Node Potentials & Potential Diagrams

A potential diagram is a running account of voltage along an ordered path. The horizontal axis is path position or node sequence, not physical distance unless the circuit model explicitly assigns distance. The vertical axis is node potential relative to an arbitrary reference.

Constructing the diagram #

Choose a starting node with $\phi_0=0$ and a traversal direction. For each crossed element, update the potential using its marked voltage:

$$\phi_{k+1}=\phi_k-v_{k,k+1},$$

where $v_{k,k+1}=\phi_k-\phi_{k+1}$. Equivalently, moving from a negative to a positive source terminal creates a rise; moving through a resistor in the direction of positive current creates a drop $IR$.

For a closed loop, the final potential must return to the starting value:

$$\phi_{end}-\phi_0=-\sum_{loop}v_k=0.$$

Failure to close is a visual KVL residual.

Reading the graph #

• The voltage between any two plotted nodes is their vertical difference.
• A horizontal segment represents an ideal connection or zero modeled drop.
• A source produces a directed jump fixed by its polarity.
• A resistor produces a jump whose direction depends on current.
• Changing the reference shifts the entire graph vertically but changes no differences.

Branched circuits #

A single one-dimensional plot follows one path at a time. Different paths that meet at the same node must land at the same potential. That makes a family of path diagrams a consistency check for a branched network.

Potential diagrams are most useful when paired with measured node potentials: theory and experiment can be overlaid without recomputing every pairwise branch voltage.

If a measured path finishes away from its starting potential, first check probe reference, polarity, and contact resistance. The diagram reveals the location of the mismatch; it does not by itself decide whether the model or measurement is wrong.