# Current without Source Voltage.

#### ben sorenson

Joined Feb 28, 2022
165
I understand the "phenomenon" where there can be a voltage without current. But I was wondering what would be going on in a situation where there would exist a current without a "voltage" or "potential difference" across the "source" of a circuit in a short circuit condition.

Consider the following circuits below.

In the "open circuit" scenario a source has a potential difference of 760mV. For obvious reasons there is no current as the switch is open.

However, in the "closed/short circuit" scenario the switch is closed. The voltage "source" that was 760mV decays to 0.00V and a current of 760uA is developed across the 1 OHM load resistor.

#### Dodgydave

Joined Jun 22, 2012
11,151
There must be 760uV then on the battery..

Joined Feb 20, 2016
4,375
The battery has internal resistance that is not shown and the voltage is "lost" across that so the external battery voltage reads as 0V. At least, close to 0V as there is the 1R resistor in line so the battery terminals will read 760uV

#### ben sorenson

Joined Feb 28, 2022
165
There must be 760uV then on the battery..
So the internal resistance of the source i
There must be 760uV then on the battery..
I will check for the 760uV accross the "soon the oscilliscope again.
The battery has internal resistance that is not shown and the voltage is "lost" across that so the external battery voltage reads as 0V. At least, close to 0V as there is the 1R resistor in line so the battery terminals will read 760uV
I will check on the oscilliscope again for the 760uV. The "source" has an extremely high amount of internal resistance, the last time I checked both of my DMM's went OL.

#### MisterBill2

Joined Jan 23, 2018
16,612
I can not believe that an actual ENGINEER is posing this question.

#### boostbuck

Joined Oct 5, 2017
419
I can not believe that an actual ENGINEER is posing this question.
Type= 'Other', so maybe nothing to do with electrics?????

#### AlbertHall

Joined Jun 4, 2014
12,293

#### Ya’akov

Joined Jan 27, 2019
8,550
There can be current with no voltage in a superconductor circuit and, it seems, in non-superconductors.
https://physics.aps.org/articles/v1/7
Well, as the article say, these (very tiny) rings have "finite resistance" and while the current—$$\mathsf{1 x 10 ^{-9}A}$$—continues to flow even in the absence of a magnetic field, unlike a superconductor, there is a resistance to plug into Ohm's Law which means to you work out the tiny voltage involved.

These rings are on the scale of 1㎛ and the temperature for the experiment is below 1K. So, this isn't really an ordinary phenomenon.

#### MrAl

Joined Jun 17, 2014
10,914
Hi,

For what it is worth, with an ideal inductor in parallel with an ideal wire and with a non-zero initial current through the inductor, the non-zero current will flow forever.
That's theory. This is the dual of an ideal open circuited capacitor, which holds the voltage indefinitely.

#### Ya’akov

Joined Jan 27, 2019
8,550
Hi,

For what it is worth, with an ideal inductor in parallel with an ideal wire and with a non-zero initial current through the inductor, the non-zero current will flow forever.
That's theory. This is the dual of an ideal open circuited capacitor, which holds the voltage indefinitely.
I think "ideal" is a very ambiguous term here. It implies a set of criteria that remains unstated and I am not convinced that ideal, which is indicative of a value judgement is a good way to think about these things.

I believe that if you replace ideal with simplified it might be more to the point. I don't think there is anything "ideal" about a model that is simplified to make it a practical impossibility, but simplified models are certainly useful for thinking about things.

In my view, an ideal model can only exist in a context and if you attempt to transport it out of that context you might as well call it "artificial" and discard it since it has no explanatory or predictive power in those areas that have been omitted in its simplification.

But, very importantly, these simple models are exceedingly useful in the context for which they've been developed. Just leave them when you leave that context or you will be spending a lot of time wandering away from reality as your reasoning piles impossibility on impossibility.

#### MrAl

Joined Jun 17, 2014
10,914
I think "ideal" is a very ambiguous term here. It implies a set of criteria that remains unstated and I am not convinced that ideal, which is indicative of a value judgement is a good way to think about these things.

I believe that if you replace ideal with simplified it might be more to the point. I don't think there is anything "ideal" about a model that is simplified to make it a practical impossibility, but simplified models are certainly useful for thinking about things.

In my view, an ideal model can only exist in a context and if you attempt to transport it out of that context you might as well call it "artificial" and discard it since it has no explanatory or predictive power in those areas that have been omitted in its simplification.

But, very importantly, these simple models are exceedingly useful in the context for which they've been developed. Just leave them when you leave that context or you will be spending a lot of time wandering away from reality as your reasoning piles impossibility on impossibility.
Hello there Ya'akov,

The idea here is that theory insists upon itself. That is, it is complete when self contained and has its own interesting facets in and of itself.
I am tempted here to say that it is complete 'only' when it is contained, but that itself would be a limited view I think.
The way I view theory is that it is like a measuring tool where we can use it to judge the imperfect, and also learn more about the imperfect practical aspects. So in that way it can be used for practical purposes also.

