# voltage and current

As was previously mentioned, we need more than just a continuous path (circuit) before a continuous flow of electrons will occur: we also need some means to push these electrons around the circuit. Just like marbles in a tube or water in a pipe, it takes some kind of influencing force to initiate flow. With electrons, this force is the same force at work in static electricity: the force produced by an imbalance of electric charge.
If we take the examples of wax and wool which have been rubbed together, we find that the surplus of electrons in the wax (negative charge) and the deficit of electrons in the wool (positive charge) creates an imbalance of charge between them. This imbalance manifests itself as an attractive force between the two objects:

If a conductive wire is placed between the charged wax and wool, electrons will flow through it, as some of the excess electrons in the wax rush through the wire to get back to the wool, filling the deficiency of electrons there:

The imbalance of electrons between the atoms in the wax and the aoms in the wool creates a force between the two materials. With no path for electrons to flow from the wax to the wool, all this force can do is attract the two objects together. Now that a conductor bridges the insulating gap, however, the force will provoke electrons to flow in a uniform direction through the wire, if only momentarily, until the charge in that area neutralizes and the force between the wax and wool diminishes.
The electric charge formed between these two materials by rubbing them together serves to store a certain amount of energy. This energy is not unlike the energy stored in a high reservoir of water that has been pumped from a lower-level pond:

The influence of gravity on the water in the reservoir creates a force that attempts to move the water down to the lower level again. If a suitable pipe is run from the reservoir back to the pond, water will flow under the influence of gravity down from the reservoir, through the pipe:

It takes energy to pump that water from the low-level pond to the high-level reservoir, and the movement of water through the piping back down to its original level constitutes a releasing of energy stored from previous pumping.
If the water is pumped to an even higher level, it will take even more energy to do so, thus more energy will be stored, and more energy released if the water is allowed to flow through a pipe back down again:

Electrons are not much different. If we rub wax and wool together, we “pump” electrons away from their normal “levels,” creating a condition where a force exists between the wax and wool, as the electrons seek to re-establish their former positions (and balance within their respective atoms). The force attracting electrons back to their original positions around the positive nuclei of their atoms is analogous to the force gravity exerts on water in the reservoir, trying to draw it down to its former level.
Just as the pumping of water to a higher level results in energy being stored, “pumping” electrons to create an electric charge imbalance results in a certain amount of energy being stored in that imbalance. And, just as providing a way for water to flow back down from the heights of the reservoir results in a release of that stored energy, providing a way for electrons to flow back to their original “levels” results in a release of stored energy.
When the electrons are poised in that static condition (just like water sitting still, high in a reservoir), the energy stored there is called potential energy, because it has the possibility (potential) of release that has not been fully realized yet. When you scuff your rubber-soled shoes against a fabric carpet on a dry day, you create an imbalance of electric charge between yourself and the carpet. The action of scuffing your feet stores energy in the form of an imbalance of electrons forced from their original locations. This charge (static electricity) is stationary, and you won’t realize that energy is being stored at all. However, once you place your hand against a metal doorknob (with lots of electron mobility to neutralize your electric charge), that stored energy will be released in the form of a sudden flow of electrons through your hand, and you will perceive it as an electric shock!
This potential energy, stored in the form of an electric charge imbalance and capable of provoking electrons to flow through a conductor, can be expressed as a term called voltage, which technically is a measure of potential energy per unit charge of electrons, or something a physicist would call specific potential energy. Defined in the context of static electricity, voltage is the measure of work required to move a unit charge from one location to another, against the force which tries to keep electric charges balanced. In the context of electrical power sources, voltage is the amount of potentialenergy available (work to be done) per unit charge, to move electrons through a conductor.
Because voltage is an expression of potential energy, representing the possibility or potential for energy release as the electrons move from one “level” to another, it is always referenced between two points. Consider the water reservoir analogy:

Because of the difference in the height of the drop, there’s potential for much more energy to be released from the reservoir through the piping to location 2 than to location 1. The principle can be intuitively understood in dropping a rock: which results in a more violent impact, a rock dropped from a height of one foot, or the same rock dropped from a height of one mile? Obviously, the drop of greater height results in greater energy released (a more violent impact). We cannot assess the amount of stored energy in a water reservoir simply by measuring the volume of water any more than we can predict the severity of a falling rock’s impact simply from knowing the weight of the rock: in both cases we must also consider how far these masses will drop from their initial height. The amount of energy released by allowing a mass to drop is relative to the distance between its starting and ending points. Likewise, the potential energy available for moving electrons from one point to another is relative to those two points. Therefore, voltage is always expressed as a quantity between two points. Interestingly enough, the analogy of a mass potentially “dropping” from one height to another is such an apt model that voltage between two points is sometimes called a voltage drop.
Voltage can be generated by means other than rubbing certain types of materials against each other. Chemical reactions, radiant energy, and the influence of magnetism on conductors are a few ways in which voltage may be produced. Respective examples of these three sources of voltage are batteries, solar cells, and generators (such as the “alternator” unit under the hood of your automobile). For now, we won’t go into detail as to how each of these voltage sources works — more important is that we understand how voltage sources can be applied to create electron flow in a circuit.
Let’s take the symbol for a chemical battery and build a circuit step by step:

Any source of voltage, including batteries, have two points for electrical contact. In this case, we have point 1 and point 2 in the above diagram. The horizontal lines of varying length indicate that this is a battery, and they further indicate the direction which this battery’s voltage will try to push electrons through a circuit. The fact that the horizontal lines in the battery symbol appear separated (and thus unable to serve as a path for electrons to move) is no cause for concern: in real life, those horizontal lines represent metallic plates immersed in a liquid or semi-solid material that not only conducts electrons, but also generates the voltage to push them along by interacting with the plates.
Notice the little “+” and “-” signs to the immediate left of the battery symbol. The negative (-) end of the battery is always the end with the shortest dash, and the positive (+) end of the battery is always the end with the longest dash. Since we have decided to call electrons “negatively” charged (thanks, Ben!), the negative end of a battery is that end which tries to push electrons out of it. Likewise, the positive end is that end which tries to attract electrons.
With the “+” and “-” ends of the battery not connected to anything, there will be voltage between those two points, but there will be no flow of electrons through the battery, because there is no continuous path for the electrons to move.

The same principle holds true for the water reservoir and pump analogy: without a return pipe back to the pond, stored energy in the reservoi cannot be released in the form of water flow. Once the reservoir is completely filled up, no flow can occur, no matter how much pressure the pump may generate. There needs to be a complete path (circuit) for water to flow from the pond, to the reservoir, and back to the pond in order for continuous flow to occur.
We can provide such a path for the battery by connecting a piece of wire from one end of the battery to the other. Forming a circuit with a loop of wire, we will initiate a continuous flow of electrons in a clockwise direction:

So long as the battery continues to produce voltage and the continuity of the electrical path isn’t broken, electrons will continue to flow in the circuit. Following the metaphor of water moving through a pipe, this continuous, uniform flow of electrons through the circuit is called a current. So long as the voltage source keeps “pushing” in the same direction, the electron flow will continue to move in the same direction in the circuit. This single-direction flow of electrons is called a Direct Current, or DC. In the second volume of this book series, electric circuits are explored where the direction of current switches back and forth: Alternating Current, or AC. But for now, we’ll just concern ourselves with DC circuits.
Because electric current is composed of individual electrons flowing in unison through a conductor by moving along and pushing on the electrons ahead, just like marbles through a tube or water through a pipe, the amount of flow throughout a single circuit will be the same at any point. If we were to monitor a cross-section of the wire in a single circuit, counting the electrons flowing by, we would notice the exact same quantity per unit of time as in any other part of the circuit, regardless of conductor length or conductor diameter.
If we break the circuit’s continuity at any point, the electric current will cease in the entire loop, and the full voltage produced by the battery will be manifested across the break, between the wire ends that used to be connected:

Notice the “+” and “-” signs drawn at the ends of the break in the circuit, and how they correspond to the “+” and “-” signs next to the battery’s terminals. These markers indicate the direction that the voltage attempts to push electron flow, that potential direction commonly referred to as polarity. Remember that voltage is always relative between two points. Because of this fact, the polarity of a voltage drop is also relative between two points: whether a point in a circuit gets labeled with a “+” or a “-” depends on the other point to which it is referenced. Take a look at the following circuit, where each corner of the loop is marked with a number for reference:

With the circuit’s continuity broken between points 2 and 3, the polarity of the voltage dropped between points 2 and 3 is “-” for point 2 and “+” for point 3. The battery’s polarity (1 “-” and 4 “+”) is trying to push electrons through the loop clockwise from 1 to 2 to 3 to 4 and back to 1 again.
Now let’s see what happens if we connect points 2 and 3 back together again, but place a break in the circuit between points 3 and 4:

With the break between 3 and 4, the polarity of the voltage drop between those two points is “+” for 4 and “-” for 3. Take special note of the fact that point 3’s “sign” is opposite of that in the first example, where the break was between points 2 and 3 (where point 3 was labeled “+”). It is impossible for us to say that point 3 in this circuit will always be either “+” or “-“, because polarity, like voltage itself, is not specific to a single point, but is always relative between two points!

