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:
Write v_total = v_1 + v_2 + ... = (L_1 + L_2 + ...) * di/dt for common current i.Identify L_total from proportionality between v_total and di/dt.Conclude L_total equals the sum of individual inductances.
Verification / Alternative check:
Measure reactance at a frequency f: X_L,total = 2 * π * f * L_total. If L_total = L_1 + L_2, then X_L,total = X_L1 + X_L2, consistent with measurement.
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:
equal to the sum of the individual inductance values
Discussion & Comments