Yes I agree that when we say 'ideal' we often have to define the parameters that make it ideal. There is an exception though I think, and that is when we accompany it with an example. In my post I mentioned the actual circuit and the operating conditions, and from those we can extrapolate the degree of ideality of each of the components. So in a manner of speaking, the circuit and conditions also insist upon themselves because they and the circuit can not exist in the manner given unless we presume, well, exactly what was given. Namely, that the current will circulate indefinitely. The current can not circulate indefinitely unless the inductor dissipates no power, and neither the wire that shorts it out. From that we can deduce that the meaning of ideal in that case is the inductor is perfect in every way, and loses no energy throughout it's entire operation.

I realize now that I could have been more specific about the degree of ideality present, but I did figure that goes with the example. If I had to be more explicit, I would state simply that the inductor never loses any energy from the time the experiment begins to the time it ends, even if it ran for a trillion years or more.
Now this may also seem like a no-go situation again because this can not happen under normal operating conditions, but we can use it to understand more about the nature of these circuits. We could allow the resistance of the wire to increase ever so slightly, and then we see the current diminishing over time, even though very slowly. We can then go on to change the inductor inductance value itself, making it go larger or smaller, and see how that changes things. The larger inductor will take longer to dissipate all the energy for example, and what we see mimics the operation of the ideal inductor shorted with a perfectly ideal wire that also does not dissipate any energy. We can set L and R to make it discharge so slow, that it acts almost like the ideal components did. In this way we may gain a little more insight into how this works.

The main topic here was seeing current flow without a voltage, and that's one of the best theoretical examples I have seen outside of superconductors. Not only that, the only way current can flow indefinitely without some voltage is it must flow in a loop with no resistance. The shorted inductor example shows this main issue.
If you would feel more comfortable if I gave better specifications about the nature of the inductor and the wire, I can do that of course, no problem.

#### ben sorenson

Joined Feb 28, 2022
165
Hello there Ya'akov,

The idea here is that theory insists upon itself. That is, it is complete when self contained and has its own interesting facets in and of itself.
I am tempted here to say that it is complete 'only' when it is contained, but that itself would be a limited view I think.
The way I view theory is that it is like a measuring tool where we can use it to judge the imperfect, and also learn more about the imperfect practical aspects. So in that way it can be used for practical purposes also.

Yes I agree that when we say 'ideal' we often have to define the parameters that make it ideal. There is an exception though I think, and that is when we accompany it with an example. In my post I mentioned the actual circuit and the operating conditions, and from those we can extrapolate the degree of ideality of each of the components. So in a manner of speaking, the circuit and conditions also insist upon themselves because they and the circuit can not exist in the manner given unless we presume, well, exactly what was given. Namely, that the current will circulate indefinitely. The current can not circulate indefinitely unless the inductor dissipates no power, and neither the wire that shorts it out. From that we can deduce that the meaning of ideal in that case is the inductor is perfect in every way, and loses no energy throughout it's entire operation.

I realize now that I could have been more specific about the degree of ideality present, but I did figure that goes with the example. If I had to be more explicit, I would state simply that the inductor never loses any energy from the time the experiment begins to the time it ends, even if it ran for a trillion years or more.
Now this may also seem like a no-go situation again because this can not happen under normal operating conditions, but we can use it to understand more about the nature of these circuits. We could allow the resistance of the wire to increase ever so slightly, and then we see the current diminishing over time, even though very slowly. We can then go on to change the inductor inductance value itself, making it go larger or smaller, and see how that changes things. The larger inductor will take longer to dissipate all the energy for example, and what we see mimics the operation of the ideal inductor shorted with a perfectly ideal wire that also does not dissipate any energy. We can set L and R to make it discharge so slow, that it acts almost like the ideal components did. In this way we may gain a little more insight into how this works.

The main topic here was seeing current flow without a voltage, and that's one of the best theoretical examples I have seen outside of superconductors. Not only that, the only way current can flow indefinitely without some voltage is it must flow in a loop with no resistance. The shorted inductor example shows this main issue.
If you would feel more comfortable if I gave better specifications about the nature of the inductor and the wire, I can do that of course, no problem.

#### MisterBill2

Joined Jan 23, 2018
16,612
I recommend caution in this discussion, and avoid mentioning that locality where ideal components are commonly available and used to achieve ideal results under all conditions.

#### MrAl

Joined Jun 17, 2014
10,914
Hi,

Oh you mean you would like more specifications about the ideal example that was set up?
That's no problem and may satisfy other readers as well, but keep in mind, you asked for it

First, the inductor has zero series resistance, and when i say zero i mean zero, not 1mOhm, not 1uOhm, etc., no resistance at all.
Second, the wire shorting the inductor has zero resistance.
Third, at a time before t=0 the inductor was provided with a current, one way or another, that established a non-zero DC current in the wire.
Fourth, neither the inductor nor the wire expels any magnetic energy of any kind. That simply means that it does not radiate any type of dynamic field. If it has a field, the field is static and does not cause the inductor or wire to radiate any energy.

What all this means is that the energy applied before t=0 never decreases. That's the only way to keep the current flowing forever, (or is it ... read on).

