** copied from SED:
On Fri, 31 Dec 2010 23:10:05 -0800, Tim Wescott
wrote:

http://www.xkcd.com/841

Pretty funny. Interesting how Usenet text has always been crystal
clear, 5-by-5.


Maybe Sloman can tell us what this circuit does, and what the resistance
of the 1 ohm array is.
**
Array calculations done two ways.

1) Via delta-to-wye transformations and wye-to-delta transformations as
well as simplifications where appropiate.
See Array.PDF and note the following:
Page one shows an enlargement of the original drawing with placement
for wye and delta transformations color coded to value.
Page 2 shows actual replacement, with color coding. Note blue is used
for one-half ohm resistors, black for one ohm and red for 2 ohms.
In Page 3, simplification has been done and the next step of
transformations is indicated in green.
In a similar manner, Pages 4 and 5 show that the array has been
reduced; not some resistors now are negative or zero.
In pages 6 and 7, the array was further reduced.
Page 8 shows the intermediate result, with "construction" lines;
orange for two ohm wye-to-delta and greenfor the other transformation.
Page 9 shows the results while keeping the color coding.
Page 10 ("A") shows the net parallel value of 1.5 & 2.5 ohms as well
as the parallel value of the two one ohm resistors. A delta-to-wye
transformation is indicated for the next step.
The transformation has been done, shown on Page 11 ("B").
A simplified version is shown on Page 12 ("C").
Again a parallel value was calculated and shown on Page 13 ("D").
The net value is also shown (0.527183179 ohms approximately).

2) An attempt was made to duplicate the array AKA mess in SPICE just
for kicks; note the net resistance is quite different.

So, there is at least one error in one or both schemes as shown.

Comments?




Version 4
SHEET 1 880 680
WIRE 224 -176 224 -192
WIRE 224 -176 -320 -176
WIRE 48 -96 -80 -96
WIRE 128 -96 48 -96
WIRE 224 -96 224 -176
WIRE 224 -96 208 -96
WIRE 240 -96 224 -96
WIRE 368 -96 320 -96
WIRE 400 -96 368 -96
WIRE -80 -64 -80 -96
WIRE 48 -48 48 -96
WIRE 96 -48 48 -48
WIRE 224 -48 224 -96
WIRE 224 -48 160 -48
WIRE 368 -48 368 -96
WIRE 368 -48 304 -48
WIRE 400 -48 400 -96
WIRE 0 0 -32 0
WIRE 96 0 96 -48
WIRE 160 0 160 -48
WIRE 224 0 224 -48
WIRE 304 0 304 -48
WIRE -80 48 -80 16
WIRE -32 48 -32 0
WIRE -32 48 -80 48
WIRE -320 64 -320 -176
WIRE 400 64 400 32
WIRE 48 80 48 32
WIRE 48 80 32 80
WIRE 160 80 96 80
WIRE 272 80 224 80
WIRE 304 80 272 80
WIRE 0 112 0 80
WIRE 48 112 0 112
WIRE 272 112 272 80
WIRE 272 112 128 112
WIRE 0 128 0 112
WIRE 304 128 304 80
WIRE 400 128 400 64
WIRE 400 128 384 128
WIRE 32 144 32 80
WIRE 48 144 32 144
WIRE 160 144 160 80
WIRE 160 144 128 144
WIRE 192 144 160 144
WIRE 0 160 0 128
WIRE 48 160 0 160
WIRE 192 160 192 144
WIRE 272 160 272 112
WIRE 128 176 128 144
WIRE 128 176 80 176
WIRE 400 192 400 128
WIRE 400 192 384 192
WIRE -80 208 -80 48
WIRE -32 224 -48 224
WIRE 48 224 48 160
WIRE 400 224 400 192
WIRE 80 240 80 176
WIRE 160 240 160 144
WIRE 208 240 160 240
WIRE 304 240 304 192
WIRE 304 240 288 240
WIRE 32 256 32 144
WIRE 160 256 160 240
WIRE 208 256 160 256
WIRE 288 256 208 256
WIRE -80 304 -80 288
WIRE -48 304 -48 224
WIRE -48 304 -80 304
WIRE 288 304 288 256
WIRE 384 304 384 240
WIRE 384 304 368 304
WIRE -80 336 -80 304
WIRE 368 352 368 304
WIRE 368 352 320 352
WIRE 400 352 400 304
WIRE 400 352 368 352
WIRE -80 368 -80 336
WIRE -64 368 -80 368
WIRE 32 368 32 336
WIRE 32 368 16 368
WIRE 64 368 32 368
WIRE 80 368 80 320
WIRE 80 368 64 368
WIRE 96 368 80 368
WIRE 192 368 176 368
WIRE 208 368 208 336
WIRE 208 368 192 368
WIRE 240 368 240 352
WIRE 240 368 208 368
WIRE -320 432 -320 144
WIRE 32 432 -320 432
WIRE 192 432 192 368
WIRE 192 432 32 432
WIRE 32 464 32 432
WIRE 192 480 192 432
FLAG 224 -192 IN
FLAG 192 480 OUT
FLAG 400 64 J
FLAG 400 352 L
FLAG 64 368 D
FLAG -80 336 C
FLAG -80 48 B
FLAG 48 -96 A
FLAG 368 -96 I
FLAG 304 80 H
FLAG 304 192 K
FLAG 0 128 E
FLAG 48 80 F
FLAG 32 144 F
FLAG 128 144 G
FLAG 32 464 0
SYMBOL res 224 -112 R90
WINDOW 0 0 56 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R1
SYMATTR Value 1
SYMBOL res 336 -112 R90
WINDOW 0 0 56 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R2
SYMATTR Value 1
SYMBOL res 416 48 R180
WINDOW 0 36 76 Left 0
WINDOW 3 36 40 Left 0
SYMATTR InstName R3
SYMATTR Value 1
SYMBOL res 416 320 R180
WINDOW 0 -31 72 Left 0
WINDOW 3 -16 35 Left 0
SYMATTR InstName R4
SYMATTR Value 1
SYMBOL res 224 368 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R5
SYMATTR Value 1
SYMBOL res 80 384 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R6
SYMATTR Value 1
SYMBOL res -80 384 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R7
SYMATTR Value 1
SYMBOL res -96 192 R0
WINDOW 0 -33 40 Left 0
WINDOW 3 -27 77 Left 0
SYMATTR InstName R8
SYMATTR Value 1
SYMBOL res -96 -80 R0
SYMATTR InstName R9
SYMATTR Value 1
SYMBOL res -16 -16 R0
WINDOW 0 -4 -5 Left 0
SYMATTR InstName R10
SYMATTR Value 1
SYMBOL res 32 -64 R0
WINDOW 0 -9 -4 Left 0
SYMATTR InstName R11
SYMATTR Value 1
SYMBOL res 80 -16 R0
WINDOW 0 9 3 Left 0
SYMATTR InstName R12
SYMATTR Value 1
SYMBOL res 144 -16 R0
WINDOW 0 9 3 Left 0
SYMATTR InstName R13
SYMATTR Value 1
SYMBOL res 208 -16 R0
WINDOW 0 9 3 Left 0
SYMATTR InstName R14
SYMATTR Value 1
SYMBOL res 288 -16 R0
WINDOW 0 9 3 Left 0
SYMATTR InstName R15
SYMATTR Value 1
SYMBOL res 288 144 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R16
SYMATTR Value 1
SYMBOL res 288 208 R270
WINDOW 0 5 141 VTop 0
WINDOW 3 48 94 VBottom 0
SYMATTR InstName R17
SYMATTR Value 1
SYMBOL res 400 224 R90
WINDOW 0 18 51 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R18
SYMATTR Value 1
SYMBOL res 384 288 R90
WINDOW 0 4 70 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R19
SYMATTR Value 1
SYMBOL res 192 240 R0
SYMATTR InstName R20
SYMATTR Value 1
SYMBOL res 64 224 R0
SYMATTR InstName R21
SYMATTR Value 1
SYMBOL res 16 240 R0
WINDOW 0 -45 55 Left 0
SYMATTR InstName R22
SYMATTR Value 1
SYMBOL res -48 240 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R23
SYMATTR Value 1
SYMBOL res 32 128 R270
WINDOW 0 18 -16 VTop 0
WINDOW 3 33 47 VBottom 0
SYMATTR InstName R24
SYMATTR Value 1
SYMBOL res 32 160 R270
WINDOW 0 -30 65 VTop 0
WINDOW 3 15 31 VBottom 0
SYMATTR InstName R25
SYMATTR Value 1
SYMBOL res 304 224 R90
WINDOW 0 4 70 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R26
SYMATTR Value 1
SYMBOL res 288 144 R90
WINDOW 0 4 70 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R27
SYMATTR Value 1
SYMBOL current -320 64 R0
SYMATTR InstName I1
SYMATTR Value -1
TEXT -194 154 Left 0 !.op
TEXT 248 -176 Left 0 ;0.747861 volts ( = ohms )

