Introduction to the True Definition of Series and Parallel – Part 3

This is for people who can’t easily tell the difference between a series versus a parallel connection. If you don’t know what “series” and “parallel” refer to, then you can read the relevant parts of Chapters 17 and 18 that cover it. Or you can use my notes.

The Most Fundamental Definitions:

  • A series connection of two same-category elements in a circuit is one that guarantees that the two elements will have exactly the same charge quantities. This is true for resistors as well as capacitors. For resistors, it would be current, both resistors getting equal current through them. For capacitors, it would be stored charge, both capacitors storing equal amounts of charge.
  • A parallel connection of two same-category elements in a circuit is one that guarantees that the two elements will have exactly the same voltage across each (when the voltage is shown by a voltmeter whose red lead is on one side of the element and the black lead is on the other side of the element.)This is true for resistors as well as capacitors in the exact same way, because volts are volts.

In addition to understanding the Fundamental Definitions from the textbook, the understanding can be enhanced by using the circuit simulator site and seeing what voltmeters do. So this page is meant to show a way to do that. But there is no substitute for actually using a real voltmeter. Availability was made for that in class as well.

If you are taking advantage of this page, go to the circuit simulator and make something like the following picture. It is two capacitors in series, and that series combination is in parallel with a third. Don’t worry if you don’t know why the last sentence is true; the purpose of this page is to do a FAST run-through of measuring to illustrate the meaning of the definitions, so that you can interpret a diagram on your own as:

  • Someone who visualizes measurement and physical behavior

AND

  • The opposite of someone who just memorizes rules and tricks that they overheard with no critical thinking.

(“I’m not a conjurer of cheap tricks!”)

Switch it to schematic so it looks like the following:

The black lead of the voltmeter is just being used as a pointer in the picture. It is pointing at a section of conductor that is in the shape of a corner with plates attached to it. The entirely of the conductor is:

  • The wire
  • The top, positive plate of the 0.10 F capacitor
  • The right, negative plate of the 0.20 F capacitor. (If your capacitors don’t match the Farad value of the ones in the picture, learn to right-click on them to modify their individual capacitances.)

The following regions are NOT a part of the conductor in question:

  • The bottom, negative place of the 0.10 F capacitor
  • The left, positive plate of the 0.20 F capacitor

because there is empty space separating these two regions from the conductor.

This conductor has a total charge of zero. (Circuit wires are neutral. Charges flow through them sometimes, but they have equal numbers of positive and negatives.) Even though the conductor being pointed to is neutral, the bottom of the conductor is the positive plate of the 0.10 F capacitor. Look for yourself, schematic or lifelike I don’t care which. So a thing that we know has 0 total charge has one region of it with positive charge. That means another region of it must have the exact same quantity of negative charge. This precisely why a plate of the 0.10 F capacitor must have the exact same amount of charge as a plate of the 0.20 F capacitor.

That is how I know those two capacitors have the same charge, and that is how I know they are in series. That is the logic that must be applied anytime when deciding whether or not two things are in series.

Recognition of Parallel Connections from Physical Rules

Go to that circuit again. This time place the voltmeter as the following diagrams tell you to.

Nothing but uninterrupted conductor lies between red and black. Inside any conductor,E field is zero. This means that potential is CONSTANT (not zero!). This means that difference in potential will be zero. The display on the instrument reads difference in potential. This idea must become obvious.

Move the leads:

The difference of red to black is 9 V. If you don’t understand difference, you can’t continue. Move just the red to any place that will cause the red-to-black difference to not change:

Move the black one exactly as the next picture tells you:

Now, without actually doing the measurements in the simulation, predict the following, don’t peak at the answers:

  1. What the voltmeter will say when placed with red near the positive of the diagonal capacitor and black near the negative of the diagonal capacitor.
  2. What the voltmeter will say when placed with red just below the battery and black near the negative of the diagonal capacitor.

Answers:

If you got 0 V for the second and 9 V for the first, you probably know enough to understand why the capacitor-pair on the right (taken as a package) is in parallel with the diagonal capacitor. It is because voltage across package equals voltage across diagonal.

This would tell me to series-combine the right capacitors first. ((0.1-1 + 0.2-1)-1 = 0.067 Then to take that combination of two, call it 0.067 F and combine that number with the diagonal one as a parallel combo: Ceq answer = 0.067 F + 0.1 F = 0.167 F.

The math formulas used here are in the book reading. If you read the book (Chapters 16 and 18), you’ll learn proofs that will show why the Ceq and Req formulas are the way they are. You might be curious about the fact that the Ceq math trick for series matches the Req math trick for parallel and vice versa. I have a very good explanation for why this is so; it depends on knowing what series and parallel really mean.