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1. Basic Terms and Modes of Operation

1.1. Basic elements of physical bodies

Every material object shows a grainy structure, where the basic elements of this structure - the atoms or molecules - consist of charge carriers of opposite polarity - the protons inside of the core and the electrons at the outer shells.
The existence of charge with opposite polarity cannot be further explained but has to be accepted as given by nature. The same holds for the fact that charges of equal polarity repel while charges of opposite polarity attract each other.
Protons and electrons carry the same elementary charge with opposite polarity. The elementary charge - as the name indicates - is the smallest amount of free charge that exists in nature. An equal amount of protons and electrons are seen from outside as neutral.
For historical reasons the charge of electrons is called negative, the charge of the protons as positive.

1.2. Definition of the unit of charge

The unit of charge has been defined - again for historical reasons - as consisting of 6,2 10¹⁸ elementary charges.
The unit is called 1 Coulomb, in honour of the French physicist Charles Augustin de Coulomb (1736-1806)

1.3. Properties of conductors and isolators

Metals as good conductors and isolators as bad conductors differ in respect to the mobility of negative charge carriers, the electrons. In both types the positive charge carriers are fixed within the cores of the atoms, and the same holds for the electrons in isolators. However, in metals one or two electrons per atom become rather mobile within the lattice structure.
A basic law has to be mentioned here: the conservation of charge. Charge cannot be created or annihilated, at least not under normal conditions within electric devices. Within a neutral electrical device the sum of all charge carriers remains constant. It follows that within an electric device electrons can only be displaced. If electrons pile up at some place it is certain that positive charge carriers will pile up at some other place which has been neutral before. Repelling forces will show up between charge carriers with equal polarity and attracting forces between charge carriers of opposite polarity - the so-called Coulomb forces. These Coulomb forces are counteracting the original separation and prevent any further displacement of electrons. Such forces show up in metals as good conductors as well as in isolators as bad conductors.

1.4. Importance of closed circuits

The big advantage of metal as good conductor does not come into its own until a closed loop, a so-called electric circuit, is formed. In such a loop the highly mobile electrons can constantly be moved around without producing any piling up of charge carriers with positive or negative polarity at different locations and as a consequence no back driving forces due to charge accumulation.
To maintain a constant flow of electrons, the same number of electrons which enter a certain volume element per unit time have to leave this element. Only under this condition no piling up of charge carriers will occur and a dynamic equilibrium or stationary state can be maintained.

1.5. Definition of electric current

A certain amount of charge q, which is flowing through a cross section of a conductor is equal to the number of electrons n, crossing this section, multiplied by the elementary charge. If this elementary charge is indicated as e we have: q = ne.
The amount of electric current at a certain cross section is determined by the charge and so by the number of electrons n, passing a specific cross section during a certain time period Δt. The electric current is indicated as I.
I = ne/Δt = q/Δt.
The unit of the electric current is called "amps", abbreviated A, in honour of the French physicist André-Marie Ampère (1775-1836).
A current of 1 A corresponds to a flow of 1 Coulomb = 6,2 10 ¹⁸ electrons per second through a cross section.

1.6. Ohm´s law

If a constant current has to be driven through a resistor it needs a certain voltage or potential difference across the outlets of the resistor.
If the voltage is changed it is plausible to expect a corresponding change of the current. What is not evident is the question if this relation is linear, if the current changes proportional to the voltage.
Under normal conditions a proportional relation is rather seldom. If the current changes, normally the temperature of the resistor and therefore its resistance changes. This implies a non-linear relation between voltage and current. If, however, the temperature of the resistor and all other properties (length, cross section) remain constant, it has been experimentally proven that for metallic and for most solid state conductors there exists a strict proportional relation between voltage and current.
Conclusion: If a constant current I is driven by a voltage V through a resistor with resistance R and if all external parameters remain constant we have: V/I = constant. This relation was first detected by the physicist Ohm and is called Ohm´s law.
By convention this constant, which is characteristic for the specific resistor, is used as definition for the resistance R.
R = V/I. The unit of resistance is Ohm, abbreviated as Ω in honour of the German physicist Georg Simon Ohm (1789-1854).

1.7. Functioning of a power source

An electric power source consists in principle of a conductive device which is connected to the outside by two metallic contacts. In addition, an essential property has to exist. A power source is able to apply a force on the internal electrons to move them from one external contact towards the other. The kind of force is different for different kinds of power sources. Within a battery chemical forces are active, within a generator electromagnetic forces can be applied. The forces are of different nature than Coulomb forces and are called Electro-Motive-Forces (short: EMK), as forces who can set electrically charged particles in motion.

Fig. 1: Battery as power source with surface charges at the metallic contacts

A basic law comes into play here: Additional electrons can never exist inside of a metallic conductor but only at its surface.
Why additional electrons do not leave such a surface but can be collected there is not easy to explain. Factors like the temperature of the conductor, the geometrical property of its surface and the electric property of the surrounding medium play an important role.
Any further explanation is not necessary for an understanding of the following. It is sufficient to accept as an experimentally proven fact that additional electrons can exist at the surface of a metallic conductor and only at its surface.
The larger the density of the additional positive or negative charges at the surface of the metallic contacts, the more these charge carries repel each other. A certain limit will be reached, which is characteristic for the actual power source, where these repelling Coulomb forces will prevent any further accumulation of electrons. A state of equilibrium will be established between the internal force of the power source (the EMK) and the back driving Coulomb forces

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