Resistance Value?

[Richard O'Neill]

Karl,

  If you eliminate all resistors except those between the two test 
points you have three resistors that measure three ohms. Add four more 
resistors (total of seven) to form a rectangle and the measurement will 
be < 1.5 ohms. Add an additional seventeen resistors to form another 
rectangle  and the resistance decreases to scarcely more than one ohm 
between the test points.

  Add progressively more of those little buggers and the resistance 
between the two test points continues to decline in ever decreasing 
amounts. From that I theorized that as 'n' (number of resistors) 
approaches infinity the equivalent resistance approaches one ohm. A 
finite number of resistors may never quite decrease the equivalent 
resistance to a value of one ohm but it sure does kick the heck out of 
it. Good enough for guvment work. Heisenberg might have been proud. ;-)

Richard

PS. That's why Physicists are only worth two points (in the original 
cartoon) while mathematicians are worth three. They take much longer to 
get the answer.


On 10/25/2012 10:23 PM, Karl W4KRL wrote:
> One ohm cannot be correct. If you eliminate all resistors except the four
> that connect the two measurement points you end up with two one ohm
> resistors in series that are in parallel with two other one ohm resistors in
> series hence one ohm between the measurement terminals. Since the rest of
> the infinite network is in parallel with these resistors the value must be
> less than one ohm.
>
> Karl W4KRL
>
> -----Original Message-----
> From: Richard O'Neill [mailto:richardoneill at earthlink.net]
> Sent: Thursday, October 25, 2012 7:04 PM
> To: tacos at amrad.org
> Subject: Re: Resistance Value?
>
>    Correct! You win the Grand Prize, a one ohm resistor. :-) Would you care
> to inform us how you arrived at the answer?
>
> Richard
>
>
> On 10/25/2012 6:34 PM, Phil wrote:
>> One ohm.
>>
>> Phil M1GWZ
>>
>>
>> On 25 Oct 2012, at 20:32, Karl W4KRL wrote:
>>
>>> My solution is based on observing that an infinite number of parallel
>>> resistors approaches zero resistance. Each row and column of
>>> resistors can be reduced to a short circuit connected to the "center"
>>> elements through two series resistors.
>>>
>>> Karl W4KRL
>>>
>>> -----Original Message-----
>>> From: Richard O'Neill [mailto:richardoneill at earthlink.net]
>>> Sent: Thursday, October 25, 2012 2:14 PM
>>> To: W4KRL at arrl.net
>>> Cc: Karl W4KRL; 'Tacos AMRAD'
>>> Subject: Re: Resistance Value?
>>>
>>>
>>>    Awaiting your drawing. :-) The proof of Fermat's last theorem
>>> required
>>> 358 years but this problem isn't that difficult to solve.
>>> In fact, it's intuitively obvious and a good exercise for EE's. :-D
>>>
>>> Richard
>>>
>>> On 10/25/2012 12:24 AM, Karl W4KRL wrote:
>>>> My non-mathematical approach yields 1/2 Ohm. Am I correct? If so I
>>>> will draw the approach tomorrow.
>>>>
>>>> Karl W4KRL
>>>>
>>> <resistor grid.jpg>_______________________________________________
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