# Basic Theory - finding voltage between two points

I'm a neophyte here trying to learn using "Practical Electronics for Inventors, 4th Edition" (which received almost a 5 star review with over 500 reviews on Amazon). The preface of the book states "little to no experience" in electronics needed to understand the concepts in the book.

Alas, I'm struggling on the Theory chapter less than 20 pages in. When asked to solve the below questions. The book presents a few sentences which are relevant, but not enough for me to understand and solve the questions posed after.

The book states (and I believe I understand) the idea that Voltage is the measurement between two points usually provided by an absolute scale which is often set at 0 on the negative terminal (ground reference). This is at least true for the DC circuits discussed. The illustrations show (with enough clarity) an example of the V between the positive and negative of a single 1.5V battery, two batteries in series (3V), and finally an example of a split supply with a common return - a ground reference between the positive and negative leads of the two batteries. While I don't understand all the ramifications of this yet, I understand the basic explanation.

Several pages later the following questions are posed, along with the answers which I am having a lot of trouble following. I understand they are trying to show some examples that don't have a ground reference and/or that the ground reference is either at the positive or negative end, but lack of a walkthrough of prior examples is leaving me stumped. Furthermore there is a possibility based on this question that the book may be incorrect - which would be very disappointing as it is hard enough for me as it is.

Any insight into how to help me interpret these answers or clarification on the basic theory being illustrated below is appreciated:

• fig 213a, do you understand why Vac = 0 AND Vad = 0? Pick just one diagram that you don't 'get', and write down what you do understand about it, and let's try and home in on that one. The importance of putting down what you do understand is that it lets us know where we can work from. There are too many diagrams for us to guess which would be best to work on, and few people are going to be willing to write up all of them. – Neil_UK Mar 12 '18 at 21:06
• Thanks...no for starters I don't get why Vac and Vad = 0. At first my guess was that these were two different circuits and thus there was no voltage between them. Much like if you held a multimeter to the + and - terminals on two non connected batteries. So I though maybe I got it and it was just super basic. But then on 213b I failed to get it. Should I be looking at each of these 12V and 9V as two separate sources (i.e. batteries) connected in series? For instance in 213b should I assume the two grounds are a "common ground"? The presentation doesn't relate to me that way. – BenH Mar 12 '18 at 21:13
• 213a, undefined not, zero – Jasen Mar 12 '18 at 21:16
• BenH where there are ground reference symbols draw in the wire connecting them and see if that makes it any clearer. You are correct in your guess about why Vac and Vad =0. For the moment ignore the comment from @Jasen that is a theoretical rathole that will not improve your understanding at this level. – RoyC Mar 12 '18 at 22:09
• @Jasen I can see where you are coming from but I think that the question is just badly worded. The question should probably say what voltage would you measure between these points. You can't know the voltage between two points in totally isolated circuits so yes it is undefined but If I tried to measure it in 2.13(a) I would measure 0V because while my DVM has an high input impedance it is not infinite. Making the measurement ties 'A' and 'C' together via several $\text{M} \Omega$ so the voltage I measure would be 0V. – Warren Hill Mar 12 '18 at 22:43

fig 213a

Why does Vac = 0? There is no connection between B and D. Connect a voltmeter of any practical input impedance between A and C to measure the voltage, and whatever the voltages were on those terminals due to stray capacitances (not shown in that diagram, so assumed to be zero), it will pull those points together, and move points B and D to whatever voltages are needed to get A and C at the same voltage.

If an infinite input impedance voltmeter was connected between A and C, it would not draw any current, and the voltage would stay at whatever it happened to be, due to charges on the capacitances of those nodes. As they're not shown, and the voltages on them are not given, not enough information is given in the question to determine Vac.

Why does Vad = 0? As above, but change 'c' for 'd'.

fig 213b

Why does Vac = 3v? There is a connection between B and D, they are both connected to the same node. The two grounds are drawn on the same schematic, so can be taken to be connected. That node happens to be 'ground', which means the node that we reference all other voltage measurements to, but it could just be another wire.

As B and D are at 0v with respect to ground, A is at 12v wrt ground, and B is at 9v wrt ground, so there is 3v difference between them.

Further thoughts

I'm inclined to agree with the various comments that the exercise in the book was badly worded, though I struggle to find a good improvement at the noob level it's intended for.

In questions like this, if something is not mentioned, then you should assume it's negligible. No capacitances to ground are illustrated, so they should be effectively zero, so unable to hold those nodes at any given potential. However, the voltmeter is not described, so you should be able to assume it's an ideal voltmeter, which doesn't load the circuit at all. This will leave the measurement of Vac indeterminate.

If instead the question specified a voltmeter with some input resistance like 10Mohms, or asked for the current that flowed through a resistor of (say) 1Mohm or 1k placed between terminals A and C, then there would be no problem.

• Ok - so can I look at ground in each diagram as a "common return"? IOW I could imagine a wire connecting each ground to the other (or practically wire two batteries this way and use a multimeter to measure the answer values? I am new to schematic drawings and didn't/don't understand how these two separate diagrams (not being shown in a circuit i.e. circular were connected). – BenH Mar 12 '18 at 21:37
• @BenH ... and not just ground symbols either. It's common on schematics to avoid drawing wires which clutter up the diagram, like power supplies. You'll see a number of 'Vcc' symbols, or a '5v' marked against lines. Again assume all like symbols are connected. We generally draw all signal lines in explicitly, but just sometimes, if replacing a signal wire with its labelled endpoints will result in a tidier more readable diagram, we'll do it. We'll often draw a multiway connector at the side of the diagram, and just mark the points it connects to, rather than draw all 40 wires! – Neil_UK Mar 13 '18 at 6:35
• @BenH added a bit more to the answer, not sure it helps though – Neil_UK Mar 13 '18 at 10:03
• @Neil_UK I was having a ton of trouble on this problem as well. So if we connect the two grounds together (as suggested in the comments), we still have two open ends in this circuit. If we connect the voltmeter does this complete the circuit, and therefore is the reason we can measure the potential difference between the terminals? Is this what you meant by " it will pull those points together". Thank you! – CL40 Aug 16 '18 at 4:26