• REVIEW:
• Electrons can be motivated to flow through a conductor by the same force manifested in static electricity.
• oltage is the measure of specific potential energy (potential energy per unit charge) between two locations. In layman’s terms, it is the measure of “push” available to motivate electrons.
• Voltage, as an expression of potential energy, is always relative between two locations, or points. Sometimes it is called a voltage “drop.”
• When a voltage source is connected to a circuit, the voltage will cause a uniform flow of electrons through that circuit called a current.
• In a single (one loop) circuit, the amount of current at any point is the same as the amount of current at any other point.
• If a circuit containing a voltage source is broken, the full voltage of that source will appear across the points of the break.
• The +/- orientation a voltage drop is called the polarity. It is also relative between two points.

## Voltage and current in a practical circuit

Because it takes energy to force electrons to flow against the opposition of a resistance, there will be voltage manifested (or “dropped”) between any points in a circuit with resistance between them. It is important to note that although the amount of current (the quantity of electrons moving past a given point every second) is uniform in a simple circuit, the amount of voltage (potential energy per unit charge) between different sets of points in a single circuit may vary considerably:

Take this circuit as an example. If we label four points in this circuit with the numbers 1, 2, 3, and 4, we will find that the amount of current conducted through the wire between points 1 and 2 is exactly the same as the amount of current conducted through the lamp (between points 2 and 3). This same quantity of current passes through the wire between points 3 and 4, and through the battery (between points 1 and 4).
However, we will find the voltage appearing between any two of these points to be directly proportional to the resistance within the conductive path between those two points, given that the amount of current along any part of the circuit’s path is the same (which, for this simple circuit, it is). In a normal lamp circuit, the resistance of a lamp will be much greater than the resistance of the connecting wires, so we should expect to see a substantial amount of voltage between points 2 and 3, with very little between points 1 and 2, or between 3 and 4. The voltage between points 1 and 4, of course, will be the full amount of “force” offered by the battery, which will be only slightly greater than the voltage across the lamp (between points 2 and 3).
This, again, is analogous to the water reservoir system:

Between points 2 and 3, where the falling water is releasing energy at the water-wheel, there is a difference of pressure between the two points, reflecting the opposition to the flow of water through the water-wheel. From point 1 to point 2, or from point 3 to point 4, where water is flowing freely through reservoirs with little opposition, there is little or no difference of pressure (no potential energy). However, the rate of water flow in this continuous system is the same everywhere (assuming the water levels in both pond and reservoir are unchanging): through the pump, through the water-wheel, and through all the pipes. So it is with simple electric circuits: the rate of electron flow is the same at every point in the circuit, although voltages may differ between different sets of points.

## Conventional versus electron flow

When Benjamin Franklin made his conjecture regarding the direction of charge flow (from the smooth wax to the rough wool), he set a precedent for electrical notation that exists to this day, despite the fact that we know electrons are the constituent units of charge, and that they are displaced from the wool to the wax — not from the wax to the wool — when those two substances are rubbed together. Thi is why electrons are said to have a negative charge: because Franklin assumed electric charge moved in the opposite direction that it actually does, and so objects he called “negative” (representing a deficiency of charge) actually have a surplus of electrons.
By the time the true direction of electron flow was discovered, the nomenclature of “positive” and “negative” had already been so well established in the scientific community that no effort was made to change it, although calling electrons “positive” would make more sense in referring to “excess” charge. You see, the terms “positive” and “negative” are human inventions, and as such have no absolute meaning beyond our own conventions of language and scientific description. Franklin could have just as easily referred to a surplus of charge as “black” and a deficiency as “white,” in which case scientists would speak of electrons having a “white” charge (assuming the same incorrect conjecture of charge position between wax and wool).
However, because we tend to associate the word “positive” with “surplus” and “negative” with “deficiency,” the standard label for electron charge does seem backward. Because of this, many engineers decided to retain the old concept of electricity with “positive” referring to a surplus of charge, and label charge flow (current) accordingly. This became known as conventional flow notation:

Others chose to designate charge flow according to the actual motion of electrons in a circuit. This form of symbology became known as electron flow notation:

