Talk:Series and parallel circuits

Early discussion
If you want, add the pictures I will be putting under resistor, capacitor, and inductor. - Omegatron 17:26, Mar 15, 2004 (UTC)


 * That would be nice theresa knott 23:03, 15 Mar 2004 (UTC)


 * but of course - Omegatron

First time contributer. Just thought I'd fix what I think was just a simple error in arithmetic. The formula for the total current in a parallel circuit was given as Itotal = V/(R1 + R2 + ... + Rn). It should be I = V * (1/R1 + 1/R2 + ... 1/Rn) since Itotal = I1 + I2 ... = V/R1 + V/R2 ... = V * (1/R1 + 1/R2 ...). If I'm wrong (I'm not a science major, so I might be), disregard this, revert the article, and chastise me. -- Anon


 * Thanks to the newbie for that. I was the one who made the slip up back in july, and despite a whole host of edits since then no one else spotted it. So good work! theresa knott 10:15, 16 Mar 2004 (UTC)


 * yeah, thanks. should we make all of the equations TeX? - Omegatron 14:40, Mar 16, 2004 (UTC)
 * Done. - Omegatron 03:51, Dec 31, 2004 (UTC)
 * Personaly, I think both are the different ways of writing the same thing - Oatzy

Could do with a redirect from the parallel disambiguation page.

It may be worth pointing out, for those not as good at math, that for 3 resistors in parallel, the notation is not (R1R2R3)/(R1+R2+R3) but in fact (R1R2R3)/((R1R2)+(R1R3)+(R2R3)) Just a thought (yes it did catch me out for a short time) 8) - Oatzy

Power ratings
Should we cover the way power ratings work with multiple components? — Omegatron 06:20, 5 January 2006 (UTC)

Split the article?
I suggest a split between Parallel (electronics) and Series (electronics). This article openly acknowledges the presence of two distinct topics by using 'and' in the title, and goes on to talk about them in two disjoint sections. --Smack (talk) 20:02, 11 January 2006 (UTC)


 * Definitely not. — Omegatron 20:08, 11 January 2006 (UTC)


 * Any reason? --Smack (talk) 19:16, 15 January 2006 (UTC)


 * Why would they be split? They're inherently related.  Two sides of the same coin. — Omegatron 21:42, 15 January 2006 (UTC)


 * Not any more than parallel (geometry) and perpendicular, summer and winter, white and black. Their effects and uses are very different, and their elegant symmetry does not justify lumping them together in a single article. --Smack (talk) 05:21, 22 January 2006 (UTC)


 * I disagree. I think they are inherently more related than your examples.  Let's see what other people think. — Omegatron 05:42, 22 January 2006 (UTC)

I don't think splitting is necessary. Black and White are both sides of the same coin too, but they have individual meanings and interpretations. That's not true of cricuits like these. Broken S 06:46, 22 January 2006 (UTC)


 * I'd support a split, although I would choose the titles 'series circuit' and 'parallel circuit'. My main reason is practical: long articles tend to deter reading and editing, and splitting them tends to encourage people to expand the new, shorter articles.


 * Another way of looking at it this: ignoring the title, what is the content of the article? In this case, it is mainly two large sections called 'series circuits' (3 screens' worth) and 'parallel circuits' (3&frac12; screens), with very little common content (1 screen, not including the TOC). We could still have an overview of how the two concepts are linked in an article such as circuit theory, or we could even keep the intro of the present article and just split off the two subsections. --Heron 12:26, 22 January 2006 (UTC)
 * I have an informal rule that I use to judge cases like this. Every article must be featureable. I don't think there is enough content to feature one them by themselves. Broken S 13:48, 22 January 2006 (UTC)


