---
title: "Equivalent inductance of two coupled coils in parallel"
subject: "Basic Electrical Engineering"
chapter: 4
key: "semester_1/basic_electrical_engineering:coupled-coils-4h-6h-parallel-3h"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/coupled-coils-4h-6h-parallel-3h
site: BCT Engineering
---

# Equivalent inductance of two coupled coils in parallel

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

- Asked in: 2068 Shrawan, 2 marks
- Video: [11. MUTUALLY COUPLED INDUCTANCE IN PARALLEL COIL](https://www.youtube.com/watch?v=9wOFz6PoXTE) — Electrical Tutorial
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/coupled-coils-4h-6h-parallel-3h
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-4

## Question

Two coils of inductance of 4 and 6 Henry are connected in parallel. If their mutual inductance is 3 Henry, calculate the equivalent inductance of the combination if mutual inductance: i) Supports the self inductance, and ii) Oppose the self inductance

## Short answer

For coupled coils in parallel, L_eq = (L1L2 − M²)/(L1 + L2 ∓ 2M). Using L1=4 H, L2=6 H, M=3 H: aiding (minus) yields 3.75 H; opposing (plus) yields 0.9375 H.

## Answer

For two coupled coils in parallel, with mutual inductance M:

L_eq = (L₁L₂ − M²) / (L₁ + L₂ ∓ 2M)

The minus sign in the denominator is for aiding (mutual flux supports self flux). The plus sign is for opposing.

Given L₁ = 4 H, L₂ = 6 H, M = 3 H.

- L₁L₂ − M² = 24 − 9 = 15
- L₁ + L₂ = 10

#### i) Mutual inductance supports (aiding)

L_eq = 15 / (10 − 2×3) = 15 / 4 = **3.75 H**

#### ii) Mutual inductance opposes

L_eq = 15 / (10 + 2×3) = 15 / 16 = **0.9375 H**

**Answer:** 3.75 H (aiding) and 0.9375 H (opposing).

## Check yourself

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

1. Which formula applies?
   A. L1L2/(L1 + L2)
   B. (L1L2 - M^2)/(L1 + L2 -/+ 2M)
   C. (L1 + L2)/(L1L2)
   D. L1 + L2 + 2M
   Answer: B. Minus for aiding, plus for opposing. (Key point: Formula)

2. Aiding value?
   A. 15 H
   B. 2.4 H
   C. 0.9375 H
   D. 3.75 H
   Answer: D. 15/(10 - 6). (Key point: Aiding)

3. Opposing value?
   A. 3.75 H
   B. 0.9375 H
   C. 1.5 H
   D. 15 H
   Answer: B. 15/(10 + 6). (Key point: Opposing)

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