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Re: 50%

At 03:25 PM 11/4/96 +0000, you wrote:
>From MALCOLM-at-directorate.wnp.ac.nzMon Nov  4 06:45:29 1996
>Date: Mon, 4 Nov 1996 20:09:43 +1200
>From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
>To: tesla-at-pupman-dot-com
>Subject: Re: 50%
>
>Wow! I just have to respond to this post on the 2 cap problem.....
>
>> Energy is conserved. Mistakes in capacitor circuit theory and
>> algebra are the problem. That is why you did not remember it from
>> college. The voltage across the two capacitors after the
>> reconnection is not V/2. It is V/sqrt2. This can be easily checked
>> by test and correct algebra.
>> 
>> The voltage will be a little less than V/sqrt2 because there is
>> some spark loss in the reconnection. In the test that I made the
>> voltage across the two capacitors was slightly less than V/sqrt2
>> because of losses but was still much more than V/2. Using V/sqrt2
>> in the equation will give a total of 100% energy (50% in each) for
>> the two capacitors if the algebra is done correctly.
>
>So we now have Q = 2C x V/sqrt2 when we started with Q = CV. I think
>your result begs an explanation. If no energy is expended in 
>connecting the two caps, how did the extra charge separation come 
>about?
>I have just this very minute done this experiment with two high 
>quality capacitors and the voltage comes to V/2 near as.
>
>Malcolm
>
-----------------------------------------

Malcolm -

      V/2          New zealand
      V/sqrt2      San Diego

The reason the reciprocals are different in New Zealand than in San Diego is
because we are on different sides of the planet.  (:>)  (:])  (:<)

This capacitor problem is a tricky question and and covers many
possibilities and is sometimes given by electrical/electronic instructors
because it has to do with both capacitor theory and unfamiliar algebra.

   Your Q = CV = coulombs is correct
   My   J = 1/2 CV^2  = joules (energy) is also correct

Coulombs are a quantity of electricity (not energy). One coulomb passing a
fixed point in one second is one ampere. You have to multiply this by
voltage, etc., to get energy. When you multiply coulombs by voltage you get
CV^2.

Joules (energy) is a unit of work (something a customer is willing to pay
for as I have said before). One joule is one watt second. Energy is always
conserved in a test when correctly performed and calculated.

There are several ways to solve this problem. However, the voltage across
the two capacitors after reconnecting them must be found by the conservation
of energy equation.

I will start with both capacitors equal to 1 farad and the voltage at 10 volts.

At start - energy in one capacitor = 1/2 CV^2 = 1/2(1)(10)^2 = 50 joules
Connecting the two capacitors  J = 1/2 CV^2    50 = (1/2)(2)(V)^2 
Voltage across both capacitors V = sqrt(2*(50)/2) = sqrt(100/2) = sqrt(50) =
7.07 volts not 5 volts.

Energy in both caps = (1/2)(1)(7.07)^2 + (1/2)(1)(7.07)^2 = 25 + 25 = 50
joules. Energy is conserved.
    
Note that Q = CV in the energy equation gives  J = (1/2)(Q)(V). The
difficulty  is that the V is in two of the variables of the equation. This
means you would have to find the volts by some other method such as the
conservation of energy equation.

This brings up the question. How did you measure the voltage in your test
and come up with V/2? Was it a rough estimate? Was the voltage on the two
caps a steady voltage or a reducing voltage? Were the caps equal, see below.
I used 200000 uf and a digital meter and got a little under V/sqrt2 and
greater than V/2. I found that smaller capacitors did not work very well to
get the accuracy required using equal capacitors..

Testing requires a person well versed in the test possibilities. For
example, in this test note that when the second capacitor is made smaller
the two caps voltage approches the original voltage!! Also, when the second
cap is made larger the two caps voltage approches zero!! You can come up in
the test with the two cap voltage of almost zero to 100% original voltage! 

Can you find the combination of unequal caps to come up with V/2 and still
have conservation of energy?? You could get 5 volts with certain unequal
capacitors in the test. The two capacitor voltage would not be V/sqrt2, this
only applies to equal capacitance capacitors. 

Whenever anyone comes up with a test that does not conserve energy you must
realize, as you did, that something is wrong with the testing even though
you do not have an immediate answer. This occurs often with tests that
supposedly proves free energy.

Try calculating the two "capacitor voltage" using unequal capacitances. If
you can do the algebra correctly (tricky) you have a good understanding of
this type of problem. 

Note that this has very little to do with Tesla coils but it is an
interesting problem that gives engineers bigger problems.

Jack C.