---
title: "Inductance, series mutual flux aiding"
subject: "Basic Electrical Engineering"
chapter: 4
key: "semester_1/basic_electrical_engineering:inductance-series-aiding"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/inductance-series-aiding
site: BCT Engineering
---

# Inductance, series mutual flux aiding

Basic Electrical Engineering · Chapter 4: Inductance & Capacitance in Electric Circuits

- Asked in: 2074 Chaitra, 4 marks
- Video: [Electrical Engineering: Ch 14 Magnetic Coupling (22 of 55) Series Aiding vs Series Opposing Connect.](https://www.youtube.com/watch?v=PBu3FaK6WLA) — Michel van Biezen
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/inductance-series-aiding
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-4

## Question

What is inductance? Derive the expression for two inductances in series, with mutual flux aiding each other.

## Short answer

Inductance is a coil’s opposition to current change, measured as flux linkage per unit current. For two coupled coils in series with mutual flux aiding, the same current induces additive emfs; equivalent inductance L_eq = L1 + L2 + 2M.

## Answer

**Inductance** is the property of a coil by which it opposes any change of current through it. It is measured as flux linkage per unit current: L = Nφ / I, in henry (H). One henry is the inductance of a coil that induces 1 V when the current changes at 1 A/s.

#### Series connection, mutual flux aiding

Let two coils of self inductance L₁ and L₂ and mutual inductance M be connected in series so that the current flows in the same sense through both. Then the flux of each coil adds to the flux of the other (aiding).

```text
   i →        L1              L2
 o------( coil 1 )------( coil 2 )------o
             \_______ M _______/
        (both fluxes in the same direction)
```

The same current i flows in both coils. The emf induced in each coil has two parts: self-induced and mutually induced.

- Coil 1: e₁ = L₁ di/dt + M di/dt
- Coil 2: e₂ = L₂ di/dt + M di/dt

Total induced emf (opposing the applied voltage):

e = e₁ + e₂ = (L₁ + L₂ + 2M) di/dt

If the combination is replaced by one equivalent inductance L_eq, then e = L_eq di/dt. Comparing,

**L_eq = L₁ + L₂ + 2M**

For opposing flux (the current enters the dotted ends in opposite senses), the sign of M changes: L_eq = L₁ + L₂ − 2M.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does inductance measure?
   A. Energy per charge
   B. Flux linkage per unit current
   C. Voltage per ohm
   D. Charge per volt
   Answer: B. L = N phi / I. (Key point: Inductance)

2. In aiding series connection, what is the emf in each coil?
   A. Self minus mutual
   B. Self plus mutual: L di/dt + M di/dt
   C. Only mutual
   D. Only self
   Answer: B. Fluxes add so each coil has both terms. (Key point: Induced emf)

3. What is L_eq?
   A. L1 + L2 + 2M
   B. L1L2/(L1 + L2)
   C. L1 + L2 + M
   D. L1 + L2 - 2M
   Answer: A. e = (L1 + L2 + 2M) di/dt. (Key point: Result)

4. What happens for opposing flux?
   A. L_eq = 0
   B. L_eq = L1 + L2
   C. L_eq = L1 + L2 + 2M
   D. L_eq = L1 + L2 - 2M
   Answer: D. Sign of M changes. (Key point: Opposing)

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