Purely inductive load: If the reactive power of a load is 12 VAR and the load is purely inductive, what is the apparent power S?

Introduction / Context:
AC power consists of real power (P), reactive power (Q), and apparent power (S). In purely reactive elements (ideal inductors or capacitors), real power is zero, while reactive power and apparent power are related directly.

Given Data / Assumptions:

• Load is purely inductive (P = 0).
• Reactive power Q = 12 VAR.
• Standard power triangle relationships apply.

Concept / Approach:
For any load, S^2 = P^2 + Q^2. For a purely inductive load, P = 0, so S = |Q|. Therefore, the apparent power equals the magnitude of the reactive power.

Step-by-Step Solution:
Given P = 0, Q = 12 VARS = sqrt( P^2 + Q^2 )S = sqrt( 0 + 12^2 ) = 12 VA

Verification / Alternative check:
Power factor PF = P / S = 0 for purely reactive loads. With PF = 0, only reactive power remains, so S = |Q| is consistent and mandatory.

Why Other Options Are Wrong:

• 0 VA: Would imply no current or no voltage; not true for reactive power flow.
• 6 VA or 24 VA: Do not follow from S = |Q| for P = 0.

Common Pitfalls:
Confusing the roles of P, Q, and S, or assuming S equals P. In a pure inductor or capacitor, real power is zero but apparent and reactive power are non-zero.

Final Answer:
12 VA