Electrical "Circuits"

"The exception proves that the rule is wrong. That is the principle of science.

If there is an exception to any rule, and if it can be proved by observation, that rule is wrong."

    – Richard Feynman, The Meaning of it All, 1999 ­­­

Getting the basics right.
There are many internet sites offering suggestions on the mysteries of electricity. A few are reasonably well presented but avoid any explanation. Others state Ohm's Law and expect the reader to understand what is happening. Some portray a flow of electrons in a circuit but get the explanation horribly wrong. Then, there are many who try to use plumbing and water as an analogy of electrical theory. This merely reinforces in their minds the concept of circular flows, pumps and pressures, but they cannot produce valid water flow models to explain capacitance (electrostatics) or inductance (electromagnetism).


When teaching the basics of electricity many articles start with a battery/switch/light bulb configuration like this:

What does it teach us about electricity? Well, almost nothing. All it really shows is what a switch does.  It  simply leads to a fallacy that they later rely on when explaining electrical theory; there must be a complete circuit for a current to exist. This leads to a further fallacy that within a battery electrons move from the positive terminal to the negative terminal, thus completing a round trip for each electron. Note the flying "angels" magically transporting the electrons to the negative terminal in this screen capture from a site claiming to teach electrical theory.

However the battery/switch/light bulb configuration could be more informative if we just put one more component in the "circuit"; a capacitor.
Watch what happens now.

When the switch is closed the lamp briefly glows but then goes out. Furthermore, repeated action of the switch has no effect whatsoever. I can imagine that those who see the lamp glow will think; "There is a continuous loop". But when the lamp goes out, they have no explanation. To them, there was a continuous loop but now there isn't. In fact, there never was a continuous loop. Not one electron ever passed through the capacitor.

So there are at least two fallacies which are being taught to students as if they were indisputable facts.

• There must be a complete circuit (a continuous loop) for a current to exist.
• Within a battery, electrons flow from the positive terminal to the negative terminal.

There's just so much wrong with these two statements that it's difficult to know where to start.
The use of the word "circuit" is misleading. Describing how a switch works, does not explain electrical theory. So let's forget all that rubbish and start from the beginning.

Protons are the largest objects in an atom. They form the centre of an atom (called the nucleus). The type of atom is determined by the number of protons in the nucleus. Protons are positively charged (shown as red in this animation). The nucleus of the atom contains protons and neutrons. Neutrons (shown as purple) are the same size as protons but they do not have any charge, so they play no part in basic electrical theory. Circling the nucleus are electrons. There are two atomic particles that are important in the study of electricity; protons and electrons.

When we say that the nucleus of an atom is positively charged, the word "positive" is purely arbitrary. But whatever we call it, we do so to distinguish between the charge of a proton and the charge of the electron. Electrons are said to be negatively charged.
In any object, when there are as many protons as there are electrons, it is neutral (uncharged). If there were more electrons than protons then it would be negatively charged. If there were more protons than electrons it would be positively charged.

Now for something to memorize:

1. Like charges repel each other. (Same repel)
2. Unlike charges attract each other. (Opposites attract)

Almost all electrical activity operates on these two principles.

In a solid, like a piece of copper wire, the copper atoms cannot move around. The best they can do is wobble a bit when they get warm. The outermost shell of a copper atom contains just one electron (the white one in the following animation). With enough energy, such as heat, this electron can be easily dislodged from the atom. It is this electron that we now call a free electron.

It is estimated that at room temperature, there will be one free electron for each copper atom. The free electrons are able to move around from atom to atom. Sometimes combining with an atom and sometimes becoming free again. The free electrons are moving around in different directions and at different speeds. But they are always responding to the balance of the forces of attraction and repulsion. Electrons are always in motion.

The next animation shows that electrons will move away from each other and will disperse to fill the available space. In doing so, they transfer the charge. It also shows what happens when a length of copper wire is connected to the positive terminal of a battery and what happens with a wire connected to the negative terminal. Electrons will move into the positive terminal so that the wire is at the same potential (charge) as the positive terminal. Same for the negative, electrons will move out of the battery and disperse to fill the space available, thus making it at the same potential (charge). It also shows how electrons move toward the positive terminal even before the terminal comes in contact with the wire. And how the electrons move away from the negative terminal as it approaches the wire. This demonstrates something called parasitic (stray) capacitance.

So how does a capacitor work?
A capacitor is made of two plates (actually two sheets of metal foil). These two plates are often separated by an insulator so that they can never come in contact with each other. In the following animation, when the lower plate is connected to the negative terminal, the electrons in the upper plate are repelled away. In this case however, the electrons have nowhere to go.

