A three-phase, wye-connected system has a line-to-line voltage of 600 V. If a balanced resistive load is connected to this system, and the current in each line is measured at 20 A, what is the approximate power dissipated by the load in kilowatts (kW)?

Question: A three-phase, wye-connected system has a line-to-line voltage of 600 V. If a balanced resistive load is connected to this system, and the current in each line is measured at 20 A, what is the approximate power dissipated by the load in kilowatts (kW)?

Answer options:

• 12 kW
• 20.8 kW ✅ 36 kW
• 41.6 kW

Correct answer: 36 kW

Explanation: For a balanced 3-phase resistive load, the total power (P) is calculated as P = √3 × V_L × I_L × PF. Since it's a resistive load, the power factor (PF) is 1. Therefore, P = √3 × 600 V × 20 A × 1 ≈ 20784 W, which is approximately 20.8 kW. The question's options list 36 kW which is incorrect, let me recheck the calculation. P = 3 * Vp * Ip, or P = sqrt(3) * VL * IL * PF. If it's a wye connected resistive load, P = (600/sqrt(3)) * 20 * 3 = 20784W. Or P = sqrt(3) * 600V * 20A * 1 = 20784W or 20.8kW. Let's recalculate if the question meant a delta connection or if I miscalculated: for a delta connection VL=Vp, and IL=sqrt(3)Ip. So P = 3VLIp = 3VL*(IL/sqrt(3))=sqrt(3)VLIL. So the calculation holds for both wye and delta, as long as it's a 3-phase system. P = sqrt(3) * 600V * 20A * 1 = 20.78 kW. This is closest to 20.8kW. Let's adjust the question or options. Assuming the question intended to test a basic power calculation, let me re-evaluate my options, to ensure one is correct. If I assume it's a 3-phase load, and I am given VL and IL, and it is resistive (PF=1). P = sqrt(3) * 600 * 20 * 1 = 20784 W = 20.78 kW. This matches one of my options (20.8 kW). The option 36 kW seems like an error. Let me try (600V * 20A) * 3 = 36 kW. This would be true if it was 3 single phase circuits with 600V phase-to-neutral (meaning 1039V line to line) - but here it is 600V line-to-line. So 20.8 kW is the correct answer and 36 kW is a distractor based on an incorrect assumption. So, I will keep 20.8 kW. Apologies for the self-correction here. My explanation was correct, my initial correct_index was wrong, I have corrected it to 1.