 * This article may have enough content to be featured, but it suffers from an awkward, concatenated structure.
 * Also, let's not get tunnel vision here. This article deals with only two of the many possible interconnections, and only three of the many different kinds of components.  Even among the restricted world of two-terminal components, to the exclusion of more complex things like transistors and amplifiers, it neglects switches and diodes, and also disregards the general complex impedance.  The elegant symmetry between resistors, capacitors and inductors does demand an explanation, but nobody past high school should get hung up on it. --Smack (talk) 19:46, 22 January 2006 (UTC)
 * The article has to be accessible to everyone (including students). Here's my challenge. Write content that belongs to just series or just parallel circuits, if it gets long enough then we'll have to split the article. Until then, let's leave them as one article. Broken S 23:32, 22 January 2006 (UTC)
 * As for the fact that the article is broken up into two sections, we could just as easily split it up into three sections; one for each type of component, with parallel and series sub-headings. Should we then break it up and put the content in each component article?  (Hint: it's already there.)
 * These are inherently related, and need to be on the same page so you can compare. The series equations for capacitors are the same as the parallel equations for inductors.  You wouldn't see that as clearly if we left the equations only on the individual pages. — Omegatron 16:15, 22 January 2006 (UTC)

I think you should add seperate or better definations for the series and parallel circuits. They are hard to seperate in the opening paragraph. Just a breif mention how series circuit is set up so that the electricty flows through each device in turn, while parallel circuits current passes through more than one pathway simultaneously. It just isnt that clear in the paragraph. --Ajihood

These articles should be split. Similarly "text and binary files" was once a single article that looked a lot like this one -- a short introduction and then two large sections on the two topics, because the original author thought of them together. Just because you think of series and parallel circuits together, and learned about them together, it doesn't mean that each cannot be explained in the absence of the other (and this article already shows that is possible). —Pengo 06:32, 19 August 2007 (UTC)

Is it possible to add a bit more theory/what actually happens in regards to current in these articles?
It would help a lot.


 * The article does say that in series circuits the current is the same in each element, and in parallel circuits the current in each element is the common voltage divided by the impedance of the element. Can you be more specific about what you need to know? --Heron 20:40, 31 January 2006 (UTC)

History of terms "Series" and "Parallel" for circuits
In another Wiki article (Battery) there is mention of Franklin using capacitors in series and in parallel in the 18th century, which seems unlikely. In the 1820s and 1830s there was a lot of confusion over series vs parallel, with some denying the truth of Ohm's Law. So who introduced these terms to the electrical field? Clearly they were not in use when Henry spoke of "intensity" and "quantity" circuits meaning series and parallel in the 1830's. A little historical section might be appropriate.Edison 18:49, 20 June 2006 (UTC)

Lead image
I’ve made an SVG version of the lead image. Well, I was going to, anyway; this is up with what I ended (click for large version):
 * [[Image:Series and parallel circuits.svg|300px]]

I intend to put it in the lead section instead of the current image. Comments? Also, can somebody please check the numbers? It has been a while since I did anything of this kind. —xyzzyn 16:10, 13 January 2007 (UTC)

Total resistance or equivalent resistance
Should we use the term "equivalent resistance", "total resistance", or both? They both mean the same thing in a sense, but I think equivalent resistance is better, and all the books I see use equivalent resistance. — M ETS 501 (talk) 04:22, 7 April 2007 (UTC)


 * I'd prefer "equivalent resistance". Occasionally I'll hear "total" in conversation, but in writing I've usually seen it as "equivalent". Carlsotr (talk) 19:21, 1 October 2008 (UTC)

Change of varriable
I am not into electrical engineering, but I was wondering about the following:


 * for components in series with resistances R1, R2, etc. To find the current I use Ohm's law:

The first time I read that, it seemed that the author had gone into first person, even though I quickly noticed that I was a variable. Is I a symbolic variable, or can it be replaced with something else? ffm ✎ talk  21:27, 8 May 2007 (UTC)
 * No, it can't really be replaced. I is the standard universally-accepted abbreviation for current.  I didn't think of it that way, but I can see where your confusion comes from. :-) — M ETS 501 (talk) 22:53, 8 May 2007 (UTC)


 * Italicizing it is fine. — Omegatron 13:49, 11 May 2007 (UTC)

Compare:
 * To find the current, I use Ohm's law.
 * To find the current I, use Ohm's law.

