Circuit Idea/How to Visualize Voltages inside Resistors

voltage bars - current loops - IV curves - stage 

Need to visualize voltage distribution
Once visualized the voltages of the internal circuit points, we can go even further and "enter" inside resistors to visualize the voltages along their resistive film. This will allow us to see some interesting points (for example, the famous virtual ground), the operation of well-known electrical devices (potentiometer, resistive summer) and electronic circuits (inverting, non-inverting, differential and instrumentation amplifiers).

The Idea
We can assume it originated sometime in the early 90s. See, for example, how this idea was sketched on a sheet of yellowed paper:



Here, for the purposes of intuitive understanding, the local voltages inside resistors are representd by a set of vertical segments whose length (height) is proportional to the local voltage magnitude (we can name it voltage diagram). This intuitive notion of voltage came from a hydraulic analogy (a garden hose with evenly drilled holes) which can be seen in old Electrical Engineering textbooks.



Implementation
It is more convenient to display only the envelope of the voltage diagram. Thus a triangle is obtained, in which the vertical leg is the voltage V, the horizontal leg is the resistance R, and the angle between the hypotenuse and the horizontal leg represents the current I (another geometric representation of Ohm's law, see the Flash picture below). It is convenient to color voltage diagrams in red (an association with pressure) to easily distinguish them from schematics drawn in black.

Sophisticated Voltage Diagrams
We can create more sophisticated voltage pictures by means of grapnic editors like Corel Draw. See, for example, the circuit of a voltage divider with constant input voltage VREF (applied from the left)...



... and of a voltage divider with varying (from the right) input voltage Vin2:



"Live" Voltage Diagrams
We can even make animated circuit tutorials (for example, with Flash animator) with "live"voltage diagrams that were changing proportionally to the voltage magnitude (you need Ruffle Flash emulator to see Flash movies because Adobe Flash player is no longer supported):



"Really Live" Voltage Diagrams
We can make even "really live" voltage diagrams that use actually measured voltages at several base points in the circuit. For this purpose, we can use some data acquisition system (see the Circuit Idea story about Ohm's experiment):



In this attractive experiment, a linear potentiometer is supplied by two DACs and the voltages of its three terminals (E1 of the left end, E2 of the right end and E3 of the wiper) are measured by three ADC inputs. The other points of the voltage diagram are calculated. Also, conventional voltmeters are connected.



When E1 and E2 have opposite polarities, the famous virtual ground appears.



Content is More Important than Form
But, as in the case of current loops and voltage bars, we can finally come to the conclusion that content is more important than form... and we can draw circuit diagrams with superimposed voltage diagrams even by hand. A typical example is the Wikibooks story about Ohm's experiment mentioned above, where the voltage diagrams are drawn by color fiber pens on a white sheets of paper. Here is an example of a voltage divider with constant input voltage V...



... and of a resistor summer with oppositely varying input voltages Vin1 and Vin2 (an illustration of an op-amp inverting amplifier):



Helping the Online Learning
As in the stories about current loops and voltage bars, in online learning, we can use the ZOOM pen to draw on existing web circuit diagrams. This is a very powerful didactic technique that we can improve for the purposes of visualizing voltage distributions. Here is a snapshot of such a picture drawn on the ZOOM whiteboard (really, the picture is not so beautiful... but attractive:-)



In the snapshot below, the Ohm's triangle is drawn on the resistive wire (the vertical leg is the voltage V, the horizontal leg is the resistance R, and the angle between the hypotenuse and the horizontal leg represents the current I):



Voltage diagrams vs voltage bars
What do voltage diagrams actually represent compared with voltage bars? The voltage diagram is a further development of the voltage bar representation. Voltage bars are a one-dimensional way of representing voltages while the voltage diagram is a two-dimensional way. The voltage diagram is a set of voltage bars.

The voltage diagram is based on a linearly distributed resistance along the length of the resistor. In most cases this representation is artificial, because ordinary resistors in electronic circuits are discrete; but it allows to illustrate the circuit operation with voltage diagram. In many cases, quantitative parameters (transfer ratios, etc.) can be directly seen.

Voltage diagrams vs oscillograms
What is the difference between a voltage diagram and voltage oscillogram at a given point in the diagram? The difference is significant, they have nothing in common. The voltage diagram shows voltage distribution along a resistance film, ie what local voltages inside a resistor are. The resistor is considered not as a "point" (without dimensions) but as a "line" (at each point of this line, in a certain step, a section perpendicular to the line is drawn, with a height proportional to the voltage at this point).

An oscillogram is a set of points that represent voltages (by a vertical displacement) at successive points in time through. So, the particular segments of a voltage diagram represent the voltages at particular points of the resistive layer at the same time while the oscillogram shows the voltages at one point but at different points in time.