To highlight the fact that electrons do not pass through a capacitor, consider this example:

When a battery is connected to two capacitors in series, Plate 1 becomes negatively charged and Plate 4 becomes positively charged. This causes the electrons in Plate 2 to move to Plate 3 of the other capacitor. The electrons in Plate 2 are repelled away from Plate 1 and attracted toward Plate 4, leaving the capacitors charged as shown. Each capacitor is now charged to half the battery voltage.
When we remove the battery and replace it with a lamp, half of the electrons in Plate 1 will move to Plate 4 thus neutralizing both plates. As this happens, the plates in-between (ie., Plates 2 and 3) will also revert to their normal neutral state of charge as the forces of attraction and repulsion are reduced. The capacitor is now discharged.
Is there a complete circuit with two capacitors in series? No. The electrons in Plates 2 and 3 and the connecting wire will never get to the battery or the lamp.

Those who assert that a closed circuit must exist before a current can exist and that this current must "flow" through each component in the circuit are misleading their students. Not one electron passes from either side of a capacitor to the other side. It is an open circuit, yet a current can exist outside the capacitor. When a capacitor is charging, there will be a current into and out of the capacitor, but never through the capacitor. When a capacitor is discharging, there will be a current into and out of the capacitor, but never through the capacitor. No current exists between the plates of a capacitor.

I can imagine some readers saying, "Oh, but to have a continuous current you must have a continuous loop".

How does this relate to Richard Feynman's quote?
Well, I only need one exception and here it is:
Shown below is a circuit which proves that a continuous loop is not necessary for a continuous current. The component values are not that critical. The 560 ohm resistor should be selected to suit the battery voltage which could be from 3 to 12 volts. For a 6 volt battery, 220 ohms will be sufficient. For a 9 volt battery, 390 ohms, and for 12 volt battery, 560 ohms. The 1M ohm resistor can be up to 5M ohm (I haven't tried greater than 5M ohms).
The point is, with the probe touching a large metal object which is not grounded, (like a toaster that is not plugged into the power outlet) the LED will flash on quickly as the metal charges. If the probe is touched on a metal object which is plugged into the power outlet then the LED will light and stay lit for as long as the probe is connected.  

Please note, there is no other electrical connection, just the probe tip. There is no possible return path. 

Basically, as indicated by ib electrons travel from the negative terminal of the battery, through the base-emitter junctions of the transistors, through the 1 megohm resistor, then to ground (the Earth). They can never return to the battery.
When there is a current ib through the transistors base-emitter junctions, there is now a current ia through the transistors collector-emitter junctions which then connects the LED to the negative battery terminal and the LED lights up.

All of the examples and explanations given above rely on the fact that like charges repel and opposite charges attract. They deal with electrostatic charges and the electrostatic fields around a conductor.
When charges move within a conductor, we call that a current.

As part of the usual excuse to argue that a circuit must have a complete loop, it is often stated that within a battery, electrons must go from the positive terminal to the negative terminal. This of course, is rubbish.
As electrons are repelled from the negative terminal and attracted toward the positive terminal, they slowly reduce the difference in charge between the terminals. The positive terminal becomes slightly less positive and the negative terminal becomes slightly less negative.

If it were possible to "transport" electrons from the positive to the negative terminal inside the battery, then the charge difference would remain the same - the battery's difference in potential (voltage) would always remain the same, even though we are using the energy that it supplies. So the battery would never go flat.

Just as with two capacitors in series, the electrons between the positive and negative terminals will never participate in illuminating the light bulb. As the positive terminal of the battery accumulates electrons from the negative terminal, the chemical ability of the battery to produce electrons in each cell is reduced. The zinc electrodes (negative terminals) are slowly dissolving in the electrolyte. The electrons produced move to the copper electrodes (the positive terminals) without going through the electrolyte. These electrons then combine with Hydrogen ions from the electrolyte to produce Hydrogen gas.

A battery is not a pump, endlessly recycling electrons. Electrons cannot pass from the positive terminal to the negative terminal. There are no "angels" magically transporting electrons to the negative battery terminal.

Finally, electrical theory is far more complex than a simple switch or any plumbing analogy.
If a student later goes on to study radio/TV transmissions then a proper understanding of electrostatics and electromagnetics will provide a segue to understanding more complex electrical and electronic equipment.

So, for students trying to understand electrical theory, beware of instructors who say things like;
"Energy is required to force the electrons to move from the zinc to the copper electrode...", or "There must be a complete loop for a current to exist",  or "Within a battery, electrons flow from the positive to the negative terminal".

It is better to think of a battery as being like a very big charged capacitor.

• Not one electron will ever return to the negative terminal of a battery.
• A circuit with batteries or capacitors is not a complete loop.
• A current can exist without a complete loop.

In AC circuits, the electrons don't actually go anywhere, they just wiggle back and forth.

This article contains artwork and animation provided by Carnegie Mellon University.

It also contains a screenshot from PhET Simulations.

The ground detector circuit and the Voltaic Pile images are mine.