The Variationof Inductance And Capacitance With Respect To Time

The Variation of Inductance and Capacitance With Respect to Time

We have heretofore established a new pair of dimensional relationships. These the magnetic inductance, L, in Henry, and the electro-static capacity, C, in Farad. Derived from these dimensional relations is a pair of electrical laws,

 (I) The Law of Dielectric Proportion

The ratio of the quantity of dielectric induction, Psi in Coulomb to the magnitude of the electro-static potential, e, in Volt.

 (1) Coulomb per Volt, Or Farad

(II) The Law of Magnetic Proportion The ratio of the quantity of magnetic induction, Phi, in Weber, to the magnitude of the M.M.F., i, in Ampere.

 (2) Weber per Ampere, Or Henry

Through algebraic re-arrangement a pair of secondary dimensional relations alternately define, in a new form, the total dielectrtic induction, Psi, in Coulomb, and the total magnetic induction, Phi, in Weber. For the dielectric induction,

 (3) Coulomb, or Volt – Farad.

And for the magnetic induction,

 (4) Weber, or, Ampere – Henry

Hence, the total dielectric induction, Psi, in Coulomb, is the product of the potential, e, in volt, and the capacitance, C, in Farad. Likewise, the total magnetic induction, Phi, in Weber, is the product of the M.M.F., i, in Ampere, and the inductance, L, in Henry

 Psi equals e times C
 Phi equals i times L

In the expression of the variation of the parameters which constitute the dimensional relations involving capacitance and inductance, two distinct conditions can exist. First is the capacitance and the inductance arfe time invariant, and the variation with respect to time resides in the relations of potential, e, and of M.M.F., i. Here derived are the suceptance and the reactance. In the alternate form of expression, it is the potential, e, and the M.M.F., i, that are time invariant, and the variation with respect to time resides in the relations of capacitance and inductance as geometric co-efficients. Geometry in time variation.

In general, time invariance of L and C, or time invariance of e and i each can be considered as a limiting case. Each can be in variation with respect to time at their own individual time rates. That is, for the dielectric both C and e can be in variation, and for the magnetic both L and i can be in variation. Consider the A.C. induction motor. Here is form of magnetic inductance in which both the inductance, L, and the M.M.F., i, are in time variation, L with the rotational geometric variation, and i with the rotational variation of M.M.F. The difference between the rotational frequency of i is called the slip frequency. The rotor continuously falls behind the rotation of the magnetic field, dragging energy out of this field and delivering it to the output shaft of the motor.

Considering the pair of primary dimensional relations, it is, for the dielectric induction.

 (5) Farad per second, or Siemens,

And for the magnetic,

 (6) Henry per second, or Ohm,

It is established that a distinct pair of conditions exist with regard to the variation with respect to time. Either the capacitance or inductance is in variation, or the potential or M.M.F. is in variation, with respect to time.

For the condition of time invariant L and C it is given,

 (7) Farad per second, or Siemens, 
 The Suceptance, B,

 (8) Henry per second, or Ohm, 
 The Reactance, X.

In the second case the L and C are in variation with respect to time. The forces, i and e, are held constant, or time invariant. Here the variation with respect to time exists with the Metallic – Dielectric geometry itself. This hereby produces a variation in the geometric co-efficients of capacitance or inductance. These relations are given as,

 (9) Farads per second, or Siemens,
 The Conductance, G

 (10) Henry per second, or Ohm,
 The Resistance, R

This CONDUCTANCE, G, and this RESISTANCE, R, represent the relations derived from the time variation of capacitance and from the time variation of inductance, respectively.

It is through this form of parameter variation that the energy stored in the electrical field bounded by the geometric structure is here given to an external form. This is to say, energy is taken out of the electric field and delivered elsewhere.

For a closed system, the energy stored within the electric field is lost, or dissipated, from this system. It is then ENERGY LEAKAGE from the closed system. Considering the condition of a time invariant, or stationary geometric structure, this structure exhibiting the dissipation of the energy stored within the electric field bound by the structure, the conductance, G, and the Resistance, R, are the representations of energy leakage from the dielectric and magnetic fields respectively.

For example, consider one span of a “J carrier” open wire transmission pair. Here the conductance, G, is the “leakage conductance” of the glass telephone insulator, the resistance, R, is the “electronic resistance” of the copperweld telephone wire. These represent the energy dissipation of one span of line.