There is an interesting side issue however, and that is what happens if we use a very, very, small resistance in series with the inductor instead of a perfect short with zero Ohms resistance. If we go really, really small, say 1uOhm or even 1pOhm, what does this change.
What happens now is that the construction does lose some energy over time, but since it is going to be very small it will take a very long time to discharge the inductor. If we go low enough, it could theoretically take years to discharge.

Here is something else interesting that relates to that last part with the very low series R.
Because, in theory, the circuit behavior is governed by the simple series RL exponential equation, we might say that it does in fact take forever to discharge any inductor. Why would this be true.
It's because the exponential never truly drops to a perfect zero, it just decreases over time. It gets so very, very, very small (and i can't stress the smallness of this here enough) that we usually consider it to be zero, but numerically, given infinite precision, the current never drops to a perfect zero in any RL circuit.
We have to be careful with the interpretation of this though, because this is almost like a theory of a theory, and so this resides only in the realm of theory, and we never really consider this to be a practical aspect of an RL circuit.
The same is true for a RC circuit that is discharging. The voltage of the cap never gets to a perfect zero, but we always consider it to be zero after it gets below some very low level like 1microvolt. If we follow it numerically though, again in theory only, we would see the voltage fall to 1e-6 volts, then eventually 1e-9 volts, then 1e-12 volts, then 1e-15 volts, etc., etc. Eventually it could get down to 1e-300 volts, which is extremely low, and that is close to where we see the normal 16 digit computer numerical precision start to declare is as a true zero. If we use 32 digits however, it would keep getting lower still but not zero. Going to 64 digits we would see again go lower but not to zero, then 128 digits, then 256 digits, etc., etc.
This level of theory however is never used, i don't think anyway, except maybe in the lab with some very high grade lab equipment.

Hope this sheds some light on the theory behind this, but remember a lot of this is PURE theory and much of it can never be realized in the real world by most of us, if any of us.

#### MisterBill2

Joined Jan 23, 2018
16,612
NONE of those "perfect" items, nor even reasonably close to perfect items, are available in the real world where I reside.

I was introduced to the concept of "perfect" circuit elements during the third week of the basic DC circuits analysis course. The explanation was that in our world we come close enough with answers to work very well, but we always must know that reality is not as exact as our math was.
This meant that we were dealing with at most three significant figures that needed to be correct. Thus slide-rule accuracy was quite suitable for most engineering calculations, the exact math was reserved for the financial realm.

#### GetDeviceInfo

Joined Jun 7, 2009
2,180
Even in perfect terms, the resistor is parallel to the sources, resulting in a voltage proportionate to current flow.

#### MrAl

Joined Jun 17, 2014
10,914
NONE of those "perfect" items, nor even reasonably close to perfect items, are available in the real world where I reside.

I was introduced to the concept of "perfect" circuit elements during the third week of the basic DC circuits analysis course. The explanation was that in our world we come close enough with answers to work very well, but we always must know that reality is not as exact as our math was.
This meant that we were dealing with at most three significant figures that needed to be correct. Thus slide-rule accuracy was quite suitable for most engineering calculations, the exact math was reserved for the financial realm.
Wasn't that made perfectly (ha ha) clear?

Ideal, or "perfect" elements are not made to be used for the real world except as a behavioral study. The behavioral study helps us to figure out what we can get away with in the real world.

The simplest example i think is with a resistor tolerance. We might chose a 100 Ohm resistor for a given circuit. When we state that "100" we are talking about an exact number, not an estimate. But when we apply it to the real world we have to remember that it could be 99 Ohms or 101 Ohms (1 percent tolerance).
Does that mean that the ideal number of 100 means nothing? Certainly not, and those two other numbers are not ideal either, yet we can use them to figure out what will happen if the resistor is out of tolerance or goes out from a temperature change or ageing. In these cases, we would use an 'ideal number either 99 or 101 to do a second analysis to see what happens with the circuit. If it was a voltage divider for example where the bottom resistor is not perfect, we would first use 99 and then use 101 and see if the voltage variation is able to be tolerated in the actual application, which may be for a voltage reference. Those two numbers 99 and 101 are not exact either, they are ideal in the sense that the resistance due to the tolerance is going to be that even though in reality it won't be. It may be 99.3 and 100.6, or 99.5 and 100.1, etc. Virtually nothing we do in theory is anything but ideal, but we use that anyway to determine what will happen in a real life circuit, and we come up with some pretty good results that way.

In the same way, we use a ruler to measure the size of a box, we use theory to measure the practicality of a circuit. We do not intend to get a perfect result in real life, but we have a way to figure out what size the box is.

Theory allows us to convey information that is vital to circuit analysis. It brings out the basic behaviors of elements and circuits so we can get an idea how they work. When we do not consider any variations that's just because we want to know the basic operation, not the exact details. However, we are always free to explore what happens with the variations also, using ideal components yet again (as in the resistor divider example). Thus, using ideal components allows us to not only understand the basic operation of circuits, but also to investigate any variations that can occur in real life. That's quite valuable.

Much of circuit theory is taught on paper using ideal components and after all, on paper, is there anything else BUT ideal components.