Coupled Conductors and Transformers Equation Formula Latex Code and Summary

Coupled Conductors and Transformers

Tags: #physics #coupled #conductors #transformers

Equation

$$M_{12}=M_{21}:=M=k\sqrt{L_1L_2}=\frac{N_1\Phi_1}{I_2}=\frac{N_2\Phi_2}{I_1}\sim N_1N_2 \\ \frac{V_1}{V_2}=\frac{I_2}{I_1}=-\frac{i\omega M}{i\omega L_2+R_{\rm load}}\approx-\sqrt{\frac{L_1}{L_2}}=-\frac{N_1}{N_2} \\ \Phi_{12}=M_{12}I_2 \\ \Phi_{21}=M_{21}I_1$$

Latex Code

                                 M_{12}=M_{21}:=M=k\sqrt{L_1L_2}=\frac{N_1\Phi_1}{I_2}=\frac{N_2\Phi_2}{I_1}\sim N_1N_2 \\
            \frac{V_1}{V_2}=\frac{I_2}{I_1}=-\frac{i\omega M}{i\omega L_2+R_{\rm load}}\approx-\sqrt{\frac{L_1}{L_2}}=-\frac{N_1}{N_2} \\
            \Phi_{12}=M_{12}I_2 \\
            \Phi_{21}=M_{21}I_1

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Introduction

Equation

$M_{12}=M_{21}:=M=k\sqrt{L_1L_2}=\frac{N_1\Phi_1}{I_2}=\frac{N_2\Phi_2}{I_1}\sim N_1N_2 \\ \frac{V_1}{V_2}=\frac{I_2}{I_1}=-\frac{i\omega M}{i\omega L_2+R_{\rm load}}\approx-\sqrt{\frac{L_1}{L_2}}=-\frac{N_1}{N_2} \\ \Phi_{12}=M_{12}I_2 \\ \Phi_{21}=M_{21}I_1$

Latex Code

            M_{12}=M_{21}:=M=k\sqrt{L_1L_2}=\frac{N_1\Phi_1}{I_2}=\frac{N_2\Phi_2}{I_1}\sim N_1N_2 \\
            \frac{V_1}{V_2}=\frac{I_2}{I_1}=-\frac{i\omega M}{i\omega L_2+R_{\rm load}}\approx-\sqrt{\frac{L_1}{L_2}}=-\frac{N_1}{N_2} \\
            \Phi_{12}=M_{12}I_2 \\
            \Phi_{21}=M_{21}I_1

Explanation

Latex code for Coupled conductors and transformers. I will briefly introduce the notations in this formulation.

$\Phi_{12}$ : part of the flux originating from I_{2{} through coil 2, which is enclosed by coil 1
$M_{ij}$ : coefficients of mutual induction
$k$ : Coupling factor

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