This conductance, G, represents a “molecular loss” WITHIN the glass of the insulator. This resistance, R, represents a “molecular loss” WITHIN the metal of the wire. Hence it is the molecular losses of the metallic-dielectric geometry itself that gives rise to an energy leakage from a closed system. The molecular agitation and cyclic hysteresis exist within the molecular dimensions of the physical mass of the bounding geometric structure. These consist of a multitude of minute variations of the capacitance and inductance of the geometric form. On a microscopic level the material substance of this form is indefine, a kind of blur in space, due to the multitude of minute variations of positions in space. These tiny motions, hereby through parameter variation, convert the energy stored in the electric field into random patterns of radiation. By experiment it can be shown that this energy leakage exists in proportion to the temperature of the material form storing energy within its bound electric field. In general, the elecro-static potential, e, in Volt, renders the insulators hot, the magneto-motive force, i, in Ampere, renders the wires hot. Also, it is found that this heating increases with increasing frequency of the potential, e, or the M.M.F., i. It is here where the prevailing concept of the “electron” is to be found. Hence it is the motions of the electrons that give rise to the energy loss in an electrical system.

Electrons represent energy dissipation. However, the pedant, the mystic, and the dis-informer all tell us that the electron is what conveys energy, the complete opposite!

Parameter Variation Continued

In the last section the dimensional relations of conductance and resistance were developed for the condition of a static, or stationary, metallic-dielectric geometry. The conductance represents the leakage of energy from the dielectric field, and the resistance represents the leakage of energy from the magnetic field. Energy loss is internal to the physical mass which constitutes the metallic-dielectric geometry. This loss is of molecular form.

Instead of the parameter variation resulting from internal motions, there exists the parameter variation which results from external motion. This parameter variation with respect to time is the result of the contiguous parts of the geometric form being in relative motion with respect to each other. Again the A.C. induction motor serves as an example of such a geometric structure. Here is a metallic-dielectric geometric structure with relative motion between its physical parts. A motor or a generator operate thru parameter variation via rotational motion. An example is the common “Electro-static” generator, such as the “Wimhurst Machine”, a rotating variable electro-static condenser.

In general the metallic-dielectric geometry delivers mechanical force as an electric motor, or is driven by mechanical force as an electric generator. Mechanical/Electrical parameter changes, these as, Farad per second and Henry per second, give rise to the metallic-dielectric geometry becoming and electric motor, taking energy from the field, or becoming an electric generator, giving energy to the field.

In the case which the geometry is taking energy as an electric motor, it is for a dielectric machine, a parametric Conductance, G, results,

 (1) Farad per second, or Siemens
 Conductance, G,

And for a magnetic machine, a parametric Resistance, R, results,

 (2) Henry per second, or Ohm,
 Resistance, R.

R and G here represent the removal of energy from the electric field, just as with the condition of molecular losses.

For the condition of a mechanically driven metallic-dielectric geometry giving energy as an electric generator, an alternate form of dimensional expression is desired. These expressions serve to distinguish that part of the relations which represent the loss of energy as distinct from that part of the relations which represent the gain of energy. The square root of positive one is the “operator” which distinguishes the gain part from loss part. It is supply, or demand.

These alternate dimensional relations are, for the dielectric field,

 (3) Farad per second, or Siemens,
 The Acceptance, S

And for the magnetic field,

 (4) Henry per second, or Ohm,
 The Receptance, H

Hence for the dielectric machine an ACCEPTANCE, S, in Siemens, and for a magnetic machine a RECEPTANCE, H, in Ohm. Where R and G represent energy consumption co-efficients, it is S and H represent energy production co-efficients.

A few observations are in order here. First, existing technology produces machines which are strictly magnetic, such as the A.C. induction motor, or strictly dielectric, such as the wimhurst machine. No machine is produced where the magnetic and the dielectric fields work together in an electric field. What relationship of the forces, potential, e, and M.M.F., i, gives rise to equal and opposite mechanical force, this now applied to a rotating geometry?

Second, not all parameter changes are the result of mechanical forces, nor random molecular motions. The magnetic amplifier is one such case, here a parametric inductance controlled by an auxiliary M.M.F. On the molecular level, certain plasma discharge tubes, such as the common fluorescent lighting tube, give rise to an assortment of parameter variations which can produce as well as consume energy from the electric field. Here is a vast realm for theory and experiment.