Path of least resistance

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Johnny Gooch

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http://ecmweb.com/mag/electric_path_least_resistance/index.html
In a previous thread Celtic referenced a Path of least resistance link to a Mike Holt explanation of a ground rod driven for a light pole. I can't get the same values shown on the slide.
Can someone work this circuit out and let me know what current they come up with for the 1000 ohm resistor and the voltage drop across the 8.5 ohm. I get the point point?but can't duplicate his math.
Breaking it down to a simple series circuit, I have 120 V. 4.67 amps. and 25.69 ohms.
Where am I getting it wrong, no values applied for the ground rod at the pole or just too much resistance between the ears?
Johnny
 
Re: Path of least resistance

1/1000 = .001, 1/17.5= .057
.001 + .057 = .058. 1/.058 = 17.24
This is the total resistance of the parallel resistors.

17.24 + 8.5 = 25.74

120/25.74 = 4.6 amps
I rounded off therefore I came up just a little short. I shall carry on future.

17.25 X 4.6 = 79.35 volts and 8.5 X 4.6 = 39.1volts (the voltage drop of this resistor)
39.1 + 79.35 = 118.45 volts again short due to the rounding off.

Current through the parallel paths

79.35/1000 = .07935 amps and 79.35/17.5 = 4.53 amps
.07935 + 4.53 = 4.6 amps

My numbers are not exact due to rounding off, but as you can see the math checks itself.
:)
 
Re: Path of least resistance

Johnny,

I believe you are correct; the numbers on the diagram are wrong.

Furthermore, I would argue that even this poor ground reduces the risk somewhat by lowering the potential to some 81V instead of 120V.

This is an example of a Thevenin equivalent circuit. That is an 81V emf with a 5.72 Ohm internal resistance. Still could be lethal though if one has enough body contact.
 
Re: Path of least resistance

May I also make the point that the 1K in parallel with 17.5 Ohms has only a minute effect on total resistance. No need to compute the parallel resistance. The point is that a potential of some 81V exists and the resistance is low enough to cause serious injury or even death to a human with wet hands standing in mud with wet shoes.

This leads to the concept of significant figures and expected error. I will let someone else delve into this subject.

I am saying that it is important to understand when it is appropriate to make approximations instead of cranking out umpteen significant figures on your calculator.

[ November 13, 2005, 06:32 PM: Message edited by: rattus ]
 
Re: Path of least resistance

Thanks for checking the math folks, the science behind the tingle is always fun.
I should send Mike Holt a drawing of my friend Terry with one hand on a portable welder, single phase 480 volt, the male end wired properly with the ground to the frame of the machine, rubber tires.
The female end was wired improperly with what should be ground going to the third phase of a 480/3ph. panel. When his other hand contacts a hand rail, ouch that had to hurt.
Johnny
 
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