Series inductor networks: identify the correct rule for finding the total inductance when multiple inductors are connected in series (assume weak coupling and ideal components).

Introduction / Context:
Combining inductors is a frequent task in filter design, power electronics, and RF circuits. For series connections, engineers need a reliable rule that does not depend on frequency. The question probes your understanding of inductance addition in series networks.

Given Data / Assumptions:

• Inductors are connected in series.
• Mutual coupling is negligible (spaced apart or oriented to minimize coupling).
• Inductors are linear and ideal over the operating current range.

Concept / Approach:
Inductance is a property independent of frequency for an ideal inductor. In series, stored magnetic energies add, and the equivalent inductance is the algebraic sum: L_eq = L1 + L2 + ... + Ln. This contrasts with reactance, which is frequency-dependent: X_L = 2 * π * f * L. You do not add reactances to find total inductance; you add the inductance values directly.

Step-by-Step Solution:
Write the series rule: L_eq = Σ Li.Note that this holds for any frequency because L is a component parameter.Conclude that the correct statement is that total inductance equals the sum of individual inductances.

Verification / Alternative check:
Energy viewpoint: W = 1/2 * L * I^2. For series currents equal in each inductor, energies add, implying L_eq is the sum of Li.

Why Other Options Are Wrong:
Sum of inductive reactances: mixes frequency-dependent reactance with inductance; not the requested quantity.Less than the smallest: characteristic of parallel, not series.Source voltage divided by total current: that yields impedance at a given frequency, not inductance directly.

Common Pitfalls:
Confusing inductance with reactance; overlooking coupling which can add or subtract via mutual inductance terms.

Final Answer:
equal to the sum of the individual inductance values