multiply the voltage times the amperage, (VI); to

obtain the power expressed in an inductor placed

across AC, is that there is a time lag between the

cause and effect; where voltage being the cause, and

its amperage being the effect. For the AC inductor,

because of this time lag, that for the external AC

source we can speculate that if the current were truly

90 degrees out of phase with the voltage, (this often

stated premise is not completely true, it depends

whether the inductor has a large enough inductive

reactance X(L)= 2pi*F*L to form a phase angle near 90

degrees); but if the amperage were near 90 degrees out

of phase with the voltage, by the time the AC voltage

input has made a complete pulse in one polarity, and

thus gone back to its zero crossing point; at that

moment in time the amperage in the coil will have

reached its maximum, again using the 90 degree phase

angle example. Up until this starting point 180

degrees into the AC cycle, a magnetic field from the

inductor is established that agrees with its polarity

input. But in the third quadrant of the AC cycle, the

voltage input reverses polarity, but the current has

not yet followed its example, because of the time lag

the current is going in the opposite direction then

what its voltage source would cause it to act. In the

third quadrant then the magnetic field of that

inductor is then causing a self induction by virtue of

its magnetic field collapse that establishes a

polarity OPPOSITE to the polarity of the source. This

is why back emf, or a backwards working voltage source

established by mistimed magnetic fields exists. The

net result of this backward working voltage during

portions of the AC cycle is that the forward working

voltage does not conduct it's OHM's law amount of

amperage, because of this extra effect of AC

resistance. We call this AC resistance inductive

reactance. The effects of both the actual resistance

and its inductive reactance is reffered to as

impedance, noted as Z where the effects of both

principles are obtained by summing the squares of both

quantities, and taking the square root of this result

shown as the impedance equation Z= sq rt[R^2+

X(L)^2].

Now some commentators note that because the coils

magnetic field establishes its own self induction, we

are actually dealing with the summation of two power

sources. They explain that because of the storage of

energy manifested as a magnetic field, in certain

portions of the AC cycle the coils collapsing magnetic

field is establishing a polarity opposite to its

source, and in terms of the AC source being a

generator, that generator as its VI apparent power

input also experiences borrowed and returned energy.

When the coils magnetic field collapses a portion of

the power input is returned to the generator. Now the

real amount of energy expeneded on the coil is just

its conversion to heat by I^2R heat losses, and the

rest is just borrowed and returned energy. The

essential question then becomes does this source also

act like a banker and charge interest on its borrowed

and returned assets? This would seem the sensible

thing to do, but perhaps nature doesnt always model

mans actions.

So we have two aspects, and this is where the third

aspect comes into being, where the concept of phase

angles comes into play. We have the apparent power

input which is just the voltage times the amperage

across the load,or (VI) of the generator as the

apparent power input. Then we have the real power

input which is undeniable because we can measure the

heat release as the I^2R quantity. Because we have a

load containing reactance, or a reactive load, the

difference between the real and apparent power inputs

is merely the % of borrowed and returned energies vs

real energy output. But we also have a method to

compute what this heat release should be by methods of

trigonometry. We can draw out the AC voltage and

amperage AC cycles, and find out the % portions where

they are in agreement, where this portion will be

expressed as a cosine angle. The real power input

therefore becomes VI* cos( acting phase angle of the

inductor), and we conclude that this also equals I^2R

as the heat loss. Recall that in trigonometry we have

a y coordinant, [expressed as X(L)in phase angles]:

where y/radius is the sine quantity of the angle, and

conversely x/radius is the cosine. (In trigonmetry we

allow the radius of the circle to be the unit 1 to

simplify these calculations.) To find the phase angle

of an inductor we let the inductive reactance to be

the positive y quantity, and the actual resistance R

to be the x quantity. But a little more trig is need

to find the actual phase angle which can be calculated

with any calculator having trig functions. The tangent

of the angle is expressed as y/x. So if we have a coil

where X(L) and R is both known, the tangent is easily

known; it is just X(L)/R, which is also the

theoretical Q factor of the coil. But what we NEED to

find out is the inverse of this, which will tell us

the radians, which can further be reduced to an angle

by multiplying by 360 degrees/ 2pi radians, which is

the conversion factor to degrees. Suppose I have an

inductive reactance 5 times the resistance; what is

the phase angle? We know the tangent is merely 5, but

this tells us nothing. Instead what we NEED to find

out is the answer to the question; the tangent of what

amount of radians will give an answer of 5. Thus we

use the inverse function, called the co-tangent, or

tan^-1 to determine the answer. And tan^-1 (5) = an

answer in radians that can be converted to degrees,

and this is the method for finding the phase angle.

Now if X(L)is very large vs the R quantity of

resistance, X((L) forms the y axis, R forms the x

axis, and the hypotenus, (ordinarily the radius

quantity in trig functions) becomes the impedance Z.

We already know by the Pythagorean theorem that the

sum of the squares of the right angle triangle sides

is equal to the square of the hypotenus, and by then

taking the square root of both sides of the equation

we reach the same equation for the impedance Z. And if

X(L)>> R then X(L)~= Z. The length of the radius and

its y reflection are almost equal, but the x

reflection as the additive vector is very small

compared to the other two quatites by definition since

we have initially made the condition X(L) is far

greater then R. The x reflection is also the cosine of

the phase angle, and it is this no. as a percentage

that is used for the real power calculations. Thus

with this condition the apparent power will be far

greater then the real power. These things are all

rudimentary for the electrical engineer.

Now we come to electrical resonance, where X(C) forms

the negative Y axis, the opposite reactances in series

can cancel, leaving R as the predominant factor for

conduction, and in this condition then we suspect that

now the apparent power will be the same thing as the

real power, and the amperage has now come closely in

phase with the impressed voltage. However because of a

factor known as "internal capacity" we may not always

arrive at a conduction that equals ohms law

requirements. The depends on the construction of the

inductor we are resonating. However a VERY

misunderstood thing can happen here. We might assume

that since now the apparent power equals the real

power, which also occurs in DC circuits after the

magnetic field is established, that % wise the

generator is no longer having a significant portion of

"borrowed and returned" energy allocations. We have

cancelled the reactive state of the circuit, so have

we not also cancelled the "borrowed and returned"

field energies? The generator would seem to indicate

so, because the apparent power equals the real power,

and we are not seeing differences between those

definitions. However in actuality the opposite thing

has occured, the borrowed and returned field energies

will have gone up q times, even though the generator

does not seem to indicate this % wise in its

allocations. A simple proof of this is the definition

of stored energy for the L and C components. The

energy stored in C is defined as [CV^2]/2, and for L

it is [LI^2]/2. In series resonance each L and C

component developes an internal voltage rise against

each other, in opposite directions with respect to

each other, so that on the outside of the circuit, the

generator only sees this net cancellation. For the C

case, since the V term is squared, and we are

obtaining series resonant internal voltage rise, the

stored energy has gone up Q times, where the acting Q

factor is the ratio of the inside voltage rise to the

outside voltage source. We then have increased the

borrowed and returned energies, but now a different

relationship exists. Formerly the energy was borrowed

and returned to the generator, but now the borrowed

and returned energies only exist between the L and C

values... It is literally as if the expanded electric

and magnetic field energies were being obtained in

resonance for free... But can we use this fact to

power another load? That isnt so easy a proposition.

If we divert the expanded voltages to another circuit,

this in turn destroys the properties of the resonance

itself, so that the actual resonant rise of voltage is

wiped out.

A little over a year ago I set up some circuits where

the resonances were obtained from a 3 phase alternator

functioning @ 480 hz. These resonances were special in

that they were designed to be maximum energy transfer

circuits, generally defined as a circuit that drops

the open circuit voltage of the source in half, but on

the only side of the coin, the maximum amount of power

to load is obtained from that generator. Between these

3 AC phases, set up as Delta Series Resonances,

(DSR's), the voltage rise q factor of 5 was noted.

What this means is that 5 times more amperage is

procurred then what exists in the reactive state, and

also the internal rise of voltage was 5 times that of

the source. Now between these three 120 degrees of

voltage rises, the AC was turned into DC by means of

full wave rectifications, which because of the poly

phased inputs, thus fills up the DC ripple without use

of a filter capacity. The load for these DC currents

was a 3/8ths inch width of a ferrite block, normally

considered an insulator. Now ferrite is actually

considered a class of semiconductor, in that it looses

resistance with heat. The ferrite in this case

gradually grew hot, its resistance decreased

phenomenally going from 30,000 ohms to around 7 ohms,

until it began to glow on a corner, the temp around

900 degree fahrenheit. Meanwhile the outside coils,

where this internal current was obtained from on the

rectifications also experienced a drop of current from

what existed in its resonant state. The addition of

this low ohmic load between the resonances had caused

its amperage input to drop, in fact it drops low

enough so that only half of the current that the coils

would consume in its reactive state was noted. We

might say that X(L) of the coils appeared to double.

What this also means is that once again we should be

dealing with apparent vs real power input ratios. Now

the inside load, being DC has no power factor

arguments associated with it, but the outside coils

do, because they are AC reactances, placed into

resonance, and then reduced from resonance by addition

of the interphasal load. This load has become a 2nd

generation maximum power transfer principle, where the

internal impedance or reactance of the outside coil

systems have been matched by an equal resistive load.

In terms of this Z(int) of the source has been given

an equal R(load) in ohmic values, the requirement for

maximum energy transfer. The outside spiral coils

themselves, constructed as maxium energy tranfer

resonances, (METR components), use the same principle

in the R(int) of the alternator stator coils equals

R(load) of the coils resistance R value.

Now in the cited circumstance, the stator lines each

serving two phases contains ~ 2.0 -2.4 Amps, and the

division into phase currents should reduce this by

about 1.7 times the stator line currents. The outer

phase currents derived from these stator line currents

are somewhat inbalanced, and the pic I took of the

power input shows 1.4, .85 and 1 amp currents on this

outer triangle, a sum of 3.25 Amps. On the DC current

procurred from the outside misphased AC currents I

arrive at a sum of 3 DC amps, obtained from this

outside AC current oscillation. Both the alternator

input voltage and the ferrite DC voltage are about

equalized at 17 volts. As such no resonant rise of

voltage is taking place, the voltage input is about

the same as the voltage output to the load. Now if we

average the phases currents to ~ 1.1 amps, with 17

volts across them, the apparent power input is 17* 1.1

= 18.7 watts per phase, or the generator is inputing

an apparent power of 56.1 watts. But the REAL power of

the inside triangle load being shown by the 900 degree

heat of the ferrite is also 17VDC*3A = 51 watts. The

coils themselves that lay on the delivery lines to the

ferrite have a combined 3 watts heat loss, close to

what the apparent power shows itself as, where the

combined loads of 51 + 3 watts almost equals the

apparent power input of 56 watts.

Here is where the kicker comes in; the apparent power

in is yeilding almost the same amount as real power

out!. We surmise that since no resonant rise of

voltage is occuring on the outer triangle coils, that

we should treat this as a apparent power input, and

not a real one. Now we have about a 84 degree phase

angle, made as tan^-!(10), from a situation that

started out with a phase angle dictated by the

tan^-1(5), from the coil systems having a q of 5.

After the load was added the coils appeared to have

about double the impedance on their conductions, which

is where the 10 figure in tan^-1 estimations comes in.

If this were true, the mechanical energy required to

turn the alternator should only reflect a real power

load of only 10 watts, by the conventional phase angle

analysis, but yet we have a bonafide real power load

of 5 times this amount!

Have we indeed turned an apparent power input into a

real one? Perhaps the apparent vs real power arguments

do not apply for this special case. What I would like

to be able to do is power the alternator with a geared

up bicycle gearing rig, and drive the alternator by

bicycled leg power. For only a 10 watt power

requirement to make 900 degrees, this seems possible

with a human energy input. Then I could stick in real

resistive power loads, and compare the respective

drags for both situations. In any case the above

arguments either show that the current electrical

phase angle theory is inadequate to explain the above

situation, or conversely we have used the "free" field

oscillations inherent in resonance to create a

situation of overunity. The calculations also show

that ~ 6 times the energy transfer occurs in the LC

field energy transfers then do the actual real power

being inputed as I^2R heat losses on the DSR's

themselves, which are just under 1 ohms resistance.

Sincerely

Harvey D Norris

Tesla Research Group; Pioneering the Applications of Interphasal Resonances http://groups.yahoo.com/group/teslafy/