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Simon Fitch
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To summarise, then,Cells and batteries of cells are voltage sources produce fixed voltages. They maintain a constant potential difference chemically (at least until they are depleted of energy, or over-charged to destruction). Their chemical and current sources providephysical construction are such that charges at one end tend to have a fixed currents, but don't otherwise provide any levelamount of controlpotential energy with respect to charges at the other thanterminal. How that happens is for the chemists to know.

The relationship between voltageOther ways exist to produce a fixed potential difference, such as charge pumps, and current is embodied by Ohm's law for resistorsit's sufficient to design a circuit that constantly monitors some potential difference, and if it changes, take some action to restore it. "Pump faster or pump slower", in the same way you occasionally pump air into a varianttyre that has a slow leak, to maintain constant pressure.

At the moment I can't think of Ohm's law which deals with changesany current sources that are able to self-regulate like chemical cells, although probably some such thing exists. However, it's possible to build regulators that maintain a constant current flowing through them, in the same way that voltage regulators do; monitor and current for everything elseadjust. (There are also formulae which deal with

At the relationship betweenrisk of confusing voltage andsources with current for inductors and capacitorssources, which introducein practice it's probably easiest to think of a current source as something that varies its own potential difference to whatever value is required to obtain the variable timerequisite current through whatever's connected to it (and, but that's another topic altogetherconsequently, itself). With resistorsThe result is the behaviour you would expect from a current source; current through it remains fixed while the voltage across may vary. As long as there's no functional difference, this relationshipthere is called "resistance"no distinction between a current source and a voltage source that varies voltage to maintain constant current.

It is not appropriateBy that same argument, you might consider a constant voltage source to apply Ohm's lawbe something that varies current, andto whatever amount produces exactly the concept of ohmic resistancecorrect fixed potential difference across it. Again, a variable current source that maintains a constant potential difference is functionally identical to a fixed voltage source. Both practically and mathematically there's no distinction.

However you envisage these sources, or tothey each only represent a currentsingle quantity in the simultaneous equations that you derive for any system. When you see a voltage source in a schematic, becauseall you know about it, until you solve for all the relationship betweenother variables, is the voltage andacross it. For a current for themsource in a schematic, all you know (until the system is not directly proportionalsolved) is the current through it. How they work is actually irrelevant in the analysis.

You can, howeverCells aside, attribute to them the properties of dynamic resistancebuild practical, whenactive voltage and current sources is not trivial. When you consider their response to changessee a source in eithera schematic, it represents an abstraction of something that, in practice, may have substantial complexity, consisting of transistors and/or op-amps, and other elements, whose role is to make continuous adjustments to maintain some fixed voltage or current. 

In that case an idealthe analysis, though, their behaviour is truly trivial. When you see a voltage source can be considered to have zero resistancein a schematic, and an idealyou know the potential difference between two points. That's all. When you see a current source, you know the current in that path. That is considered to have infinite resistanceall.

To summarise, then, voltage sources produce fixed voltages and current sources provide fixed currents, but don't otherwise provide any level of control other than that.

The relationship between voltage and current is embodied by Ohm's law for resistors, and a variant of Ohm's law which deals with changes in voltage and current for everything else. (There are also formulae which deal with the relationship between voltage and current for inductors and capacitors, which introduce the variable time, but that's another topic altogether). With resistors, this relationship is called "resistance".

It is not appropriate to apply Ohm's law, and the concept of ohmic resistance, to a voltage source, or to a current source, because the relationship between voltage and current for them is not directly proportional.

You can, however, attribute to them the properties of dynamic resistance, when you consider their response to changes in either voltage or current. In that case an ideal voltage source can be considered to have zero resistance, and an ideal current source is considered to have infinite resistance.

Cells and batteries of cells are voltage sources. They maintain a constant potential difference chemically (at least until they are depleted of energy, or over-charged to destruction). Their chemical and physical construction are such that charges at one end tend to have a fixed amount of potential energy with respect to charges at the other terminal. How that happens is for the chemists to know.

