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

# Magnetic vs electric circuits, work law and Ohm's law

Electrical Machines I · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2079 Chaitra, 2+3+3 marks
- 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-electric-circuit-similarities-laws
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-1

## Question

List out the similarities between magnetic circuit and electric circuit. Deduce work law and Ohm's law for magnetic circuit.

## Short answer

MMF (NI) corresponds to EMF, flux to current, and reluctance (l/μA) to resistance. Ampère’s work law gives ∮ H·dl = NI; magnetic Ohm’s law is φ = F/S, where S = l/(μA).

## Answer

A **magnetic circuit** is the closed path followed by magnetic flux, e.g. the iron core of a transformer with its air gaps. It behaves much like an electric circuit, with mmf driving flux against reluctance.

#### Similarities

| Magnetic circuit | Electric circuit |
|---|---|
| MMF, $F = NI$ (AT) | EMF, $E$ (V) |
| Flux, $\phi$ (Wb) | Current, $I$ (A) |
| Reluctance, $S = l/\mu A$ (AT/Wb) | Resistance, $R = \rho l/A$ (Ω) |
| Permeance, $1/S$ | Conductance, $1/R$ |
| Permeability, $\mu$ | Conductivity, $\sigma = 1/\rho$ |
| Flux density, $B = \phi/A$ | Current density, $J = I/A$ |
| Field intensity, $H$ (AT/m) | Electric field, $E$ (V/m) |
| $\phi = F/S$ | $I = E/R$ |
| Series: $S = S_1 + S_2 + \dots$ | Series: $R = R_1 + R_2 + \dots$ |

Differences (in brief): flux does not actually flow and needs no energy to keep it up, while current does; $\mu$ changes with B (saturation), while R is nearly constant.

#### Work law (Ampere's circuital law)

The work done in moving a unit magnetic pole once round a closed path equals the ampere-turns enclosed:

$$
\oint \vec H \cdot d\vec l = NI
$$

For a path made of sections in which H is constant,

$$
H_1 l_1 + H_2 l_2 + \dots = NI = F
$$

So the total mmf equals the sum of the "magnetic drops" $Hl$ round the circuit, just as KVL says the emf equals the sum of IR drops.

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

Take a ring of mean length $l$, area $A$, permeability $\mu = \mu_0\mu_r$, with $N$ turns carrying $I$. From the work law $H = NI/l$. Then

$$
\begin{aligned}
B &= \mu H = \frac{\mu NI}{l} \\
\phi &= BA = \frac{\mu A NI}{l} = \frac{NI}{l/(\mu A)}
\end{aligned}
$$

$$
\phi = \frac{F}{S}, \quad S = \frac{l}{\mu_0 \mu_r A}
$$

i.e. **flux = mmf / reluctance**, the magnetic form of $I = V/R$.

## Check yourself

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

1. Which pairing of magnetic and electric quantities is correct?
   A. Flux - voltage
   B. Reluctance - resistance
   C. MMF - current
   D. Permeability - resistivity
   Answer: B. Flux pairs with current, mmf with emf, reluctance with resistance, permeability with conductivity. (Key point: Analogous quantities)

2. Ampere's circuital (work) law states that the line integral of H round a closed path equals:
   A. The flux linked
   B. The ampere-turns enclosed, NI
   C. Zero always
   D. The flux density B
   Answer: B. The closed integral of H.dl = NI, analogous to KVL: total mmf equals the sum of Hl drops. (Key point: Work law)

3. Deducing phi = BA with B = mu NI / l gives:
   A. phi = F x S
   B. phi = F/S with S = l/(mu0 mu_r A)
   C. phi = S/F
   D. phi = F/(mu A l)
   Answer: B. phi = NI / (l/(mu A)), i.e. flux = mmf / reluctance. (Key point: Ohm's law)

4. A key difference between the two circuits is:
   A. Reluctance never changes with B
   B. Permeability changes with B (saturation) while R is nearly constant
   C. Flux flows and uses energy
   D. Magnetic circuits have no series connections
   Answer: B. Iron saturates so mu varies; also flux does not truly flow and needs no energy to be maintained. (Key point: Differences)

## Close variants set in other exams

- [Magnetic circuit, similarities with electric circuit, Ohm's law](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Amagnetic-circuit-define-similarities-ohms-law) — 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