Inductors in Networks: Series vs. Parallel Combination Rule Consider the statement: “Inductors add in parallel.” Decide whether this statement is correct in the context of ideal components and steady-state AC analysis.

Introduction / Context:
Combining inductors is common in filter and power designs. Knowing when inductances add directly helps avoid design mistakes and interpret equivalent circuits correctly. The rule differs for series and parallel connections, similar to resistors but with an important inversion in parallel.

Given Data / Assumptions:

• Ideal inductors with inductances L1, L2, …
• No mutual coupling (unless explicitly stated otherwise).
• Linear operation in steady-state AC or DC conditions.

Concept / Approach:

For series: inductances add directly. For parallel: the reciprocal inductances add, i.e., the total is smaller than the smallest branch (analogous to resistors but with roles reversed compared to capacitors). With mutual coupling, equivalent inductance can differ, but the basic no-coupling rule stands.

Step-by-Step Solution:

Verification / Alternative check:

Impedance perspective: Z_Lk = j ω L_k. For parallel branches, admittances add: Y_total = Σ (1/Z_Lk) = Σ (1/(j ω L_k)) = (1/j ω) Σ (1/L_k) ⇒ L_eq = 1 / Σ (1/L_k). This matches the reciprocal rule.

Why Other Options Are Wrong:

“True” contradicts the formula. “True only when mutual coupling is present” is misleading; coupling modifies values but does not make parallel addition into simple arithmetic sums. “True for DC, false for AC” is irrelevant; the formula is topological, independent of frequency (aside from reactance magnitude). “Indeterminate without Q” confuses loss with inductance combination rules.

Common Pitfalls:

Assuming capacitors’ rules apply to inductors; in fact, capacitors add in parallel, not inductors. Also, forgetting mutual inductance when coils are magnetically close.

Final Answer:

False