%% This document created by Scientific Word (R) Version 2.5


\documentclass[12pt,thmsa]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="23">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="Title" CONTENT="Reference/Physics/Coupled Conductors and Transformers ">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 16:14:48 1997}
%TCIDATA{CSTFile=Reference.cst}
%TCIDATA{PageSetup=72,72,72,72,0}
%TCIDATA{<LINK REL="author" HREF="Johan_Wevers.tex">}
%TCIDATA{<LINK REL="contents" HREF="Physics.tex">}
%TCIDATA{<LINK REL="index" HREF="../ReferenceIndex.tex">}
%TCIDATA{<LINK REL="next" HREF="Osc06.tex">}
%TCIDATA{<LINK REL="parent" HREF="Osc_contents.tex">}
%TCIDATA{<LINK REL="previous" HREF="Osc04.tex">}
%TCIDATA{EvenPages=
%H=36,\PARA{038<p type="texpara" tag="Body Text" >\noindent \thepage\hfill \QTR{bf}{A Scientific Report}}
%}

%TCIDATA{OddPages=
%H=36,\PARA{038<p type="texpara" tag="Body Text" >\QTR{bf}{A Scientific Report}\hfill \thepage}
%}

%TCIDATA{FirstPage=
%F=36,\PARA{035<p type="texpara" tag="center" >\thepage}
%}


`
\input{tcilatex}
\begin{document}


\section{\label{Coupled conductors and transformers}\label{Conductors}\label%
{Transformers}Coupled Conductors and Transformers}

For two coils enclosing each other's flux the following holds:

\begin{itemize}
\begin{itemize}
\begin{itemize}
\item  if $\Phi _{12}$ is the part of the flux originating from $I_{2}$
through coil 2 which is enclosed by coil 1, then 
\begin{eqnarray*}
\Phi _{12} &=&M_{12}I_{2} \\
\Phi _{21} &=&M_{21}I_{1}
\end{eqnarray*}
\end{itemize}
\end{itemize}
\end{itemize}

For the coefficients of mutual induction $M_{ij}$ the following holds: 
\[
M_{12}=M_{21}:=M=k\sqrt{L_{1}L_{2}}=\frac{N_{1}\Phi _{1}}{I_{2}}=\frac{%
N_{2}\Phi _{2}}{I_{1}}\sim N_{1}N_{2} 
\]
where $0\leq k\leq 1$ is the \textit{coupling factor}. For a transformer, $%
k\approx 1$. At full load the following holds: 
\[
\frac{V_{1}}{V_{2}}=\frac{I_{2}}{I_{1}}=-\frac{i\omega M}{i\omega L_{2}+R_{%
\mathrm{load}}}\approx -\sqrt{\frac{L_{1}}{L_{2}}}=-\frac{N_{1}}{N_{2}} 
\]

\subsection{\ Related Reference Topics}

{\small \hyperref{Calculus}{}{}{../Mathematics/CAL_contents.tex}}

{\small \hyperref{Differential Equations}{}{}{../Mathematics/ODE_contents.tex%
}}

{\small \hyperref{Table of Integrals}{}{}{%
../Mathematics/TAB_integrals.tex#table of integrals}}

{\small \hyperref{Table of Derivatives}{}{}{%
../Mathematics/TAB_derivatives.tex}}

{\small \hyperref{Table of Physical Constants}{}{}{PhysicalConstants.tex}}

{\small \hyperref{Table of SI Units}{}{}{SIUnits.tex}}

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Basic Techniques for Doing Mathematics}{}{}{%
../../Help/DM1.tex}}

{\small \hyperref{Numbers, Functions, and Units}{}{}{../../Help/DM2.tex}}

{\small \hyperref{Algebra}{}{}{../../Help/DM3.tex}}

{\small \hyperref{Trigonometry}{}{}{../../Help/DM4.tex}}

{\small \hyperref{Function Definitions}{}{}{../../Help/DM5.tex}}

{\small \hyperref{Plotting Curves and Surfaces}{}{}{../../Help/DM6.tex}}

{\small \hyperref{Calculus}{}{}{../../Help/DM7.tex}}

{\small \hyperref{Matrix Algebra}{}{}{../../Help/DM8.tex}}

{\small \hyperref{Vector Calculus}{}{}{../../Help/DM9.tex}}

{\small \hyperref{Differential Equations}{}{}{../../Help/DM10.tex}}\hfill

\noindent \hrulefill

\begin{center}
\begin{tabular}{ccc}
{\small \hyperref{\FRAME{itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Computing Techniques}{%
}{}{../../Help/DMindex.tex}} & {\small \hyperref{\FRAME{itbpF}{13.9375pt}{%
14.4375pt}{3pt}{}{}{nblogo.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
13.9375pt;height 14.4375pt;depth 3pt;original-width
24.0625pt;original-height 24.8125pt;cropleft "0";croptop "0.9959";cropright
"0.9937";cropbottom "0";filename 'Nblogo.wmf';file-properties
"XNPEU";}}General Information}{}{}{../../Help/Index.tex}} & {\small 
\hyperref{\FRAME{itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Reference Library}{}{}{%
../ReferenceIndex.tex}}
\end{tabular}
\end{center}

\noindent \hrulefill

\end{document}