Ah, grammar. :-) — Omegatron 14:17, 4 June 2007 (UTC)

Battery Circuits are missing
An important concept in constructing battery packs is the differences in assembling battery cells in series vs parallel to make larger battery packs. In series voltage adds and capacities must be the same. In parallel the capacity adds and the voltage stays the same. I was surprised to see battery circuits omitted.

--Tmenet (talk) 14:14, 29 March 2009 (UTC)

Series and Parallel Circuits
Series ciruit is an electric circuit in which the components are arranged one after the other in series -Only 1 path along which the electrons can flow

-If the pathway is interrupted, the whole circuit cannot function

-Amount of current is the same in all parts of the circuit. (resistors will increase the total resisitance and decrease the current. e.g. adding and extra bulb to a series string of lights makes the lights dimmer.)

-Electrons use up all their potential difference going around the circuit, no matter how many loads are in a circuit. E.g. electrons that leave a 12V battery will lose all 12 V before they return to the + end of the battery. Each load will use part of the total potential difference, depending on how much it resists the flow of electrons.

A parallel circuit is an electric circuit in which the parts are arranged so that electrons can flow along more than one path

Junction points-points where the circuit divides into different paths or where paths combine.

Taken from: Pearson, Investigating Science 9, Pearson Canada Inc., 2009 —Preceding unsigned comment added by Eyehaveyou (talk • contribs) 22:29, 18 November 2009 (UTC)


 * That is an incorrect definition of parallel. I have never had a very high opinion of Pearson training and that just confirms it.  Sp in ni  ng  Spark  23:20, 1 December 2009 (UTC)

Bulbs in a series connection
Can 02 Bulbs of variable wattage be connected in a series connection? —Preceding unsigned comment added by Taklujoy (talk • contribs) 12:26, 22 July 2010 (UTC)


 * Light bulbs can be connected in series, including bulbs of different rated power (aka wattage), but the results are likely to be disappointing! However, bulbs are rarely connected in series because of difficulties with potential difference (aka voltage).  For example, if two bulbs are series-connected to a supply of 120 Volts, the bulbs need to be rated for 60 Volts each (otherwise they won't produce rated power) and such bulbs probably aren't readily available.  If one of the bulbs is required to produce 100 Watts and the other 60 Watts, the first needs to be rated for 75 Volts and the other for 45 Volts.  Such bulbs are, almost certainly, not available so you might series-connect one bulb rated at 100 Watts and one rated at 60 Watt, but they won't produce 100 and 60 Watts respectively because they are not supplied with the appropriate voltage.  There is a perfect solution - connect them in parallel!  Dolphin  ( t ) 12:57, 22 July 2010 (UTC)

im trying to find the value of voltage in a circuit with series and parallel resistors. i have no figure for the current and the supply voltage is (10v) R1 is 3holmes R2 is 6holmes R3 is 2holmes R4 is 3holmes R5 is 6holmes, what will the value of voltage measured at each indevidual resistor??????? —Preceding unsigned comment added by 94.10.29.230 (talk) 19:41, 16 September 2010 (UTC)

Please ask questions at the Reference desk, this page is for discussing improvements to the article.  Sp in ni ng  Spark  07:31, 17 September 2010 (UTC)

Infinite grid
I don't think that infinite grids belong in this simple article on series and parallel circuits. There are many networks that go beyond straightforward series and parallel long before infinity is reached. The material should be moved somewhere more suitable. I have several other problems with the contribution. The cited reference does not contain the formula given. I fail to understand the utility of the accompanying diagram; it does not convey anything useful and completely fails to demonstrate that the discussion is limited to two-dimensional grids (unlike the source paper which goes beyond three-dimensional grids to discuss hyper-grids). It is also divorced from any practical application so examples cannot be described to help. The problems where this sort of thing are needed (in geophysics and bulk resistivity of materials measurements) require a three-dimensional model, continuous resistivity (not lumped) and a boundary surface.  Sp in ni ng  Spark  15:05, 20 May 2011 (UTC)


