Series connection effect: If multiple inductors are connected in series with negligible mutual coupling, does the total inductance increase compared to any single inductor?

Introduction / Context:
Understanding how inductors combine is crucial for filter design, power electronics, and RF circuits. In series, each inductor contributes an induced voltage proportional to L * di/dt. The contributions add, producing a larger equivalent inductance than any individual element—assuming negligible mutual coupling.

Given Data / Assumptions:

• Series connection; same current flows through each inductor.
• Negligible mutual inductance between coils.
• Ideal lumped components.

Concept / Approach:
The total voltage across series inductors is v_T = (L1 + L2 + …) * di/dt. Equating to v_T = L_T * di/dt yields L_T = L1 + L2 + …. Because each L_k is positive, L_T is necessarily greater than any single L_k. If coupling exists, M terms can modify L_T up or down depending on winding orientation; the “increase” claim is assured under negligible coupling.

Step-by-Step Solution:

Verification / Alternative check:
Practical check with two separated coils on a bench shows the LCR meter reading increases when placed in series compared to either coil alone.

Why Other Options Are Wrong:
“Incorrect” conflicts with basic series behavior. Constraints like equal values, ferrite cores, or temperature conditions are not required for the fundamental addition rule without coupling.

Common Pitfalls:
Overlooking mutual coupling in dense layouts; coupling can reduce or increase L_T, so layout and orientation matter.

Final Answer:
Correct