2.2d.1 Mesh-Current Method

Mesh-Current Method

The Mesh-Current Method is a technique used to find the current flowing in each loop (or mesh) of a circuit. A mesh is defined as a loop that does not enclose any other loops. This method simplifies the process of solving for unknown currents in planar circuits by applying Kirchhoff’s Voltage Law to each independent loop.

\usepackage{circuitikz}
\begin{document}
 
\begin{circuitikz} \draw
    % Mesh 1
    (0,0) to[V, v=$V_1$] (0,3) 
    to[R=$R_1$, i=$I_1$] (3,3)
    to[R=$R_3$, i_=$I_1 - I_2$] (6,3) 
    -- (6,0) to[short] (0,0)
    
    % Mesh 2
    (6,0) to[V, v=$V_2$, invert] (6,-3)
    to[R=$R_2$, i=$I_2$] (3,-3)
    -- (0,-3) to[short] (0,0)
    
    % Closing loop for mesh 2
    (3,-3) to[R=$R_3$, i_=$I_2 - I_1$] (3,0)
    ;
    
    % Labels for the mesh currents
    \node at (1.5, 1.5) {$I_1$};
    \node at (4.5, -1.5) {$I_2$};
 
    % Loops around each mesh
    \draw[dashed, thick, blue] (1.5,0) circle(2);
    \node[blue] at (1.5,4) {Mesh 1: $V_1 = I_1R_1 + (I_1 - I_2)R_3$};
    
    \draw[dashed, thick, red] (4.5,0) circle(2);
    \node[red] at (7.5,-3) {Mesh 2: $V_2 = I_2R_2 + (I_2 - I_1)R_3$};
 
\end{circuitikz}
 
\end{document}