### applications + R, L, C laws

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differential-equations/electrical.pdf
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differential-equations/electrical.tex

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 @ -206,11 +206,29 @@ The Van der Pol oscillator can be forced too, however, this work does not aim to     \section{Applications in Electronics} %The modeling met some more advanced applications in electronics field, too. We will briefly summarize some of them, in this section. This is the main section of our work. We will investigate, what is the behavior of electrical components in circuits with respect to time and model them with differential equations.   \textbf{Resistor} is a linear component. It is described by an \textbf{Ohm's law}, which states, that the voltage $V$ across it is proportional to the current $I$ passing through it's resistance $R$. $$V=IR$$   \textbf{Inductor} is one nonlinear component. It produces a voltage drop, that is proportional to the \textit{rate of change} of the current through it, as described by \textbf{Faraday's Law} $$V=L\frac{dI}{dt}$$   \textbf{Capacitor} is another nonlinear component. Voltage drop across it, is on the other hand proportional to the charge stored in it. This behavior is derived from \textbf{Coulumb's law} $$V=\frac{1}{C}\int idt$$   TU POJDE ESTE KIRCHOFF   \subsection{First Order} asfasdf   \subsection{Second Order } adsfsa     \subsection{Josephson Junctions} Last but not least, we mention the miscellaneous phenomenon regarding nonlinear dynamics applied in the field of electrical engineering.   \textbf{Josephson junctions} are superconducting devices that are capable of generating voltage oscillations of extraordinary high frequency, typically 10\textsuperscript{10} - 10\textsuperscript{11} cycles per second \cite{van1981principles}. They consist of two superconducting layers, separated by a very thin insulator that weakly couples them, as shown on \cref{f:jjunc}.   \begin{figure}[ht!]