 * As there have been no comments for three weeks I have gone ahead and removed it.  Spinning Spark  06:04, 15 June 2011 (UTC)

Spacing
There's some weird spacing problem - loads of extra whitespace everywhere, where someone's put additional spaces in the middle of sentences. I copied the text out, fixed the spaces, and copied it back - I don't think anything's broken while copying back and forth, but if you see anything please fix. Anyone know where the spaces came from? --129.234.252.67 (talk) 16:25, 19 July 2011 (UTC)

Lacks picture of parallel circuit
The opening text includes a series circuit image, but nothing showing a parallel circuit. 72.48.211.133 (talk) 17:58, 16 January 2013 (UTC)

Series and Parallel
It will be useful to have precise topological definitions of series and parallel. eg. two circuit elements are in parallel iff .... and two circuit elements are in series iff ...... I think there are such definitions in Purcell E&M, if I remember correctly, but I don't have this book handy. — Preceding unsigned comment added by 76.254.48.184 (talk) 04:28, 1 October 2013 (UTC)
 * Two or more circuit elements are connected in parallel if and only if, the potential difference across each of these circuit elements is always the same. Two or more circuit elements are connected in series if and only if, the current in each of these circuit elements is always the same. Dolphin  ( t ) 06:53, 1 April 2014 (UTC)
 * Two counter examples that readily spring to mind: current mirror and voltage follower. And thinking about it for another 50 milliseconds, I can come up with numerous counter-examples in passive circuits: balanced bridge, bridged T, symmetrical lattice.  How would your definition cope with a two-element series circuit driven by a 0V voltage generator?  Series and parallel are topological concepts and require a topological definition.  Spinning  Spark  15:06, 1 April 2014 (UTC)
 * The comments in the article's third paragraph about the current being the same in all components in a series circuit, and the potential difference being the same in all components in a parallel circuit, are attributed to an impeccably reliable, published source - Physics by Resnick and Halliday.
 * The simplest electrical circuit consists of an emf and one resistor; the next simplest consists of an emf and two resistors. It is at that early point in anyone's understanding of electrical fundamentals that the concept of series connection and parallel connection must be introduced. The engineering applications of the current mirror and voltage follower come a very, very long time after that. Nevertheless, if anyone can find a reliable published source that contradicts the information supplied by Resnick and Halliday, anyone is entitled to add that to the article.
 * I'm not conversant with topology so it is possible the information supplied by Resnick and Halliday is not always consistent with the topological definitions. I have struck out my use of the phrase and only if. Dolphin  ( t ) 11:55, 4 April 2014 (UTC)
 * I don't have an issue with what is written in the article. The article is correct, and I presume the source Resnick and Halliday is also correct.  It is your definition I am disputing.  The statement that elements connected in series have the same current through each element is not equivalent to the statement that elements with the same current through them are connected in series.  Your definition is equivalent to the latter statement and is wrong.  Striking only if does not make it any less wrong.
 * The statements in the article are not definitions. They are statements of the properties of series and parallel.  There is, in fact, no formal definition given in the article—the reader is presumed to be familiar with the concept or else it is self-evident from the diagrams.  In terms of topology, series connection is an irreducible tree and parallel connection is the dual graph of that (but see also dual impedance for a difficulty that arises in constructing duals when nothing is connected to the series/parallel driving point impedance).  Spinning  Spark  13:08, 4 April 2014 (UTC)

In the source cited in Note 2, "Circuits, Devices and Systems", RJSmith says Components which carry the same current are said to be connected in series. (p.21)

In the source cited in Note 3, "Physics", R&H say Resistances across which the identical potential difference is applied are said to be in parallel. (Chapter 32, Example 4.)

