In a balanced three-phase load, how is power shared among the three phases?

Introduction / Context:
Power distribution in balanced three-phase systems is uniform by design. Each phase draws the same power, ensuring symmetrical loading of lines and equipment. Recognizing this principle is crucial for load balancing and system planning.

Given Data / Assumptions:

• Balanced three-phase load (equal Z per phase, 120° spacing).
• Sinusoidal steady-state.

Concept / Approach:
Total three-phase power P_total equals three times the per-phase power P_phase in a balanced system. Therefore each phase consumes an equal share: P_phase = P_total / 3. This holds for Y or Δ connections when the system is truly balanced.

Step-by-Step Reasoning:

Verification / Alternative check:
Using P = √3 * V_line * I_line * cosφ for total power and P_phase = V_phase * I_phase * cosφ, with V_line = √3 V_phase (Y) and I_line = I_phase (Y), you can show P_total = 3 P_phase for balanced systems.

Why Other Options Are Wrong:

• One-third of total: That statement describes the share per phase (P_phase), but the option as written does not make clear equality across phases; the best answer is that each phase has an equal amount.
• Two-thirds of total: Incorrect apportionment.
• Equal to I_L: Power is not “equal to current”; it depends on voltage, current, and power factor.

Common Pitfalls:

• Misreading phrasing—remember each of the three phases shares equally in a balanced system.

Final Answer:
an equal amount of power