KHTK Factor # 15: As reality is simplified according to principles, it is reduced to classification based on scales.
The viewpoint and dimension points, together, form our reality. As they expand they become complex. As they are consolidated they reduce to principles and relationships that appear as classifications.
Such classes may be arranged further into subclasses for analysis and understanding. All such classes and subclasses remain consistent per the dimensional scale principle.
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Scientology
Compare the above to the following factor in Scientology.
Scientology Factor # 15. The dimension point can be different from other dimension points and thus can possess an individual quality. And many dimension points can possess a similar quality, and others can possess a similar quality unto themselves. Thus comes about the quality of classes of matter.
The system of classification emerges based on similarities and differences and according to the principle of dimensional scales.
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Logic
The concept of classification is vital to logical analysis.
DC CIRCUIT,R-C CIRCUIT, R-L CIRCUIT, L-C CIRCUIT, AC CIRCUIT, IN PHASE, OUT OF PHASE, RMS VALUE, CAPACITIVE REACTANCE, IMPEDANCE (R-C CIRCUIT), INDUCTIVE REACTANCE, IMPEDANCE (R-L CIRCUIT), R-L-C CIRCUIT
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GLOSSARY
For details on the following concepts, please consult Chapter 11.
DC CIRCUIT A DC (direct current) circuit generally consists of a battery acting as the energy source, through its EMF, and causing a steady voltage to act across one or more resistors, capacitors or inductors. In the steady state, after all transient phenomena have stopped, there is no voltage across an inductor, since the current is no longer changing. There is a steady voltage across a capacitor, equal to Q/C, but there is no current flowing to or from the capacitor. The voltage across a resistor will equal V = IR.
R-C CIRCUIT A DC circuit with a resistor R and a capacitor C shows a transient response when the switch is connected or disconnected.
At the moment the switch is closed, there is current in the circuit but no charge on the capacitor, and when the capacitor is fully charged, there is no current in the circuit. The current decays exponentially, which can be expressed as,
The situation is very similar in the case of the discharge of a capacitor.
R-L CIRCUIT A DC circuit with a resistor R and an inductor L also shows a transient response when the switch is connected or disconnected.
In a similar manner, if current is decreasing in an L-R circuit, it will decay exponentially with a time constant L/R.
L-C CIRCUIT In this circuit there is no dissipation of energy because there is no resistor. The capacitor stores energy in the form of separated charges or electric fields. The inductor stores energy in the form of moving charges or magnetic fields. The total energy remains in the system.
Therefore, the separated charges and the current interchange. This would bean oscillatory situation, with a repetitive interchange of energy between the capacitor and the inductor ad infinitum.
In the above circuit wefirst close switch S1 while S2 is open, and charge the capacitor to a voltage V, and charge Qmax. We then open S1 with the capacitor charged, and close S2 to permit the capacitor to discharge through the inductor. The capacitor discharges and then charges up again. This is similar to the case of simple harmonic motion (SHM).
This frequency, f, is called the resonance frequency of the circuit.
AC CIRCUIT An AC (alternate current) circuit generally consists of asource of voltage that is varying sinusoidally.In that case we expect that the variables of the circuit will also vary sinusoidally, after there has been sufficient time for the circuit to reach a steady state. This time is usually short enough that the effect of the transients can be neglected.
Whenever we have sinusoidal variation, we can express the variables as sine or cosine functions of time. The frequency f of the sinusoidal variation can be expressed in terms of an angular frequency ω, which simplifies the equations. Of course, the frequency can also be related to the period, T, by the relationship f= 1/T.
IN PHASE In AC circuit with a resistor,both current i and voltage v vary identically with time as cos ωt. We say that the two are “in phase”. This means that they both attain their maximum value at the same time, and both go through zero at the same time. We will see that this is true only for a resistor, while for capacitors and inductors, the voltage will not be in phase with the current.
The voltage at any time is just a fixed multiple of the current.
OUT OF PHASE When a generator causes a sinusoidal current to flow through the capacitor given by i = I0 cos ωt the capacitor is alternately charging each plate positively and negatively at a frequency: f = ω/2π. The voltage across the capacitor is defined to be from positive to negative plate and is always given as v = q/C. Both v and q will vary sinusoidally at the same frequency as the current. When the voltage reaches its peak, the current is zero. The current and voltage are said to be 90° or π/2 out of phase, and the current “leads” the voltage. We thus know that, for a capacitor, we can represent the voltage by v = VI0 sin ωt if the current is given by i = I0 cos ωt.