Other ways exist to produce a fixed potential difference, such as charge pumps, and it's sufficient to design a circuit that constantly monitors some potential difference, and if it changes, take some action to restore it. "Pump faster or pump slower", in the same way you occasionally pump air into a tyre that has a slow leak, to maintain constant pressure.

At the moment I can't think of any current sources that are able to self-regulate like chemical cells, although probably some such thing exists. However, it's possible to build regulators that maintain a constant current flowing through them, in the same way that voltage regulators do; monitor and adjust.

At the risk of confusing voltage sources with current sources, in practice it's probably easiest to think of a current source as something that varies its own potential difference to whatever value is required to obtain the requisite current through whatever's connected to it (and, consequently, itself). The result is the behaviour you would expect from a current source; current through it remains fixed while the voltage across may vary. As long as there's no functional difference, there is no distinction between a current source and a voltage source that varies voltage to maintain constant current.

By that same argument, you might consider a constant voltage source to be something that varies current, to whatever amount produces exactly the correct fixed potential difference across it. Again, a variable current source that maintains a constant potential difference is functionally identical to a fixed voltage source. Both practically and mathematically there's no distinction.

However you envisage these sources, they each only represent a single quantity in the simultaneous equations that you derive for any system. When you see a voltage source in a schematic, all you know about it, until you solve for all the other variables, is the voltage across it. For a current source in a schematic, all you know (until the system is solved) is the current through it. How they work is actually irrelevant in the analysis.

Cells aside, to build practical, active voltage and current sources is not trivial. When you see a source in a schematic, it represents an abstraction of something that, in practice, may have substantial complexity, consisting of transistors and/or op-amps, and other elements, whose role is to make continuous adjustments to maintain some fixed voltage or current. 

In the analysis, though, their behaviour is truly trivial. When you see a voltage source in a schematic, you know the potential difference between two points. That's all. When you see a current source, you know the current in that path. That is all.

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Simon Fitch
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We're talking about ideal sourcesThere are only two quantities that can be considered fundamental, or "real", in the sense that they actually exist, and those are voltage and current. It'sResistance is artificial, a contrived quantity that merely describes the relationship between voltage and current.

Voltage across some component, and current through it, are usually inappropriaterelated somehow. For instance, for a resistor we find that the two values are directly proportional to apply Ohm's law to themeach other. Ohm's lawThat is, if you double the voltage \$V\$ across a resistor, the current \$I\$ through it also doubles, or if you halve current \$I\$, voltage \$V\$ is halved too. That particular relationship is called "Ohm's law":

$$ V = R \times I $$

The constant of proportionality in this relationship is resistance \$R\$. This formula only applies to resistors. For other elements that have a very clear dependency, such as voltage sources, current sources, capacitors, diodes and so on, the relationship between current and voltage is not directly proportional. For instance, the current \$I\$ through a silicon diode, as a function of the voltage \$V\$ across it is:

$$ I = I_S\left(e^{\frac{qV}{kT}}-1 \right) $$

It will be helpful to draw graphs of voltage vs. current for three components, a 10V voltage source (blue), a 1A current source (red), and a 2.5Ω resistor (green):

enter image description here

The key features of these graphs are:

  • The voltage source (blue) has a constant voltage across it, regardless of the current through it. It is a straight, horizontal line, with gradient (slope) \$\frac{dV}{dI} = 0\$. Notably, current and voltage are independent of each other, when current changes, voltage does not.

  • The current through the current source (red) is fixed at 1A, regardless of the voltage across it. It is also a straight line, but this time it's vertical, having slope \$\frac{dV}{dI} = \infty\$. Again, current and voltage are independent; when voltage changes, current does not.

  • The resistor (green) is not vertical or horizontal. Its slope is non-zero and finite: \$\frac{dV}{dI} = 2.5\$. The line passes through the origin \$(I=0, V=0)\$. This is a graph showing direct proportionality between \$V\$ and \$I\$. When current changes, voltage does too, in proportion to the change in current, and vice versa.

That facts that neither voltage source nor current source have any relationship at all between voltage and current (they have infinite/zero V-I gradients), and that their V-I curves do not pass through themthe origin, whichare clear indicators that the concept of resistance is not the case for idealapplicable to sources. Resistance implies direct proportionality between voltage and current, a behaviour which sources simply do not exhibit.

