What is an Electric Circuit?
An electric circuit is a closed path that allows electric current (I) to flow due to an applied electromotive force (EMF). It typically includes a source (battery or supply), conductors, and loads (resistors, capacitors, inductors).
- Driving force: EMF, measured in volts (V).
- Flow quantity: Current, measured in amperes (A).
- Opposition: Resistance (R), measured in ohms (Ω). Conductance (G) = 1/R.
- Key laws: Ohm’s Law (I = V/R), Kirchhoff’s Voltage Law (KVL), Kirchhoff’s Current Law (KCL).
- Energy: Power dissipates as heat in resistive elements while current flows.
What is a Magnetic Circuit?
A magnetic circuit is a closed path for magnetic flux (Φ), often formed by a high-permeability core (iron, silicon steel) with coils that create flux when energized. Used in transformers, motors, relays, and inductors.
- Driving force: Magnetomotive force (MMF), measured in ampere-turns (AT).
- Flow quantity: Magnetic flux, measured in webers (Wb).
- Opposition: Reluctance (ℜ), measured in AT/Wb. Permeance (𝒫) = 1/ℜ.
- Analogue to Ohm’s Law: Φ = MMF / ℜ (Hopkinson’s Law).
- Energy: Ideally little energy to maintain flux once established (real devices have core & copper losses).
Key Differences Between Magnetic and Electric Circuits
| Basis | Electric Circuit EMF–Current–Resistance | Magnetic Circuit MMF–Flux–Reluctance |
|---|---|---|
| Definition | Closed path for electric current. | Closed path for magnetic flux. |
| Driving force | Electromotive force (EMF), V | Magnetomotive force (MMF), AT |
| Flow quantity | Current (I), A | Flux (Φ), Wb |
| Opposition | Resistance (R), Ω | Conductance G = 1/R | Reluctance (ℜ), AT/Wb | Permeance 𝒫 = 1/ℜ |
| Material property | Resistivity (ρ) / Conductivity (σ) | Reluctivity (1/μ) / Permeability (μ) |
| Density / Intensity | Current density J = I/A | Flux density B = Φ/A (T) |
| Field relation | Electric field E = V/d | Magnetic field H = NI/l |
| Ohm-like law | I = EMF / R | Φ = MMF / ℜ |
| Circuit laws | KVL, KCL | MMF loop law; flux junction law (analogous to KVL/KCL) |
| Energy behavior | Continuous dissipation in resistances | Ideally minimal to maintain flux; real cores lose energy via hysteresis & eddy currents |
| What “moves” | Electrons (charge carriers) | No particles move; magnetic domains align to establish flux |
| Insulators | Many true insulators (PVC, rubber, dry air) | No perfect magnetic insulator; flux can pass through air, glass, etc. |
| Linearity | R ≈ constant (temperature affects ρ) | ℜ varies with B due to saturation; hysteresis present in ferromagnets |
Design Notes & Practical Insights
- Air gaps drastically increase reluctance and reduce flux; they also linearize the B–H curve in inductors.
- Leakage & fringing cause flux to stray outside intended paths—account for them in precise designs.
- Losses matter: copper (I²R) losses in windings; hysteresis and eddy current losses in cores.
- Analogy limits: Treating magnetic paths exactly like resistors fails near saturation and when frequency-dependent losses dominate.
Frequently Asked Questions
1) Is MMF the magnetic equivalent of voltage?
Yes. MMF “pushes” magnetic flux around a magnetic circuit just as voltage drives current in an electric circuit.
2) What is the exact analogue of resistance?
Reluctance (ℜ) is the magnetic analogue of resistance. A high-permeability core has low reluctance.
3) Do magnetic circuits follow Kirchhoff’s laws?
There are analogous loop and node laws: the algebraic sum of MMFs around a closed magnetic path is zero, and the algebraic sum of fluxes at a junction is zero (neglecting leakage).
4) Why does resistance stay almost constant but reluctance changes?
Because resistivity (ρ) varies mainly with temperature, while permeability (μ) of ferromagnets changes with flux level (saturation) and has hysteresis.
5) Where is this used in practice?
Transformers, motors, solenoids, inductors, magnetic sensors, and relays are all designed using magnetic-circuit models.