---
title: "Magnetic circuit, analogy with electric circuit"
subject: "Electrical Machines"
chapter: 1
key: "semester_4/electrical_machines:magnetic-circuit-ohms-law"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/magnetic-circuit-ohms-law
site: BCT Engineering
---

# Magnetic circuit, analogy with electric circuit

Electrical Machines · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2073 Bhadra (old course), 8 marks
- Video: [Electrical Machines | Lecture - 1C | Magnetic Circuits | Magnetic-Electric Circuit Analogy](https://www.youtube.com/watch?v=fjvbJP9pHGo) — Engineering Devotion
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/magnetic-circuit-ohms-law
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-1

## Question

Define magnetic circuit and hence list out the similarities between magnetic and electric circuits. Deduce Ohm's law for magnetic circuit.

## Short answer

A magnetic circuit is a closed flux path. Analogies: mmf ↔ emf, flux ↔ current, reluctance ↔ resistance. From B = μH, H = NI/l, Φ = BA = μA NI/l = NI/(l/(μA)), so Ohm's law: Φ = F/S.

## Answer

A **magnetic circuit** is the closed path followed by magnetic flux, made up of ferromagnetic material (and possibly air gaps), in which the flux is set up by an mmf such as that of a current-carrying coil.

#### Similarities with an electric circuit

| Electric circuit | Magnetic circuit |
|---|---|
| emf $E$ (volt) | mmf $F = NI$ (ampere-turn) |
| Current $I$ (A) | Flux $\Phi$ (Wb) |
| Resistance $R = \dfrac{\rho l}{A}$ | Reluctance $S = \dfrac{l}{\mu A}$ |
| Conductivity $\sigma$ | Permeability $\mu$ |
| Current density $J$ | Flux density $B$ |
| Ohm's law $I = E/R$ | $\Phi = F/S$ |
| Series: $R = R_1 + R_2$ | Series: $S = S_1 + S_2$ |
| Parallel: $G = G_1 + G_2$ | Parallel: $P = P_1 + P_2$ |
| Kirchhoff's laws apply | $\sum\Phi = 0$ at a junction, $\sum F = \sum\Phi S$ around a loop |

**Differences:** current flow dissipates $I^2R$ energy, but a constant flux needs no energy to maintain it. Resistance is nearly constant, but reluctance changes with $B$ because $\mu$ is not constant (saturation). Flux leaks out of the core (leakage, fringing), but current can be kept inside the conductor.

#### Ohm's law for the magnetic circuit

$$
\begin{aligned}
H &= \frac{NI}{l} \\
B &= \mu H = \frac{\mu NI}{l} \\
\Phi &= BA = \frac{\mu A}{l}\,NI = \frac{NI}{l/\mu A}
\end{aligned}
$$

$$
\Phi = \frac{F}{S}\qquad \text{i.e. flux} = \frac{\text{mmf}}{\text{reluctance}}
$$

This is Ohm's law for a magnetic circuit: the flux set up is directly proportional to the mmf and inversely proportional to the reluctance of the path.

## Check yourself

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

1. What is a magnetic circuit?
   A. A closed path of magnetic flux set up by an mmf
   B. A loop of wire carrying current
   C. A circuit of capacitors
   D. A path through air only
   Answer: A. It is the closed path of flux in ferromagnetic material (and gaps) driven by mmf. (Key point: Magnetic circuit definition)

2. In the electric-magnetic analogy, which pair is correct?
   A. Current - mmf
   B. Resistance - flux
   C. emf - flux
   D. Resistance - reluctance
   Answer: D. emf is analogous to mmf, current to flux, resistance to reluctance. (Key point: Analogy mapping)

3. What does Ohm's law for a magnetic circuit state?
   A. Flux = mmf x reluctance
   B. Flux = reluctance / mmf
   C. Flux = mmf / reluctance
   D. mmf = flux / reluctance
   Answer: C. Phi = F/S, derived from Phi = BA = (mu A/l) NI. (Key point: Ohm's law for magnetic circuit)

4. Which is a difference between magnetic and electric circuits?
   A. Reluctance is nearly constant while resistance varies
   B. Flux needs no energy to be maintained, but current dissipates I^2R
   C. Flux cannot leak
   D. Reluctance dissipates power
   Answer: B. A steady flux needs no continuing energy, and reluctance varies with saturation. (Key point: Key difference)

## Related in Electrical Machines

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