Electricity has two components: the magnetic field and the dielectric field. Both fields consist of lines of force in the space around a conductor.
Magnetic lines of force encircle the conductor. Dielectric lines of force radiate outward from the conductor.
The figure shows a cross-section of a conductor. The solid lines represent magnetic lines of force, and the dashed lines represent dielectric lines of force.
In a circuit, two conductors are arranged in parallel to carry power to the load. The figure shows a cross-section of the conductors of a circuit with the surrounding lines of force. Magnetic lines of force are always closed loops. Dielectric lines of force always end on a conductor.
Prior to Einstein, these lines of force were understood to be stress and strain in the ether. Even as the electrical dichotomy began to fall out of favor, the pioneers of electrical theory continued to champion this intuitive and engineerable model. Notably, Charles Steinmetz, the architect of the modern power grid, rejected the notion of the electron:
Unfortunately, to a large extent in dealing with the dielectric fields the prehistoric conception of the electrostatic charge on the conductor still exists, and by its use destroys the analogy between the two components of the electric field, the magnetic and the dielectric, and makes the consideration of dielectric fields unnecessarily complicated.
There obviously is no more sense in thinking of the capacity current as current which charges the conductor with a quantity of electricity, than there is of speaking of the inductance voltage as charging the conductor with a quantity of magnetism. But while the latter conception, together with the notion of a quantity of magnetism, etc., has vanished since Faraday's representation of the magnetic field by the lines of magnetic force, the terminology of electrostatics of many textbooks still speaks of electric charges on the conductor, and the energy stored by them, without considering that the dielectric energy is not on the surface of the conductor, but in the space outside of the conductor, just as the magnetic energy.
Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients (1911)
We can conceive lines or tubes of force which physically exist, being formed of rows of directed moving molecules; we can see that these lines must be closed, that they must tend to shorten and expand, etc. It likewise explains in a reasonable way, the most puzzling phenomenon of all, permanent magnetism, and, in general, has all the beauties of the Ampère theory without possessing the vital defect of the same, namely, the assumption of molecular currents [electrons].
Experiments with Alternate Currents of Very High Frequency and Their Application to Methods of Artificial Illumination (1891)
Even J. J. Thomson, the man credited with the discovery of the electron, was a firm believer in the lines of force, which he called "Faraday tubes." Whenever Thomson gave a toast, he would proclaim: "To the electron - may it never be of any use to anyone."
The lines of force reveal the physical workings of the two fundamental electrical storage components: inductors and capacitors.
Inductors, which are coils of wire, store magnetism. The magnetic lines of force wrap around the coil in a toroidal pattern.
Capacitors store dielectricity. A capacitor consists of two conductive plates separated by an insulating material called a dielectric (in this context dielectric refers to a non-conductive material). The dielectric lines of force extend between the plates, bridging the gap.
An electrostatic voltmeter is basically a capacitor which measures the strength of the dielectric lines of force between its plates. Dielectric lines of force are contractive, so they will pull the plates together. One of the plates is allowed to move, resisted by a spring. The displacement of the plate determines the voltage measurement.
Voltage is a direct measurement of dielectric field strength.
A simple ammeter is a conductive loop placed between two magnetic poles. The magnetic field around the loop creates an electromagnet, causing the loop to rotate. This rotation is resisted by a spring, and the amperage, or current, is determined by how far the loop rotates.
Current is a direct measurement of magnetic field strength.
From Steinmetz:
The component i, called the current, is defined as that factor of the electric power P which is proportional to the magnetic field, and the other component e, called the voltage, is defined as that factor of the electric power P which is proportional to the electrostatic [dielectric] field.
Current i and voltage e, therefore, are mathematical fictions, factors of the power P, introduced to represent respectively the magnetic and the electrostatic phenomena.
Theory and Calculation of Transient Electric Phenomena and Oscillations (1909)
When an electrostatic voltmeter is connected to a capacitor, the voltmeter directly measures the dielectric induction in the capacitor.
When an ammeter is connected to a capacitor, the capacitor will discharge through the ammeter, and the ammeter measures the rate of change of the dielectric induction in the capacitor.
When an ammeter is connected to an inductor, the ammeter directly measures the magnetic induction of the inductor.
When an inductor discharges through a resistor, the voltmeter measures the rate of change of magnetic induction of the inductor.
Therefore, depending on the context, voltage is either a measurement of the dielectric field or a rate of change of the magnetic field. Likewise, current is either a measurement of the magnetic field or a rate of change of the dielectric field.
Motors and generators operate via electromagnets. An electromagnet is just an inductor.
The magnetic field around a conducting coil (solenoid) behaves just like an ordinary permanent magnet.
When the magnetic field switches direction, the polarity flips.
Prior to Tesla's AC system, motors and generators were dynamo machines.
All motors and generators have an armature and a stator. The armature is the part that spins, and the stator is the part that surrounds the armature.
The components of a dynamo machine are similar to those of an ammeter. The stator is made up of north and south pole permanent magnets.
The armature is an electromagnet formed from a conductive loop. The magnetic field around the conductive loop creates an electromagnet with poles perpendicular to the armature coil. Like any electromagnet, the direction of the magnetic field can be reversed, flipping the poles.
Unlike an ammeter, the dynamo machine has no spring resisting the rotational force; the coil is allowed to spin freely. The ends of the armature coil are connected to a device called a commutator, a conductive ring with two separations.
When current flows through the armature, it will rotate so that its poles align with the poles of the stator.
As the commutator ring rotates, the sliding contacts switch the direction of the current through the armature. As a result, the magnetic field around the armature repeatedly reverses polarity, prompting the armature to spin continuously.
Therefore, dynamos, despite the fact that they are referred to as DC motors, use AC in their armatures. In a DC power distribution system, the commutator on a dynamo generator converts AC to DC, and the motor commutator converts DC back into AC.
Because of this redundancy, Tesla called these commutators the "useless operations" of the dynamo transmission system:
A New System of Alternate Current Motors and Transformers (1888)
The induction motor Tesla invented ran directly off of alternating current and eliminated the need for redundant and costly commutators.
The elimination of the commutators from the transmission of power made the distribution of power more efficient.
AC power transmission also allowed for the use of transformers:
Tesla's two-phase AC transformer setup was almost identical to his induction motor: he wrapped four primary coils around an iron ring.
In Tesla's time, there was no way to control the voltage or current levels in a DC transmission system. Since power loss is , where i is the current and R is the resistance of the line, the inability to lower the current during transmission of DC power resulted in massive losses. Tesla's AC transformers solved this problem. A step-up transformer at the generator minimized power during transmission by increasing the voltage and lowering the current. At the destination, a step-down transformer lowered the voltage to a safe level for use. This dramatic increase in efficiency allowed electricity to travel much further from the source without significant power loss. This constituted the central advantage of AC over DC: AC allowed for the use of transformers, and transformers allowed electricity to be transmitted much longer distances.
To delve deeper into the mathematical theory behind AC and induction motors, read Theory and Calculation of Alternating Current Phenomena by Charles Steinmetz.