AP Syllabus focus: 'Electric potential values at points in a circuit can be represented by a graph of potential as a function of position within a loop.'
Electric potential graphs turn a circuit loop into a visual map of energy per charge, helping you track where potential rises, falls, or stays constant as you move through the loop.
What the graph represents
An electric potential graph shows how the potential changes as you travel around one chosen closed path in a circuit. The vertical axis represents electric potential, usually measured in volts, while the horizontal axis represents position along the loop. That horizontal axis is not usually the real physical distance in the circuit. Instead, it is the order in which you encounter points and circuit elements.
Electric potential graph: A graph that shows the electric potential at successive positions along a chosen circuit loop.
This kind of graph is useful because it connects the circuit diagram to the idea of energy per unit charge. At each position, the graph tells you the potential of that location. The change in height between two points on the graph tells you the potential difference between those two locations. If the graph goes upward, the potential increases. If it goes downward, the potential decreases.
= change in electric potential, in volts
= final electric potential, in volts
= initial electric potential, in volts
When reading a graph, a positive value of means an upward change in potential, and a negative value means a downward change. The graph is therefore a visual record of potential changes around the loop.
Potential (voltage) vs. position along a simple loop containing a source and resistive elements. The upward jump corresponds to a potential rise provided by the source, while downward segments represent potential drops across resistances; flat portions indicate ideal-wire segments with negligible change in potential. Source
Reading potential from the graph
Potential at a point
The vertical value of the graph at any location gives the electric potential of that point in the circuit. If two points lie at the same vertical level, they have the same electric potential. Their potential difference is zero, even if they are separated along the loop.
Potential difference between points
The vertical separation between two positions on the graph is what matters, not the horizontal separation. A large vertical change means a large potential difference. A small vertical change means a small potential difference. Because of this, the graph allows you to compare points in a circuit quickly without redrawing the full schematic.
In idealized AP Physics 2 circuit graphs, sections of ideal wire are usually shown as flat horizontal segments.
Voltage plotted as you traverse a closed circuit loop, with labeled points marking the order in which elements are encountered. The graph rises across the battery (energy added per unit charge) and steps downward across each resistor, while remaining constant along the connecting wires where the resistance is negligible. Source
That means the potential stays constant as you move through those parts of the loop. Flat regions do not mean “nothing is happening” in the circuit; they mean there is no change in electric potential along that part of the chosen path.
How circuit elements appear
Elements that raise potential
A source such as a battery appears as an upward step when you move through it from lower potential to higher potential. On the graph, the size of that rise matches the potential difference provided by the source in the direction you are traveling.
Elements that lower potential
A resistor or other load usually appears as a downward step when you move through it in the direction of the potential drop. The size of the drop equals the potential difference across that element for the chosen direction of travel. If you reverse your direction through the same element, the sign of the change reverses on the graph.
This is why the graph depends on the path direction you choose. The circuit itself does not change, but your description of the rise or drop can change sign depending on how you move around the loop.
Sketching a potential graph around a loop
To sketch the graph clearly, move through the loop in a systematic order.
Choose one closed loop in the circuit.
Pick a direction to travel around that loop.
Select a starting point and assign it a convenient potential value.
Move through the loop one element at a time.
Draw a rise, drop, or flat segment based on how the potential changes across each part.
Label important points if you need to compare specific locations.
The exact starting value is often chosen for convenience. What matters most is the change in potential from point to point. Different starting choices can produce graphs at different vertical levels, but the relative rises and drops remain the same.
At the end of one complete trip around a closed loop, the graph must return to the same potential value where it started. If it does not, then a sign, value, or element order has been represented incorrectly.
Common interpretation issues
One common mistake is to treat the graph as if it were a picture of the circuit’s shape. It is not. A long wire on the page does not have to produce a long flat segment, and a short symbol does not have to produce a short jump. The horizontal axis mainly tracks sequence, not physical size.
Another mistake is to confuse this graph with a current-versus-position or potential-versus-time graph. An electric potential graph around a loop shows how potential varies from place to place along one chosen path at an instant.
It is also important to remember that electric potential is a scalar. The graph shows levels of potential, not vector arrows. Direction matters only because it determines whether a change is described as a rise or a drop.
Finally, when comparing two points, always use the difference in their vertical values. The graph is most powerful when you use it to identify which points are at equal potential, which elements create the biggest changes, and whether the full loop has been represented consistently.
FAQ
Electric potential in a circuit graph is usually relative, not absolute.
You may assign any convenient reference value because the measurable quantity is the potential difference between points. Shifting the entire graph up or down by the same amount does not change any rise or drop across an element.
Ground is just a chosen reference level, not a required physical location in every circuit problem.
Every rise becomes a drop of the same size, and every drop becomes a rise of the same size.
The order of the features also reverses. The circuit itself has not changed; only your description of the potential changes has changed because your direction of travel changed.
A correct reversed graph still ends at the same potential where it began.
Yes. Equal height on the graph means equal electric potential, even if the points are separated by several components.
This can happen when separate potential rises and drops cancel before you reach another point. It can also happen when different locations are effectively part of the same node.
Equal potential does not mean the points are physically close together.
Both styles are meant to show a change in electric potential.
A vertical step emphasizes the before-and-after values across an element.
A slanted segment emphasizes that the change occurs while moving through the element.
For AP Physics 2, the important idea is the size and sign of the change, not the artistic style of the graph.
Treat the horizontal axis as an ordered path, not a ruler.
Pick a starting point.
List the elements in the order you encounter them around the loop.
Place flat or changing segments in that same order.
Ignore bends, crossings, and exact wire lengths unless spatial information is specifically given.
A potential graph follows the loop sequence, not the physical appearance of the diagram.
Practice Questions
An electric potential graph for a complete loop shows a rise of across one element and then two drops of and across the remaining elements. Identify the element most likely responsible for the rise and state the net change in electric potential after one trip around the loop.
1 mark for identifying the element as a battery or other source of emf
1 mark for stating that the net change in electric potential is
A student starts at point A with potential defined as and moves once around a circuit loop. The graph rises to across element X, remains flat, drops to across element Y, remains flat again, and then drops to across element Z.
(a) Determine the potential difference across Y.
(b) Determine the potential difference across Z.
(c) Which element is most likely the battery? Explain.
(d) What do the flat sections represent?
(a) 1 mark for stating that Y has a potential drop of
(b) 1 mark for stating that Z has a potential drop of
(c) 1 mark for identifying X as the battery or source
(c) 1 mark for explaining that X is the element across which the potential rises by
(d) 1 mark for stating that the flat sections represent no change in electric potential, typically along ideal wire or points on the same node
