Circuitos Magneticos Ejercicios — Resueltos

Problema: Un anillo toroidal (dona) hecho de un material magnético con permeabilidad relativa $\mu_r = 1000$ tiene las siguientes dimensiones:

Se pide: a) Calcular la reluctancia del núcleo. b) Calcular el flujo magnético ($\phi$). c) Calcular la densidad de flujo ($B$).

Resolución:

Paso 1: Convertir unidades al Sistema Internacional (SI). circuitos magneticos ejercicios resueltos

Paso 2: Calcular la Permeabilidad Magnética ($\mu$). $$ \mu = \mu_0 \cdot \mu_r = (4\pi \times 10^-7) \cdot 1000 = 4\pi \times 10^-4 , \textH/m $$

Paso 3: Calcular la Reluctancia ($\mathcalR$). $$ \mathcalR = \fracl\mu \cdot A = \frac0.6283(4\pi \times 10^-4) \cdot (2 \times 10^-4) $$ $$ \mathcalR = \frac0.628325.13 \times 10^-8 \approx 2.5 \times 10^6 , \textAv/Wb , (

A magnetic circuit is analogous to an electric circuit. Understanding these analogies is key. Problema: Un anillo toroidal (dona) hecho de un

| Electric Circuit | Magnetic Circuit | Unit (Magnetic) | | :--- | :--- | :--- | | Electromotive Force (EMF) $E$ (Volts) | Magnetomotive Force (MMF) $\mathcalF = N \cdot I$ | Ampere-turns (At) | | Current $I$ (Amperes) | Magnetic Flux $\Phi$ (Webers) | Wb | | Resistance $R = \frac\rho \cdot lA$ | Reluctance $\mathcalR = \fracl\mu \cdot A$ | At/Wb | | Conductance $G = 1/R$ | Permeance $\mathcalP = 1/\mathcalR$ | Wb/At | | Ohm’s Law: $E = I \cdot R$ | Hopkinson’s Law: $\mathcalF = \Phi \cdot \mathcalR$ | - | | Kirchhoff’s Voltage Law (KVL) | Kirchhoff’s MMF Law: $\sum \mathcalF = \sum \Phi \cdot \mathcalR$ | - | | Kirchhoff’s Current Law (KCL) | Kirchhoff’s Flux Law: $\sum \Phi_\textin = \sum \Phi_\textout$ | - |

Critical Material Property: Permeability $\mu = \mu_r \cdot \mu_0$, where $\mu_0 = 4\pi \times 10^-7$ H/m.

Magnetic circuits are the magnetic analog of electric circuits. They form the basis for the design and analysis of electromagnetic devices such as transformers, electric motors, generators, relays, and inductors. Understanding how to solve magnetic circuit problems is essential for predicting flux, magnetic field intensity, and the required magnetomotive force (MMF). Se pide: a) Calcular la reluctancia del núcleo

This report presents:

Problem:
A magnetic circuit consists of an iron core (mean length ( l_core = 0.3 ) m, ( A = 4 \times 10^-4 ) m², ( \mu_r = 1000 )) and an air gap of length ( l_g = 1 ) mm (( A_g = A )). The coil has ( N = 500 ) turns. Find the current ( I ) needed to produce a flux density ( B_g = 0.8 ) T in the air gap. Neglect fringing.

Solution:

Answer: ( I \approx 1.66 ) A.

(Note: The air gap dominates reluctance despite its small length.)