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When I use dependent voltage sources, the polarity of the device changes based on the computer I compile the document on (it's not random; my home laptop will always display the sources in one direction, at work the other direction). This is a huge problem, because I frequently write assignments for my students at home, re-compile at work, and then have the incorrect polarity when I print them out. Is there some way I can mandate the direction of the source, so that the computer doesn't change it?

Example:

\begin{circuitikz}[font=\sffamily, american voltages]
    \draw (-2,2) to [V, l_=8~V] (-2,0);
    \draw (0,0) to [cV, l_=4~V] (0,2);
    \draw (-2,2) to [R, bipoles/length=1cm, l_=2~k$\Omega$, v^>=$V_1$] (0,2);
    \draw (-2,0) to [short] (0,0);
\end{circuitikz}

This looks like: example of dependent voltage sources

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with your code i reproduce your right image. but i assume, that you like to have left one produced on work.

please test the following redesign your circuit scheme. its code is slightly shorter and use siunitx for units. it produce left scheme (you obtain at work) in your question:

\documentclass[margin=3mm]{standalone}
\usepackage{siunitx}
\usepackage[siunitx]{circuitikz}

\begin{document}
\begin{circuitikz}[font=\sffamily, american voltages]
\ctikzset{bipoles/length=1cm}
\draw   (0,2)   to [V, l_=8<\volt>] (0,0)
        (0,2)   to [R, l_=2<\kilo\ohm>, v^>=$V_1$] (2,2)
                to [cV,l^=4<\volt>] (2,0)
                to [short] (0,0)                    
                ;
\end{circuitikz}
\end{document}

if gives on both computers the same result (as is expected):

enter image description here

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