Chapter 12. Electrical Current

Like water flowing through a pipe, the magnitude of a flow of electrons (current i) depends upon the pressure both behind it (potential V) and before it (resistance R) such that:

V = i R (109

The SE values of the magnitudes of V, i, and R can only be integers. If an electrical current is quantized, so also must its corresponding potential and resistance be quantized.

A. Electrical Current in SI Units

Using the SI units of measure, Equation 109 takes the form:

1 V = (1 A)(1 Ω) (110

or 1 volt equals 1 ampere times 1 ohm.

Converting the SI units into SE units gives an equation that can contain only integral values (no fractional values). First, we determine the SE values for the equation's three factors, V, A, and Ω.

Potential

In the Real World, electrical potential can be a variable quantity of energy that is applied to a variable quantity of electrons. In the Quantum World, the smallest-possible amount of energy that can be applied to the smallest-possible electronic charge is the rest-mass energy of one electron, E_e, applied to the charge of one electron, q_e. This is the quantum electrical potential V_e and is:

V_e = E_e·q_e^-1 = m_e·λ_e²·t_e^-2·q_e^-1 (111

Current

In the Real World, electrical current can be a variable quantity of electricity that moves past a point in a variable period of time. In the Quantum World, the smallest-possible amount of electricity that can move in the smallest-possible period of time is the charge of one electron, q_e, in one unitary time attribute of the electron, t_e. This is the quantum electrical current, i_e, and is:

i_e = q_e·t_e^-1 (112

Resistance

In the Real World, electrical resistance can be a variable quantity of resistance to the flow of a variable quantity of electricity that is caused by the force of a variable quantity of electrical potential. In the Quantum World, the smallest-possible amount of resistance to the smallest-possible electrical current is the amount of resistance that the quantum electrical potential of one electron, V_e, overcomes to force one electron, q_e, past a point in one unitary time attribute of the electron, t_e. This is the quantum electrical resistance, R_e, and is:

R_e = V_e i_e^-1 = (E_e·q_e^-1) (q_e·t_e^-1)^-1 = E_e·t_e·q_e^-2 (113

The factor, (E_e·t_e) is equal to Planck's constant; therefore, the quantum electrical resistance can be expressed in its historical form as:

R_e = h q_e^-2 (114

which value Klaus von Klitzing discovered and earned him the Nobel Prize in physics.

Magnetic Flux

From the quantum electrical resistance, R_e, we easily can calculate the quantum magnetic flux, Φ_e, because the dimensions of the two attributes differ by Q, as follows:

Φ_e = R_e·q_e = (E_e·t_e·q_e^-2)(q_e) = E_e·t_e·q_e^-1 = h q_e^-1 (115

B. Electrical Current in SE Units

We restate Equation 110 in SE units, which creates an equation that can contain only integral values (no fractional values):

1 V = (1 A) (1 Ω) (116

m_e·λ_e²·t_e^-2·q_e^-1 = (q_e·t_e^-1) (E_e·t_e·q_e^-2) (117

Cancelling factors reduces the equation to 1 = 1, which is what is supposed to happen.