Inductors in series (no coupling): For inductances connected in series with negligible mutual coupling, is the total inductance LT equal to L1 + L2 + L3 + … ?

Introduction / Context:
Just as resistances in series add, inductances in series also add when there is negligible mutual coupling. This rule is used to realize a desired inductance by stacking multiple coils and is fundamental in filter and timing networks. However, coupling between coils can change the result, so the assumption matters.

Given Data / Assumptions:

• Series connection of inductors carrying the same current.
• Negligible mutual inductance (coils are physically separated or oriented to minimize coupling).
• Lumped-element operation.

Concept / Approach:
For series inductors with the same current, total flux linkages sum, yielding an equivalent inductance equal to the arithmetic sum of individual inductances: L_T = L1 + L2 + .... If there is coupling, cross terms involving mutual inductance M appear (L_T = L1 + L2 ± 2M for two coils), which can increase or decrease L_T depending on relative winding sense.

Step-by-Step Solution:

Verification / Alternative check:
Measure with an LCR meter: two inductors 10 mH and 15 mH well separated read about 25 mH in series. Bringing them close and aligned changes the reading due to mutual M—evidence that the simple sum assumes negligible coupling.

Why Other Options Are Wrong:
Requiring an iron core, identical values, or DC operation is unnecessary. The relation is general under the stated assumption. “Incorrect” ignores standard series behavior.

Common Pitfalls:
Ignoring coupling effects; in compact layouts, mutual inductance can be significant and must be accounted for in precision designs.

Final Answer:
Correct