RMS VALUE In most formulas used in AC circuits, the quantity we use for the “magnitude” of currents and voltages will be the RMS value, and therefore when we write just I or V we will refer to the RMS values. The term RMS actually stands for “root-mean-square”, which refers to the method used to determine its value. To get the RMS value of a variable, we have to take the square root of the average (mean) of the square of the quantity. The current will vary as i = I0 cos ωt.I0 is the amplitude of the variation, and it represents the maximum value the current can have. We have the “RMS” value: IRMS = I0 √2.
CAPACITIVE REACTANCE We expect that if the maximum current is increased then the maximum charge on the capacitor will increase proportionally, and therefore also the maximum voltage. Consequently, we can write that V0 = χcI0, where the constant of proportionality χc is called the capacitive reactance of the capacitor. Similarly, VRMS = χcIRMS, or V = χcI. This capacitive reactance depends on the capacitance and on the frequency. Therefore, we have,
IMPEDANCE (R-C CIRCUIT) When theResistor and Capacitor are in Series, with the current given by as i = I0 cos ωt, the voltage across the entire circuit is
INDUCTIVE REACTANCE An AC generator produces a current I = I0 cos ωt in the inductor. The inductor produces a back EMF equal to (- L ∆I/∆t). This back EMF is balanced by the electrostatic voltage across the inductor, vL, as shown in the figure.
The voltage across the inductor is 90° out of phase with the current. The voltage leads the current,
IMPEDANCE (R-L CIRCUIT) When the Resistor and are in Series, with the current given by as i = I0 cos ωt, the voltage across the entire circuit and impedance is given by
We see that cos φ is again the power factor for an R-L circuit as it was for an R-C circuit. We can generally write that cos φ = X/R, where X is the reactance of the circuit, and equals XL for a circuit with inductance and -XC for a circuit with capacitance. Similarly, the impedance can then be written as Z = (R2 + X2)1/2, which will be valid for both R-C and R-L circuits. Additionally, we can write that the total voltage will vary with time as vT = V0T cos (ω t + φ), both for the case of the R-C and the R-L circuits, For the R-C circuit, φ is negative, and in the R-L circuit, φ is positive. We will find that we can extend these ideas to the last case, the R-L-C circuit also.
R-L-C CIRCUIT Here we have Resistor, Inductor and Capacitor in Series. We can write the equations giving these respective voltages as functions of time as:
From the phasor diagram we can deduce other relationships:
KHTK Factor # 14: The viewpoints and dimension points grow in complexity; it takes admiration to consolidate them into simplicity of oneness.
The more details we come up with the more complex the knowledge gets. This knowledge may be consolidated into various forms. Thus, there are larger gases, fluids and solids. And there is energy and matter.
The only way all this knowledge can be simplified is by finding the underlying principles and fundamental relationships. It takes the understanding of the unity of the whole to discover those principles and relationships. This requires admiration for what is there.
We have consolidated our knowledge of this complex physical universe quite nicely; but we are far from consolidating our knowledge of the mankind and its various institutions. Throughout this consolidation, the principle of the oneness of reality has been the key. Admiration of reality is the major factor that helps maintain that integrity.
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Scientology
Compare the above to the following factor in Scientology.
Scientology Factor # 14. Many dimension points combine into larger gases, fluids or solids. Thus there is matter. But the most valued point is admiration, and admiration is so strong its absence alone permits persistence.
The KHTK factors are basically consolidating the knowledge form Vedas, Buddhism, and Scientology.
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Logic
The ultimate logic lies in the expansion and consolidation of viewpoints and dimension points guided by the principle of oneness towards the goal of knowing the Unknowable.
KHTK Factor # 13: All viewpoints and dimension points are substantial and they form our reality.
One can sense the dimension points. The viewpoint appears as the prominently repeated pattern among the dimension points. The viewpoints and dimension points are categorized as thought, energy and matter.
Our body definitely consists of matter. It is infused with energy that extends far beyond the material body. All this matter and energy is wrapped up in thought.
If there is matter, then there is energy and thought too. They cannot be separated from each other, though we can consider them separately for analysis purposes. We may assign different names to different aspects of what we sense, but this process of naming does not separate these things from one another.
The whole system of what we sense forms a single reality. It is always continuous, consistent and harmonious with small or large gradients.
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Scientology
Compare the above to the following factor in Scientology.
Scientology Factor # 13. The dimension points are each and every one, whether large or small, solid. And they are solid solely because the viewpoints say they are solid.
The meaning of dimension points being solid can only be interpreted as having a definite characteristic common to them. This is the characteristic of being viewed or sensed. There is nothing arbitrary about it. This is just how it is. This is the basis of the universe and reality.
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Logic
We identify one thing that we sense as different from another thing that we sense, and name them so. But they are ultimately related because we sense them all. They cannot be completely separated from each other.
Self-Inductance, Mutual Inductance, Inductor, Energy in an Inductor, Energy Density in Space, Transformers
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GLOSSARY
For details on the following concepts, please consult Chapter 10.
SELF-INDUCTANCE Self-inductance arises from the flux that a current circuit produces within its own area. It is distinguished from mutual inductance. Self-inductance depends only on the geometry of the circuit. It connects the flux with the current as follows,
The unit for inductance is Wb/A, which is given the name henry. Practical circuits have inductance much smaller than one henry, more in the range of millihenries. The main use of the concept of inductance will be in circuits where the current changes, thus causing a proportional change in flux. This changing flux induces an EMF:
Solenoid The self-inductance, L, of the solenoid is: L = μ0 n2Ad; and the inductance per unit length is: L/d = μ0 n2A.
Toroid The self-inductance, L, of the solenoid is: L = μ0 N2A/2πr. If the toroid is filled with material of permeability μ, then: L = μ N2A/2πr.
MUTUAL INDUCTANCE Whenever one has two circuits near each other, it will be possible for a current which exists in one circuit to produce flux through the second circuit. If φ12 is the flux in circuit 2 caused by a current I1, in circuit 1, Then, the mutual inductance, M12, connects these two quantities, as follows,
The exact value of M12 is determined by the geometrical relationship between the two circuits. The change in current in circuit 1 changes the flux in circuit 2 proportionally, which produces an EMF in circuit 2, given by
There is only one mutual inductance for the two circuits meaning M12 = M21. We can measure the mutual inductance by measuring the induced EMF produced in one circuit by a known rate of change in current in the other circuit.
Coil on Solenoid
Coil on Toroid
Coil Near Long Wire
Coil at Center of Loop
INDUCTOR Any circuit element that generates an inductance when current flows through it (e.g. a coil, a solenoid, a toroid) is called an inductor. An inductor has the property that it produces a back EMF if the current is changing, but does nothing if the current is steady. While an inductor will not affect a DC circuit once a current has been established it will be of great importance during the time that the current is being turned on or off.
ENERGY IN AN INDUCTOR In order to increase the current in the inductor, an external driving voltage must be imposed on the circuit to overcome the back EMF, and this voltage will do work against the resisting EMF. The voltage will continue to do work until the current reaches its final value, at which time the current is no longer changing and no back EMF is being produced. During the time that the current is building up from zero to its final value, however, work must be done on the inductor. The work, or energy stored in the inductor is,
This result is similar to the case of storing energy in a capacitor by virtue of the charge that we have placed on the plates of the capacitor. There the energy stored = (1/2)Q2/C.
In terms of the magnetic field that have been set up in space, we have,
At any point in space, where there is a magnetic field, a certain amount of energy is stored. This energy equals the energy density times the volume of space being considered. The same general consideration holds for electric fields as well and indeed the electric field energy density is given by (1/2) ε0E2. In other words, wherever electric or magnetic fields exist in space, energy is being stored in the form of these fields
ENERGY DENSITY IN SPACE The total energy density at any point in space is the sum of the electric and the magnetic field energy densities. Since the units for energy density are the same irrespective of their source, this offers a means of comparing the relative magnitudes of electric and magnetic fields. Electric and magnetic fields with the same energy density can be considered to be comparable to each other. The electric and the magnetic fields associated with electromagnetic waves have equal energy densities. These considerations lend credence to the idea that these fields are real physical quantities that actually exist in space and are not merely mathematical contrivances that make it easier to calculate the forces exerted by the electric and magnetic interactions.
TRANSFORMERS We can induce EMFs in one circuit by changing the current in another circuit. This forms the basis of the transformer, which is used to transform voltage in one circuit into a different voltage in a second circuit. All the magnetic flux established by the first winding, called the primary coil, passes through the turns of the other winding, called the secondary coil. In order to get large fluxes, it is useful to place ferromagnetic material within the solenoid that has a large permeability, such as iron. The figure below shows a typical transformer:
Here, the primary winding, with N1 turns, is wound on one side of the rectangular ring, and the secondary winding, with N2 turns, is wound on the other side of the ring. This is a typical transformer. If one changes the voltage in the primary circuit, the current in the primary circuit will change, and therefore the flux. For a perfect transformer, the flux through one turn of the secondary is the same as the flux through one turn of the primary. Therefore, the total EMF developed in each winding will depend on the number of turns in that circuit.
A transformer is useful only with currents that are changing, as with AC. In that case, it is possible to use a transformer to convert a voltage applied to the primary circuit into a larger or smaller voltage in the secondary circuit. This ability to easily convert (transform) voltages in AC, which is much more difficult for DC, is the main reason why AC is the primary source of power throughout the world.
