# Negative voltage?

Discussion in 'Homework Help' started by Teszla, Jun 12, 2013.

1. ### Teszla Thread Starter Member

Jun 7, 2013
43
0
What is is that actually determines whether a voltage is positive or negative? Doesn't it just depend on from which direction you look at it?

For example here:

How can both Vs and V2 be positive when their polarities are in opposite directions?

2. ### MrChips Moderator

Oct 2, 2009
12,440
3,360
If you follow Kirchhoff's Voltage Law (KVL), the sum of the voltages around the loop equals zero.

When you are solving for unknowns such as v1 and v2, you may assign any arbitrary polarity.
When you apply KVL, you maintain consistency on how the polarity is applied. The end result is v1 and v2 can be either +ve or -ve values depending on your initial assumptions.

3. ### WBahn Moderator

Mar 31, 2012
17,737
4,789
A voltage is ALWAYS a voltage DIFFERENCE. It is good to keep that in mind.

So when we say that Vfred = 5V, what we are really saying is that the voltage on node "fred" is 5V higher than some particular node that we have agreed, at least implicitly, to use as a reference node. We generally call this node "ground" or "common".

When we talk about the voltage across a component, it is important that we indicate which is the "positive" node and which is the "negative" node. Our voltage value is then the voltage of the positive node relative to the voltage of the negative node. We can pick which node is which arbitrarily, we just have to then be consistent with that choice.

This is often referred to as the "symbolic" voltage. We assign a symbol to represent a voltage and we assign a polarity to that voltage. This says absolutely nothing about the polarity of the "actual" voltage between those two points.

When we perform an analysis or make a design, we generally try to pick symbolic voltages (and currents) that will make the analysis/design easier and less error prone. But if we "guess" wrong, then we will simply end up with an actual value that is negative, meaning that the actual polarity is the opposite of what our symbol indicates.

4. ### Teszla Thread Starter Member

Jun 7, 2013
43
0
Thank you for the explanations.

I can see why we choose the polarity arbitrarily before knowing it (similar to that we choose current direction arbitrarily before knowing it), but if it is possible to calculate the polarity, shouldn't we try to do that then?

Here's an example:

Start by just looking at picture (1). Then when deciding polarity, would (1a) or (1b) be correct?

I think (1a) would be correct if one always wants potential difference to go from high to low (someone said that it ALWAYS does, is that a law?)

On the other hand I think (1b) would be correct because the upper right corner is a node (which I've marked in green) so the polarity should be the same there, right? Isn't the polarity on a node always the same?

Which image is correct?

5. ### WBahn Moderator

Mar 31, 2012
17,737
4,789
Both are correct -- they are just different selections of the arbitrary choices.

Choice (1a) would be what most people would choose, specifically because we like to choose symbolic polarities so that the actual values will come out positive. Less chance for confusion and error -- human beings aren't particularly good at dealing with signed quantities.

Your reasoning regarding choice (1b) is flawed. The polarities you are showing are for the polarities of the voltages ACROSS the resistors. The voltage of the NODE does not need a polarity indicator because it is understood that the symbolic voltage associated with a node is positive if that node is at a higher voltage relative to the reference node. In your circuit, you have not indicated a reference node, so the very notion of a node voltage is meaningless. Most people, for this circuit, would choose the negative side of the battery as the "ground" node and put a ground symbol there to indicate this. In a theoretical circuit the choice of reference node is completely arbitrary. In a real circuit, the choice is often not so arbitrary because one node is connected to the chassis or the power line neutral or some such. You can actually still call another other node your reference, but then your chassis or neutral or some such probably has a non-zero voltage relative to your reference. Technically, that's just fine and, occasionally, it might actually make sense to do this. But, again, people tend to choose the options that result in the clearest communication and that minimize the likelihood of mistakes.

6. ### screen1988 Member

Mar 7, 2013
310
3
Let's call the voltage across battery is V, across resistor R1 is V1 and across R2 is V2. With all V, V1, V2, larger than zero.
Is this case possible?

File size:
31.2 KB
Views:
136
7. ### WBahn Moderator

Mar 31, 2012
17,737
4,789
Nope.

V = IR

V1 = Io*R1

I'm using Io instead of I because I want to use V, I, and R to be generic variables and not specific symbolic parameters of the circuit)

But

V2 = -Io*R2

Since R1 and R2 are (assumed) to always be positive, this means that V1 and V2 always have opposite sign.

This is a good example of why it is so important to make it clear what the polarities of all the voltages and currents are.

Also, note that using arrows to indicate polarity of a voltage is just asking for miscommunication. Does the arrow point from the + to the -, or from the - to the +? Both are used and it is not obvious which one is correct because you can describe the meaning of the arrow sensibly for either case. So just use a + sign at the positive terminal of the indicated symbolic voltage (and preferably also a - at the other end since this makes it clear exactly which node is the negative terminal of the symbolic voltage).

screen1988 likes this.
8. ### MrChips Moderator

Oct 2, 2009
12,440
3,360
Here are two examples where you cannot know the correct polarity of the voltage and current before analysis:

The polarity of the voltage across resistor R1 in Example (a) cannot be determined until the values of the voltages Vs1 and Vs2 are known.

In Example (b), the values of the resistors R1-R4 must be known in order to determine the polarity of the voltage across resistor R5.

In circuit analysis, one can select any polarity to begin. The correct polarity will be ascertained after analysis.

Last edited: Jun 14, 2013
Andreas, screen1988 and Metalmann like this.
9. ### screen1988 Member

Mar 7, 2013
310
3
Do you mean values of the resistors from R1 to R4?

10. ### MrChips Moderator

Oct 2, 2009
12,440
3,360
Yes, I mean resistors R1, R2, R3 and R4.

screen1988 likes this.
11. ### WBahn Moderator

Mar 31, 2012
17,737
4,789
And sometimes it may be reasonable to assign a polarity that you know is going to end up wrong.

When looking at schematics, most people get comfortable with the general notion that things flow left to right and top to bottom. So if you define the current in the resistor according to that convention you may be less likely to make mistakes setting you your equations.

Regardless of whether you do this or not, if you know in advance that you expect some results to be negative (or that they might end up negative), it is helpful to make a note of that off to the size (or circle the component reference or some other way of noting it). Then when the analysis is done, make checking those part of your sanity checks.