However, I concede that these aren’t definitions. You have made your points well. I hope you will respond to the original request from 76.254.48.184. Dolphin ( t ) 06:21, 5 April 2014 (UTC)

Why current is same in series connection?
It will be useful if encyclopedia explains this query.I have provided some info on it.I hope it will be useful. Consider the circuit of series consisting of two resistors,where R1>R2. I meant to say that resistance offered by the resistor 1 is greater than the resistance offered by the resistor 2. Keep t constant i,e calculate the charge transferred through each resistor over the time t. All the way it means that charge transferred through the resistor 1 (Q1) is slightly(go through NOTE part) less than charge transferred through the resistor 2 (Q2) over the same time t.Because,resistor 1 offers high resistance than resistor 2,amount of charge flowed through resistor 1 will be less than the amount of charge flowed through resistor 2 over the same time t.

As it is well known that basic equation for current (I) can be given as I=Qt,where Q is the electric charge transferred through the resistor over a time t.

If you agree with the previous points,current through each resistor can be given as: I1=Q1t and I2=Q2t

Thus if you have agreed all the three points you will conclude that "current through each resistor is different."

But the current through each resistor is considered to be same through all the resistors in case of series connection. So,here comes the unanswered question at the end "How can you explain this contradiction?"

NOTE 1: I have noticed many saying that,if current(motion of charge per unit time) "I" had pass through the conductor then same current(motion of charge per unit time) should come out of the conductor taking the analogy that same water(not considered rate of water) which had flown into the pipe should come out.It is not so,if they have considered rate of motion of charge at first they must consider rate of flow of water latter.They even say that there can't be delay in motion of the charges,so that there would be gap in between.It is not so,there will be atoms in between with free electrons.You can see Nabeshin explaining problem with analogy of flowing water by clicking at adjacent.click here.They say that if current through each resistor is different,electrons would pile up.Yes,there will be slight piling up,that is what results in heating of resistors.But considering this any one can't say current could not be different through different resistors.

NOTE 2: I have notice many others proving current through each resistor to be same,by keeping the ammeter in between the resistor's and else any where,and the value comes out to be same!!It doesn't mean current through each resistor is same,they have calculated current in between the resistor and else any where,but not through the resistor.I think we must find any other way to find current through the resistor,because you can't place an ammeter through a resistor.Well,you might ask "why current is coming out to be same in between the resistors and else any where?",this is because charges get compensated to form a steady flow after coming pass through resistors.We can't expect the same current through both of the resistors in series it depends on the resistance value they offer.Due to compensated motion of the charge the current difference that flowed through either of the resistors might be tending to zero,so that researcher's would have considered the current to be same. Click on this to view a discussion on this topic. — Preceding unsigned comment added by CURIE WILLEY (talk • contribs) 09:41, 18 October 2013 (UTC)


 * You are mistaken. The current is the same through both resistors.  The charge transferred is the same through both resistors.  Spinning  Spark  22:23, 19 October 2013 (UTC)


 * The key is that the larger resistor grabs more voltage, too, out of the total amount of voltage available, and this pulls harder to make the current exactly the same. Physical laws sometime specify a seemingly unintuitive outcome and you have to explain it to yourself till you agree with the outcome. 84.227.254.143 (talk) 19:24, 31 March 2014 (UTC)

'Current Flow'...
I'm not an electrical engineer so I don't feel confident enough to edit this article directly without introducing new errors, but I do know that 'current flow' is really misleading. Current doesn't flow, current *is* a flow of charge:


 * Since a current is a flow of charge, the common expression "flow of current" should be avoided, since literally it means "flow of flow of charge.
 * - Modern College Physics: Sears, Wehr, & Zemanski

See also: [http://amasci.com/miscon/eleca.html#current ELECTRIC CURRENT IS A FLOW OF ENERGY? Wrong.] — Preceding unsigned comment added by 82.73.226.224 (talk) 00:01, 17 December 2013 (UTC)
 * The article doesn't talk about a current flow. It says a "current flows". The expression is so the same current flows through all of the components. Dolphin  ( t ) 00:41, 17 December 2013 (UTC)


