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][1]][1]
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.
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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:
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You might think that there's a conflict here, but there isn't. The only job of voltage source V1 is to apply a fixed potential difference of 10V between A and B. The only job of current source I1 is to ensure that 1A flows around the loop. Neither of those roles are in conflict with the other. Source V1 has no problem with I1's insistence that current be 1A, and source I1 has no problem with V1's insistence that the voltage across it be 10V.
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:
$$ V = 10V $$
$$ I = 1A $$
That's it. Where's the R?
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If you insist on assigning some kind of resistance value to a source, then you must first define what that resistance means. A practical definition of resistance in these circumstances goes as follows: resistance is the ratio of *change* in voltage to *change* in current:
$$ r = \frac{\Delta V}{\Delta I} $$
In mathematical treatments you will normally see the above relationship written:
$$ r = \frac{dV}{dI} $$
If you paid attention in math class, then you'll understand that this is referring to the *gradient* (slope) of the graph of \$V\$ vs. \$I\$, at some particular point \$(I, V)\$ on that graph. I've used a small \$r\$ to indicate that this is *dynamic* resistance, as distinct from *ohmic*, which applies only to resistors.
By that new definition, the dynamic resistance of a voltage source will be the gradient of its \$V\$ vs. \$I\$ plot, which is zero:
$$ r_{V1} = 0\Omega $$
The dynamic resistance of a current source is also the gradient of it's \$V\$ vs. \$I\$ plot:
$$ r_{I1} = \infty\Omega $$
The dynamic resistance of a resistor is the same as its ohmic resistance, because the gradient is constant, and proportionality is direct. For a resistor, Ohm's law is always true, for all values of \$V\$ and \$I\$, and both \$V\$ and \$I\$ are able to change:
$$ R = r = \frac{dV}{dI} = \frac{V}{I} $$
Dynamic resistance is a very useful concept. For any component that does not have a linear (straight line) \$V\$ vs. \$I\$ curve, the gradient of the curve changes as you vary either voltage or current. Take the silicon diode, for example. Its V-I curve is the blue line here:
[![enter image description here][2]][2]
The response of the diode to very small changes in current is different depending on where you "reside" on this graph, since the gradient of the curve is different everywhere. In other words, by passing an average (DC) current of 18mA through the diode, and making small ±100μA fluctuations (the "AC signal") , the resulting voltage *changes* across the diode will be much smaller than the changes you can expect if the average DC current through it were 3mA. This permits you to control gain.
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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.
[1]: https://i.sstatic.net/SaOZY.png
[2]: https://i.sstatic.net/mtJ0C.png