Re: Three Voltages and Series Resistor (was - Magnetic quenching.)

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Ed Phillips <evp-at-pacbell-dot-net> 

Tesla list wrote:
 >
 > Original poster: "John H. Couture" <couturejh-at-mgte-dot-com>
 >
 > Ed, Jim, Robert, All -
 >
 > This problem caught my attention so I dug further. I at first thought that
 > it would not be possible to find the unknown load reactance without using a
 > capacitor or inductor.
 > I found that only one resistor is needed and three voltage readings and no
 > capacitor or inductor.
 > This will also give you input watts without a wattmeter for your Tesla coil.
 >
 > Here is a problem to work on -
 > Given 3 voltages (60 Hz) and a series resistor
 > Find the resistance and inductance of the load.
 >
 > Volts across load & res   = 120
 > Volts across load (TC?)   = 108
 > Volts across resistor     = 15
 > Series resistor ohms      = 15
 >
 > There is more than one way to solve this problem. In fact there is one
 > method that is very easy. Just find the sides of two right angle triangles.
 > One is the triangle with the load and series resistor and the other the
 > triangle with only the load.
 >
 > I have simplified the problem somewhat by using a 15 ohm resistor and 15
 > volts across the resistor for a one amp current in the circuit. Try the
 > problem with a 10 ohm resistor and 20 volts across the resistor.
 >
 > The load and resistor triangle -
 >     x= 100    y = 66.14    z = 120
 >
 > The load triangle -
 >     x = 85   y = 66.14    z = 108
 >
 > The load resistance is 85 ohms
 > The inductance is 66.14/377 = .17543 = 175.43 mh
 >
 > Can you fill in the calc details? Find the power factor? Input Watts?
 > Can you solve the problem in another way?
 > I wonder how Ed's students would solve this problem now?
 > I wonder if I got it right?
 >
 > John Couture

	About right.  I get load resistance = 83.7 ohms and
inductance = 0.181.  How? wrote a very simple Excel spreadsheet working
out the geometry!  That's how today's student would have done it, but
he'd have gotten the program from someone else as no one seems to use
his brains any more. (Bitch, bitch)  Anyone want me to send the file
direct?

Using your numbers, not mine and assuming correct arithmetic:

Input current = 15 volts / 15 ohms = 1 amp
Input power = (input current)^2 x (external resistor plus load resistor)
             = 1 x (15 + 85) = 100 watts
Input va = Vin x Iin = 120 x 1 = 120 voltamps
Load power = (input current)^2 x (load resistor) =  85 watts
Load power factor = load power/input power = 85/120 = 0.708 = 70.8%

Ed