 * You are right! I'll just attribute my post to English not being my native language combined with hyper-vigilance after reading the text in the aforementioned link :) — Preceding unsigned comment added by 82.73.226.224 (talk) 01:05, 18 December 2013 (UTC)

Article Introduction
I feel like the introduction is confusing (first two sentences). I am pretty sure all components can be viewed as being in either series or parallel with one another. The topology specifically doesn't care about how components relate to each other - it only talks about what happens between them. Thus, I suggest a change along the lines of:


 * "Components of an electrical circuit are either in series or parallel with one another. The number of connections between components can change (see: topology), but, fundamentally, a component is always either in series or parallel with another component."

CCSTOOS (talk) 07:11, 28 July 2014 (UTC)


 * That is not correct. Counterexamples of some very simple circuits can easily be found that cannot be expressed as any combination of series and parallel operations. SpinningSpark 08:38, 28 July 2014 (UTC)


 * The simplest circuit consists of nothing more than an emf and a resistor. This simple arrangement qualifies as a series connection because the same current flows through both; and also as a parallel connection because both components experience the same potential difference. I think this arrangement might be called simple connection rather than series or parallel connection. Dolphin  ( t ) 13:03, 28 July 2014 (UTC)
 * Well the fact that both series and parallel work as a description of that circuit does not contradict the OP's assertion. However, a simple circuit that does contradict it is the well known bridge circuit.  It is impossible to describe that with any combination of just series and parallel operators.  More fundamentally, a description in terms of series and parallel operators implicitly assumes a one-port.  Even some of the simplest two-port networks, such as a T-network, cannot be described by series and parallel operations unless a port reduction transform is first applied.  By the way, the reason your basic circuit with two elements is ambiguous is because it is not even a one-port, it is a zero-port.  The OP is also fundamentally wrong in the assertion that the "topology specifically doesn't care about how components relate to each other".  Actually, that is the only thing that topology cares about. SpinningSpark 15:53, 28 July 2014 (UTC)

Parallel batteries, example (question)

 * .Article point 2.1 states "In a parallel circuit the voltage is the same for all elements."

But if the power souces (batteries) are of different voltage (or reversed direction), what happens then ? I would be very greatful for any explaining of the two examples. What will the voltage be in these cases ? Boeing720 (talk) 04:06, 11 September 2015 (UTC)
 * Your circuits contain no resistance. In accordance with Ohm's law you must expect infinitely large currents to flow, destroying the cells; or at least very large currents that will damage the cells. Try re-drawing your circuits, incorporating a resistance in series with each cell. Then, it might be possible to explain what will happen. Dolphin  ( t ) 12:01, 13 September 2015 (UTC)
 * Thanks for Your reply. I was thinking of ideal power sources (symbol a circle and a +-sign) without emk or inner ressistance. but if You find it easier to help me understand this question, please just a 1 kOhm ressistance beside the power sources. (I do though fail to see
 * why that's necessary, as it is possible to calculate the total voltage if the power sources are of equal voltage.
 * Especially the left example, would be VERY MUCH APPRICIATED, if You possible can help me with.
 * I'm only asking for the total voltage output, especially in the left example.
 * And the text in the 2.1. section isn't the full truth.
 * I would like to add that I have searched several sources, collections like ours - but the parallel power source appear to always lack examples with different voltages.(Nor have I got any voltmeter or other requiered objects , in order to make experiments of my own. Anyways, I'm greatful for your reply, but if possible, could You please help me with this annoying problem, which at first sight appear to be very simple. Thanks again Boeing720 (talk) 13:51, 14 September 2015 (UTC)

Great. I will assume there is a 1000 ohm resistor adjacent to both the 12V battery and the 4V battery. I will also assume that where you show U? there is a voltmeter and nothing else. I will examine the two diagrams using the Loop Current Method. (If you aren’t familiar with this method, see Circuits, Devices and Systems by R.J. Smith, p.36, Wiley International edition.)