In conventional flow notation, we show the motion of charge according to the (technically incorrect) labels of + and -. This way the labels make sense, but the direction of charge flow is incorrect. In electron flow notation, we follow the actual motion of electrons in the circuit, but the + and – labels seem backward. Does it matter, really, how we designate charge flow in a circuit? Not really, so long as we’re consistent in the use of our symbols. You may follow an imagined direction of current (conventional flow) or the actual (electron flow) with equal success insofar as circuit analysis is concerned. Concepts of voltage, current, resistance, continuity, and even mathematical treatments such as Ohm’s Law (chapter 2) and Kirchhoff’s Laws (chapter 6) remain just as valid with either style of notation.
You will find conventional flow notation followed by most electrical engineers, and illustrated in most engineering textbooks. Electron flow is most often seen in introductory textbooks (this one included) and in the writings of professional scientists, especially solid-state physicists who are concerned with the actual motion of electrons in substances. These preferences are cultural, in the sense that certain groups of people have found it advantageous to envision electric current motion in certain ways. Being that most analyses of electric circuits do not depend on a technically accurate depiction of charge flow, the choice between conventional flow notation and electron flow notation is arbitrary . . . almost.
Many electrical devices tolerate real currents of either direction with no difference in operation. Incandescent lamps (the type utilizing a thin metal filament that glows white-hot with sufficient current), for example, produce light with equal efficiency regardless of current direction. They even function well on alternating current (AC), where the direction changes rapidly over time. Conductors and switches operate irrespective of current direction, as well. The technical term for this irrelevance of charge flow is nonpolarization. We could say then, that incandescent lamps, switches, and wires are nonpolarized components. Conversely, any device that functions differently on currents of different direction would be called a polarized device.
There are many such polarized devices used in elctric circuits. Most of them are made of so-called semiconductor substances, and as such aren’t examined in detail until the third volume of this book series. Like switches, lamps, and batteries, each of these devices is represented in a schematic diagram by a unique symbol. As one might guess, polarized device symbols typically contain an arrow within them, somewhere, to designate a preferred or exclusive direction of current. This is where the competing notations of conventional and electron flow really matter. Because engineers from long ago have settled on conventional flow as their “culture’s” standard notation, and because engineers are the same people who invent electrical devices and the symbols representing them, the arrows used in these devices’ symbols all point in the direction of conventional flow, not electron flow. That is to say, all of these devices’ symbols have arrow marks that point against the actual flow of electrons through them.
Perhaps the best example of a polarized device is the diode. A diode is a one-way “valve” for electric current, analogous to a check valve for those familiar with plumbing and hydraulic systems. Ideally, a diode provides unimpeded flow for current in one direction (little or no resistance), but prevents flow in the other direction (infinite resistance). Its schematic symbol looks like this:

Placed within a battery/lamp circuit, its operation is as such:

When the diode is facing in the proper direction to permit current, the lamp glows. Otherwise, the diode blocks all electron flow just like a break in the circuit, and the lamp will not glow.
If we label the circuit current using conventional flow notation, the arrow symbol of the diode makes perfect sense: the triangular arrowhead points in the direction of charge flow, from positive to negative:

On the other hand, if we use electron flow notation to show the true direction of electron travel around the circuit, the diode’s arrow symbology seems backward:

For this reason alone, many people choose to make conventional flow their notation of choice when drawing the direction of charge motion in a circuit. If for no other reason, the symbols associated with semiconductor components like diodes make more sense this way. However, others choose to show the true direction of electron travel so as to avoid having to tell themselves, “just remember the electrons are actually moving the other way” whenever the true direction of electron motion becomes an issue.
In this series of textbooks, I have committed to using electron flow notation. Ironically, this was not my first choice. I found it much easier when I was first learning electronics to use conventional flow notation, primarily because of the directions of semiconductor device symbol arrows. Later, when I began my first formal training in electronics, my instructor insisted on using electron flow notation in his lectures. In fact, he asked that we take our textbooks (which were illustrated using conventional flow notation) and use our pens to change the directions of all the current arrows so as to point the “correct” way! His preference was not arbitrary, though. In his 20-year career as a U.S. Navy electronics technician, he worked on a lot of vacuum-tube equipment. Before the advent of semiconductor components like transistors, devices known as vacuum tubes or electron tubes were used to amplify small electrical signals. These devices work on the phenomenon of electrons hurtling through a vacuum, their rate of flow controlled by voltages applied between metal plates and grids placed within their path, and are best understood when visualized using electron flow notation.
When I graduated from that training program, I went back to my old habit of conventional flow notation, pimarily for the sake of minimizing confusion with component symbols, since vacuum tubes are all but obsolete except in special applications. Collecting notes for the writing of this book, I had full intention of illustrating it using conventional flow.
Years later, when I became a teacher of electronics, the curriculum for the program I was going to teach had already been established around the notation of electron flow. Oddly enough, this was due in part to the legacy of my first electronics instructor (the 20-year Navy veteran), but that’s another story entirely! Not wanting to confuse students by teaching “differently” from the other instructors, I had to overcome my habit and get used to visualizing electron flow instead of conventional. Because I wanted my book to be a useful resource for my students, I begrudgingly changed plans and illustrated it with all the arrows pointing the “correct” way. Oh well, sometimes you just can’t win!
On a positive note (no pun intended), I have subsequently discovered that some students prefer electron flow notation when first learning about the behavior of semiconductive substances. Also, the habit of visualizing electrons flowing against the arrows of polarized device symbols isn’t that difficult to learn, and in the end I’ve found that I can follow the operation of a circuit equally well using either mode of notation. Still, I sometimes wonder if it would all be much easier if we went back to the source of the confusion — Ben Franklin’s errant conjecture — and fixed the problem there, calling electrons “positive” and protons “negative.”