Robert Baer wrote:
** copied from SED:
On Fri, 31 Dec 2010 23:10:05 -0800, Tim Wescott
wrote:

http://www.xkcd.com/841

Pretty funny. Interesting how Usenet text has always been crystal
clear, 5-by-5.


Maybe Sloman can tell us what this circuit does, and what the resistance
of the 1 ohm array is.
**
Array calculations done two ways.

1) Via delta-to-wye transformations and wye-to-delta transformations as
well as simplifications where appropiate.
See Array.PDF and note the following:
Page one shows an enlargement of the original drawing with placement
for wye and delta transformations color coded to value.
Page 2 shows actual replacement, with color coding. Note blue is used
for one-half ohm resistors, black for one ohm and red for 2 ohms.
In Page 3, simplification has been done and the next step of
transformations is indicated in green.
In a similar manner, Pages 4 and 5 show that the array has been
reduced; not some resistors now are negative or zero.
In pages 6 and 7, the array was further reduced.
Page 8 shows the intermediate result, with "construction" lines;
orange for two ohm wye-to-delta and greenfor the other transformation.
Page 9 shows the results while keeping the color coding.
Page 10 ("A") shows the net parallel value of 1.5 & 2.5 ohms as well
as the parallel value of the two one ohm resistors. A delta-to-wye
transformation is indicated for the next step.
The transformation has been done, shown on Page 11 ("B").
A simplified version is shown on Page 12 ("C").
Again a parallel value was calculated and shown on Page 13 ("D").
The net value is also shown (0.527183179 ohms approximately).

2) An attempt was made to duplicate the array AKA mess in SPICE just
for kicks; note the net resistance is quite different.

So, there is at least one error in one or both schemes as shown.

Comments?



Found that there is a problem in the delta-to-wye conversion; it
ain't as simple as what i used.
For example, taking a delta configuration of all one-ohm resistors
would give a wye configuration of 1/3 ohm resistors, not one-half ohm.
Just that alone raises the net value from above 0.5 ohm to above 0.67
ohm.