The short answer to your question is that a voltage source "outputs" only a voltage, and doesn't impose any constraint on the current through it. A current source "outputs" only a current, imposing no constraint on voltage across it.


Perhaps the simplest demonstration of a source's independence of voltage and current is when we connect a current source in parallel with a voltage source:

The two sources behave as follows:

  • A voltage source always has a fixed potential difference across it, but will not impose any constraints on what current flows through it. The only thing it has to say about anything is what voltage is across it, having absolutely no control over current that flows. Issues of current are left up to other elements of the circuit.

  • A current source always has a fixed current through it, and has nothing to say about what voltage exists across it, and has no control over that voltage. It leaves all decisions regarding voltage up to the other elements in the circuit.

There's no ambiguity about the current, here, or the voltage, and either source can change whatchoose the conditions that it "imposes" without the other so much as batting an eyelid. In other words, where does resistance play a role here? No equations that you derive for the behaviour of this circuit make any mention of "resistance" at all. There are two equations:

That's it. Where's the R?

Let's look at the current vs. voltage curves for the voltage source (blue), current source (red) and a 2.5Ω resistance (green):

enter image description here

The voltage source's voltage (blue) remains fixed at 10V regardless of the current through it. By contrast, regardless of the voltage (red) across the current source, its current remains constant at 1A.

The key difference between those two graphs and the green (resistance) one is that the green trace passes through the origin (0, 0). This means that it obeys at all times the relationship:

$$ R = \frac{V}{I} = \frac{5}{2} = 2.5\Omega $$

Ohm's law therefore describes a direct proportionality between current and voltage, which results in 0V across a resistor when 0A passes through it. Both proportionality and passing through the origin are features missing from the sources' behaviours. Therefore it's not appropriate to apply Ohm's law to sources.

 

We're talking about ideal sources. It's usually inappropriate to apply Ohm's law to them. Ohm's law applies to elements that have a very clear dependency between the voltage across and current through them, which is not the case for ideal sources.

Perhaps the simplest demonstration of a source's independence of voltage and current is when we connect a current source in parallel with a voltage source:

The two sources behave as follows:

  • A voltage source always has a fixed potential difference across it, but will not impose any constraints on what current flows through it. The only thing it has to say about anything is what voltage is across it, having absolutely no control over current that flows. Issues of current are left up to other elements of the circuit.

  • A current source always has a fixed current through it, and has nothing to say about what voltage exists across it, and has no control over that voltage. It leaves all decisions regarding voltage up to the other elements in the circuit.

There's no ambiguity about the current, here, or the voltage, and either source can change what the conditions that it "imposes" without the other so much as batting an eyelid. In other words, where does resistance play a role here? No equations that you derive for the behaviour of this circuit make any mention of "resistance" at all. There are two equations:

That's it. Where's the R?

Let's look at the current vs. voltage curves for the voltage source (blue), current source (red) and a 2.5Ω resistance (green):

enter image description here

The voltage source's voltage (blue) remains fixed at 10V regardless of the current through it. By contrast, regardless of the voltage (red) across the current source, its current remains constant at 1A.

The key difference between those two graphs and the green (resistance) one is that the green trace passes through the origin (0, 0). This means that it obeys at all times the relationship:

$$ R = \frac{V}{I} = \frac{5}{2} = 2.5\Omega $$

Ohm's law therefore describes a direct proportionality between current and voltage, which results in 0V across a resistor when 0A passes through it. Both proportionality and passing through the origin are features missing from the sources' behaviours. Therefore it's not appropriate to apply Ohm's law to sources.

There are only two quantities that can be considered fundamental, or "real", in the sense that they actually exist, and those are voltage and current. Resistance is artificial, a contrived quantity that merely describes the relationship between voltage and current.

