In another thread here on The Lounge I showed Paul Horowitz's paradoxical machine that suspends a weight from an apparatus of two springs and three pieces of string. When you cut string #2 the weight *rises* which is quite surprising.
His article goes on to describe an electronic example that is kind of lame in my opinion. It uses current sources and phony baloney 0.375 volt Zener diodes to create a not-very-paradoxical result that, again in my opinion, doesn't appeal to intuition the same way as the rising weight machine.
But the following modification is paradoxical, at least in my opinion. It can be (and should be) solved by pure circuit design without resort to trickery or loopholes or funny business, just as Horowitz's weight + springs + string machine does not resort to trickery or loopholes.
The real-life, real-world prototype I've got on my solderless breadboard right now, has a score of twenty. Battery current after cutting the blue wire is 20% higher than battery current before cutting the blue wire. But LTSPICE tells me that higher scores are quite achievable. I'm sure diyAudio members will beat 20% rather easily.
His article goes on to describe an electronic example that is kind of lame in my opinion. It uses current sources and phony baloney 0.375 volt Zener diodes to create a not-very-paradoxical result that, again in my opinion, doesn't appeal to intuition the same way as the rising weight machine.
But the following modification is paradoxical, at least in my opinion. It can be (and should be) solved by pure circuit design without resort to trickery or loopholes or funny business, just as Horowitz's weight + springs + string machine does not resort to trickery or loopholes.
You are given a 3.0 volt battery pack (two AA cells in series), a 6 inch piece of blue insulated wire, fifty 1N914 / 1N4148 silicon diodes, and an infinite number of 1% resistors from the E96 series. Construct a circuit such that, when you cut the blue wire, battery current *increases*. Your score on the assignment is the percentage increase of battery current,
No tricks allowed, no loopholes allowed, no inductors or capacitors or transformers or antennas allowed. Battery current greater than 100mA is forbidden. Diode current greater than 100mA is forbidden. Resistor current greater than 100mA is forbidden. AC circuits are forbidden. Matched components are forbidden. Your solution schematic will be evaluated by your worst enemy who wants to see you fail; he will interpret any ambiguities or second-order-effects or other funny business, in the most damaging way possible.- Score = 100 * (I_after_cut - I_before_cut) / I_before_cut
The real-life, real-world prototype I've got on my solderless breadboard right now, has a score of twenty. Battery current after cutting the blue wire is 20% higher than battery current before cutting the blue wire. But LTSPICE tells me that higher scores are quite achievable. I'm sure diyAudio members will beat 20% rather easily.
Sorry, I have only red wire, so I failed. And the diodes are identical (since virtual ones). Also the resistors I used are probably not in E96, and these are very important factors, not like temperature...
BTW Can you tell me why is this task different from the previous? OK, more simple, since scalar by nature, but otherwise...
BTW Can you tell me why is this task different from the previous? OK, more simple, since scalar by nature, but otherwise...
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Thank you!
I must say this is a cool solution, since low ambient temperature is needed to work optimally. 🙂 I don't have time to optimize it, and I can't find temperature variable in LT Spice. I estimate the optimum should be somewhat under 0 Celsius for these resistor values.
I must say this is a cool solution, since low ambient temperature is needed to work optimally. 🙂 I don't have time to optimize it, and I can't find temperature variable in LT Spice. I estimate the optimum should be somewhat under 0 Celsius for these resistor values.
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