Circuits I · Node, mesh, superposition, and equivalent circuits

A network has essential nodes A, B, C, and reference node N

Problem

A network has essential nodes $A$, $B$, $C$, and reference node $N$. The branches are: - $4\,\Omega$ between $A$ and $N$; - $2\,\Omega$ between $A$ and $B$; - $4\,\Omega$ between $B$ and $N$; - $4\,\Omega$ between $B$ and $C$; - $4\,\Omega$ between $C$ and $N$; - $4\,\Omega$ between $A$ and $C$; - an independent $2\,\mathrm{A}$ current source between $N$ and $A$, arrow from $N$ toward $A$; - an independent $2\,\mathrm{A}$ current source between $N$ and $C$, arrow from $N$ toward $C$. Write the $3\times 3$ nodal conductance equation for $(v_A,v_B,v_C)$. Solve the system for the three node voltages in volts. Then compute the three currents leaving node $B$ through the resistors incident on $B$, and verify that their algebraic sum is zero.

Hint

Node $B$ has no current source, so the three resistor currents that leave $B$ must sum to zero once the voltages are correct.

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