\documentclass{report}

\input{preamble}
\input{macros}
\input{letterfonts}

\title{\Huge{Modules in Electrical and Computer Engineering}}
\author{\huge{Aidan Sharpe}}

\usepackage{circuitikz}

\begin{document}

\maketitle
\date{}
\newpage% or \cleardoublepage
% \pdfbookmark[<level>]{<title>}{<dest>}
\pdfbookmark[section]{\contentsname}{toc}
\tableofcontents
\pagebreak

\chapter{Node Voltage Analysis}
\chapter{Mesh Current Analysis}
While a loop can be any closed path in a circuit, a mesh must be a loop with no loops contained. To perform mesh analysis:
\begin{enumerate}
    \item Identify all of the meshes in the circuit
    \item Pick a direction to be positive for the currents in the meshes (clockwise or counter-clockwise)
    \item Apply Kirchhoff's Voltage Law (KVL), adding voltage increases and subtracting voltage drops.
\end{enumerate}

\begin{center}
\begin{circuitikz}[american voltages,american inductors]
\draw 
    (0,3) to [V,l_=$V_1$](0,0)
    (4,3)
    node[label={above:$\text{V}_{x}$}] {}  
    to [R,*-*, l^=$R_1$] (4,0)
    node[ground] {}
    (8,3) to [short] (8,0)
    (0,0)--(8,0)
    (0,3) to [C,  l^=$C_1$] (4,3)
    to [L, l^=$L_1$] (8,3);
    \draw[->,shift={(2,1.5)}] (120:.7cm) arc (120:-90:.7cm) node at(0,0){$I_1$};
    \draw[->,shift={(6,1.5)}] (120:.7cm) arc (120:-90:.7cm) node at(0,0){$I_2$};
\end{circuitikz}
\end{center}


\nt
{
 It is safe to assume that a resistor will always cause a voltage drop in the direction of the mesh current, but pay attention to what direction voltage sources are oriented. When the current goes from the negative terminal to the positive terminal of a voltage source, add the voltage, but when the current goes from the positive terminal to the negative, subtract the voltage.
}

\section{Special Cases}

\subsection{Dependent Sources}

\subsection{Current Sources}

\subsection{Super Mesh}
A \emph{super mesh} is created when a current source is shared between two meshes. To perform mesh analysis with super meshes or dependent sources:

\begin{enumerate}
    \item Identify all of the meshes in the circuit
    \item Pick a direction to be positive for the currents in the meshes (clockwise or counter-clockwise)
    \item If there are any current sources shared between two meshes, temporarily remove it to create a larger mesh.
    \item Apply the super mesh constraint
    \item Apply Kirchhoff's Voltage Law (KVL), adding voltage increases and subtracting voltage drops.
\end{enumerate}

\paragraph{The Super Mesh Constraint}
The super mesh constraint is a simple equation that relates a current source shared between two meshes to the mesh currents of those meshes. The super mesh constraint will be of the form:
$$I_s = I_1 - I_2$$
Where:
\begin{itemize}
    \item[$I_s$] is the value of the shared current source
    \item[$I_1$] is the mesh current parallel to the current source
    \item[$I_2$] is the mesh current anti-parallel to the current source
\end{itemize}

\end{document}