Voltage across some component, and current through it, are usually related somehow. For instance, for a resistor we find that the two values are directly proportional to to each other. That is, if you double the voltage \$V\$ across a resistor, the current \$I\$ through it also doubles, or if you halve current \$I\$, voltage \$V\$ is halved too. That particular relationship is called "Ohm's law":

$$ V = R \times I $$

The constant of proportionality in this relationship is resistance \$R\$. This formula only applies to resistors. For other elements, such as voltage sources, current sources, capacitors, diodes and so on, the relationship between current and voltage is not directly proportional. For instance, the current \$I\$ through a silicon diode, as a function of the voltage \$V\$ across it is:

$$ I = I_S\left(e^{\frac{qV}{kT}}-1 \right) $$

It will be helpful to draw graphs of voltage vs. current for three components, a 10V voltage source (blue), a 1A current source (red), and a 2.5Ω resistor (green):

enter image description here

The key features of these graphs are:

  • The voltage source (blue) has a constant voltage across it, regardless of the current through it. It is a straight, horizontal line, with gradient (slope) \$\frac{dV}{dI} = 0\$. Notably, current and voltage are independent of each other, when current changes, voltage does not.

  • The current through the current source (red) is fixed at 1A, regardless of the voltage across it. It is also a straight line, but this time it's vertical, having slope \$\frac{dV}{dI} = \infty\$. Again, current and voltage are independent; when voltage changes, current does not.

  • The resistor (green) is not vertical or horizontal. Its slope is non-zero and finite: \$\frac{dV}{dI} = 2.5\$. The line passes through the origin \$(I=0, V=0)\$. This is a graph showing direct proportionality between \$V\$ and \$I\$. When current changes, voltage does too, in proportion to the change in current, and vice versa.

That facts that neither voltage source nor current source have any relationship at all between voltage and current (they have infinite/zero V-I gradients), and that their V-I curves do not pass through the origin, are clear indicators that the concept of resistance is not applicable to sources. Resistance implies direct proportionality between voltage and current, a behaviour which sources simply do not exhibit.

The short answer to your question is that a voltage source "outputs" only a voltage, and doesn't impose any constraint on the current through it. A current source "outputs" only a current, imposing no constraint on voltage across it.


Perhaps the simplest demonstration of a source's independence of voltage and current is when we connect a current source in parallel with a voltage source:

There's no ambiguity about the current, here, or the voltage, and either source can choose the conditions that it "imposes" without the other so much as batting an eyelid. In other words, where does resistance play a role here? No equations that you derive for the behaviour of this circuit make any mention of "resistance" at all. There are two equations:

That's it. Where's the R?

 
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Simon Fitch
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To summarise, then, voltage sources produce fixed voltages and current sources provide fixed currents, but don't otherwise provide any level of control other than that.

The relationship between voltage and current is embodied by Ohm's law for resistors, and a variant of Ohm's law which deals with changes in voltage and current for everything else. (There are also formulae which deal with the relationship between voltage and current for inductors and capacitors, which introduce the variable time, but that's another topic altogether). With resistors, this relationship is called "resistance".

It is not appropriate to apply Ohm's law, and the concept of ohmic resistance, to a voltage source, or to a current source, because the relationship between voltage and current for them is not directly proportional.

You can, however, attribute to them the properties of dynamic resistance, when you consider their response to changes in either voltage or current. In that case an ideal voltage source can be considered to have zero resistance, and an ideal current source is considered to have infinite resistance.


To summarise, then, voltage sources produce fixed voltages and current sources provide fixed currents, but don't otherwise provide any level of control other than that.

The relationship between voltage and current is embodied by Ohm's law for resistors, and a variant of Ohm's law which deals with changes in voltage and current for everything else. (There are also formulae which deal with the relationship between voltage and current for inductors and capacitors, which introduce the variable time, but that's another topic altogether). With resistors, this relationship is called "resistance".

It is not appropriate to apply Ohm's law, and the concept of ohmic resistance, to a voltage source, or to a current source, because the relationship between voltage and current for them is not directly proportional.

You can, however, attribute to them the properties of dynamic resistance, when you consider their response to changes in either voltage or current. In that case an ideal voltage source can be considered to have zero resistance, and an ideal current source is considered to have infinite resistance.

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Simon Fitch
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