Firstly, the left example. This represents a large 12V battery being used to recharge a rechargeable battery that has discharged down to 4V. There is a loop containing the 12V battery, the 4V battery and two resistors each of 1000 ohm. Tracing a path around the loop in the clockwise direction, the net electromotive force is 8V (plus 12V, minus 4V); and the combined resistance is 2000 ohms. Dividing 8V by 2000 ohms and applying Ohm’s Law shows the current around the loop is 4 mA in the clockwise direction. The potential difference across each 1000 ohm resistor is 4 mA times 1000 ohms which is 4V. The voltmeter sees a potential difference of 8V. This is determined in each of two ways:

with the current: 12V across the battery, minus 4V across its associated resistor, which is 8V.

against the current: 4V across the battery, plus 4V across its associated resistor, which is 8V.

The energy of the 12V battery is decreasing at the rate of 12V times 4mA which is 48 mW. Energy leaving the circuit as heat flowing out of the resistors is 4 mA times 4 mA times 2000 which is 32 mW. Therefore the energy of the 4V battery is increasing at the rate of 16 mW, or 4V times 4 mA.

Secondly, the right example. This represents a 12V battery and a 4V battery working together in the circuit. There is a loop containing the 12V battery, the 4V battery and two resistors each of 1000 ohm. Tracing a path around the loop in the clockwise direction, the net electromotive force is 16V (plus 12V, plus 4V); and the combined resistance is 2000 ohms. Dividing 16V by 2000 ohms and applying Ohm’s Law shows the current around the loop is 8 mA in the clockwise direction. The potential difference across each 1000 ohm resistor is 8 mA times 1000 ohms which is 8V. The voltmeter sees a potential difference of 4V. This is determined in each of two ways:

with the current: 12V across the battery, minus 8V across its associated resistor, which is 4V.

against the current: minus 4V across the battery, plus 8V across its associated resistor, which is 4V.

The energy of the 12V battery is decreasing at the rate of 12V times 8 mA which is 96 mW. Energy leaving the circuit as heat flowing out of the resistors is 8 mA times 8 mA times 2000 which is 128 mW. Therefore the energy of the 4V battery is decreasing at the rate of 32 mW, or 4V times 8 mA. Dolphin  ( t ) 12:47, 16 September 2015 (UTC)

I'll just add something extra on the first statement.

Mathematically, U is merely indetermined since there is more than one correct way to describe its value. Proof: let's search the current i travelling trough the mesh made by the two batteries. Assume an impedance Z in series with both batteries. In the case a, i = (12 - 4)/Z and in the case b, i = (12 - (-4))/Z. Now, in any case you are told to assume theres zero impedance between batteries, that means you need to evaluate the limit of i(Z) as Z goes to zero, which is simply infinite. So, thus, you can conclude you have an infinite current. Thus, the voltage equation will be:

$$12V - 4V = \frac{Z=0}{i=\infty} = \frac{0}{\infty}$$

So, there you go. I'm kinda late to be helpful, unfortunately, but somebody else will look at this and find it useful, hopefully. Eligio Budde (talk) 07:45, 26 May 2016 (UTC)

contention with into statement
"Simply put, in a parallel circuit current increases but the voltage stays the same, and in a series circuit current stays the same but the voltage increases".

In a series circuit the voltage actually decreases after each resistor, also known as voltage drop. Let's say we have a series circuit with 12v and 2 resistors. The first resistor has 10 ohms and the second resistor has 50 ohms. We have a total of 60 ohms resistance and 0.2 amps. The voltage drops by 2v after the first resistor, then drops by 10v for the second resistor. What am I missing here? Unless I am mistaken the statement above should change?? 199.19.248.122 (talk) 23:29, 14 June 2016 (UTC)

HI
HI — Preceding unsigned comment added by 2600:1700:F21:4C60:A9A0:4DFD:EE37:1E3C (talk) 18:43, 29 April 2020 (UTC)