a 3-phase system?
3. How would the line current change if the motor's power factor was 1 (unity)?
4. How can you improve the power factor of an electric motor?
5. What are the potential consequences of operating a motor with a low power factor?

**Tip:** In 3-phase systems, the power factor plays a critical role in determining the current drawn by the load. Higher power factors result in lower currents for the same power output, improving efficiency.

Calculate the line current required for a 30KW 3 PHASE motor having a power factor of 0.85 lagging if it is connected to a balanced source with line voltage of 440V.

Calculate the line current for a 30KW 3-phase motor with a 0.85 lagging power factor and a line voltage of 440V. This problem covers the power calculation for balanced AC circuits and is suitable for electrical engineering students.

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