---
title: "Magnetic circuit, similarities with electric circuit, Ohm's law"
subject: "Electrical Machines I"
chapter: 1
key: "semester_4/electrical_machines_i:magnetic-circuit-define-similarities-ohms-law"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/magnetic-circuit-define-similarities-ohms-law
site: BCT Engineering
---

# Magnetic circuit, similarities with electric circuit, Ohm's law

Electrical Machines I · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2073 Bhadra, 8 marks
- Video: [magnetic circuit and ohms law||Chapter -1 || Electric machine || ioe](https://www.youtube.com/watch?v=pnXSSZ06_T0) — E Learning
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/magnetic-circuit-define-similarities-ohms-law
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/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 the closed path of magnetic flux. It is analogous to an electric circuit: flux φ corresponds to current, mmf F = NI to emf, reluctance S = l/(μA) to resistance. Ohm's law for the magnetic circuit states φ = F/S.

## Answer

A **magnetic circuit** is the closed path followed by magnetic flux. It is usually made of high-permeability iron (sometimes with air gaps) and is excited by a coil carrying current, e.g. the core of a transformer, relay or electrical machine.

```text
     +-----------------+
     |    phi -->      |
   ==|== N turns       |  iron core,
   ==|== I             |  mean length l,
     |                 |  area A
     +-----------------+
```

#### Similarities between magnetic and electric circuits

| Magnetic circuit | Electric circuit |
|---|---|
| Flux $\phi$ (Wb) | Current $I$ (A) |
| MMF $F = NI$ (AT) | EMF $E$ (V) |
| Reluctance $S = l/(\mu_0\mu_r A)$ | Resistance $R = \rho l / A$ |
| Permeance $= 1/S$ | Conductance $= 1/R$ |
| Permeability $\mu$ | Conductivity $\sigma$ |
| Flux density $B = \phi/A$ | Current density $J = I/A$ |
| Magnetic field strength $H$ | Electric field strength $E$ |
| $\phi = F/S$ | $I = E/R$ |
| Reluctances add in series; permeances add in parallel | Resistances add in series; conductances add in parallel |
| Kirchhoff's laws: $\sum \phi = 0$ at a node, $\sum F = \sum \phi S$ in a loop | $\sum I = 0$, $\sum E = \sum IR$ |

Points of difference: flux does not truly flow, no energy is spent to maintain a constant flux (but $I^2R$ loss occurs with current), and $\mu$ is not constant because iron saturates, while R is nearly constant.

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

Take a uniform ring of mean length $l$ (m), area $A$ (m²), relative permeability $\mu_r$, wound with $N$ turns carrying $I$.

By Ampere's circuital law, $\oint H\,dl = NI$, so

$$
H = \frac{NI}{l}
$$

Then

$$
\begin{aligned}
B &= \mu_0\mu_r H = \frac{\mu_0\mu_r NI}{l} \\
\phi &= BA = \frac{\mu_0\mu_r A\, NI}{l} \\
\phi &= \frac{NI}{\dfrac{l}{\mu_0\mu_r A}} = \frac{F}{S}
\end{aligned}
$$

So **flux = mmf ÷ reluctance**, which is Ohm's law for the magnetic circuit ($I = E/R$). For a composite circuit (iron + air gap) the reluctances add: $\phi = NI/(S_i + S_g)$.

## Check yourself

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

1. A magnetic circuit is:
   A. A closed path followed by magnetic flux
   B. The path of electric current
   C. A winding only
   D. An air gap
   Answer: A. It is the closed flux path, usually high-permeability iron possibly with air gaps, excited by a coil. (Key point: Definition)

2. Which statement is correct?
   A. Permeance is analogous to resistance
   B. Flux density is analogous to current density, and reluctance to resistance
   C. MMF is analogous to current
   D. Flux is analogous to emf
   Answer: B. B = phi/A mirrors J = I/A; S mirrors R; permeance mirrors conductance. (Key point: Analogies)

3. For a composite circuit (iron plus air gap in series):
   A. Permeances add
   B. Reluctances add: phi = NI/(S_i + S_g)
   C. Fluxes add
   D. Reluctances multiply
   Answer: B. Series reluctances add, just like series resistances. (Key point: Series rule)

4. The magnetic Ohm's law is:
   A. F = phi / S
   B. phi = F / S
   C. S = phi F
   D. phi = S / F
   Answer: B. Flux = mmf / reluctance, the analogue of I = E/R. (Key point: Ohm's law)

## Close variants set in other exams

- [Magnetic vs electric circuits, work law and Ohm's law](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Amagnetic-electric-circuit-similarities-laws) — Electrical Machines I, chapter 1, asked 2×

## Related in other subjects

- [Magnetic circuit, analogy with electric circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Amagnetic-circuit-ohms-law) — Electrical Machines, chapter 1