Series inductors: for uncoupled inductors in series, what is the total inductance of the circuit?

Introduction / Context:Inductors in series combine to increase total opposition to changes in current. In the absence of mutual coupling, the equivalent inductance is the arithmetic sum of the individual inductances, a result frequently used when building inductors from series sections or estimating choke values.

Given Data / Assumptions:

• Two or more inductors connected in series.
• Negligible mutual coupling (M ≈ 0) or physically separated coils.
• Linear operation, no saturation.

Concept / Approach:

• Voltage across an inductor: v = L * di/dt.
• Series connection: total voltage v_total = Σ L_k * di/dt = (Σ L_k) * di/dt.
• Therefore L_total = Σ L_k.

Step-by-Step Reasoning:

Verification / Alternative check:

Why Other Options Are Wrong:

• Sum of inductive-reactances: That depends on frequency and is not an intrinsic L-combination rule.
• Less than the smallest inductor: That is the parallel rule for inductors, not series.
• Source voltage divided by total current: That defines impedance, not inductance.
• None of the above: Incorrect because the sum rule is correct.

Common Pitfalls:

• Forgetting mutual inductance terms when coils are magnetically coupled (L_total = L_1 + L_2 ± 2M).
• Confusing series and parallel combination rules.

Final Answer: