Joseph Newman on the concept of "Power per second"

[kmarinas86]

[FOR] e^x=.5 when x=ln(.5)=-0.693147181, and this is where the power delivered to the magnetic field will match the power delivered to the resistance of the coil.

This is correct.

However, for the energy delivered to the magnetic field to match the energy delivered to the resistance, the integration of e^x is equal to 0.5.

This is false.

Thus e^x+xe^x, the integration of e^x, must equal 1/2. So when the energy delivered to the magnetism matches the energy delivered to the resistance, x=-.314923=-time*(Resistance/Inductance), such that time=0.314923*Inductance/Resistance. e^x becomes 0.72984507 and current would be 1-e^x or 27.015493% of its maximum value. Any less than this will result in having the energy delivered to magnetic field energy to exceed the energy delivered to the resistance of the wire.  The only power utilized from the batteries in net is the heat dissapated in the resistor while all power delivered to the magnetic field will return to its origin (because the power delivered to the magnetic field is reactive power and reactive power is not consumed).

So this is all wrong.

Now for the correction:

both
e^x*(1-e^x)   
and
(1-e^x)^2
must be integrated from x to 0, for x<0

Only by doing so can it be arrived that when the energy delivered to the energy of the magnetic field=energy delivered as heating in the coil:

real power/apparent power = apparent power/final apparent power

Where
real power = 0.467584558 * final apparent power
apparent power = 0.683801548 * final apparent power
final apparent power = 100% of final apparent power, when current reaches a maximum for a given voltage
x=-1.151385251
time=1.151385251*Inductance/Resistance
time=1.151385251*(L/R time constant)
current=68.3% of final current

So when all the LHS of the equations above are less than their corresponding RHS would the energy delivered to the magnetic field exceed that which was delivered as ohmic heating.

[Michelinho]

Hi kmarinas86,

So when all the LHS of the equations above are less than their corresponding RHS would the energy delivered to the magnetic field exceed that which was delivered as ohmic heating.

Don't forget that the Newman motor coil is colder than the ambient temperature while doing work. So you have to use a negative ohmic heating factor.

Take care,

Michel