# Test case. In this case, to simplify the ascii-graphics, I'm not # actually drawing the resistors; each line is a one-ohm resistor: # # a (1V) # /|\ # / | \ # / b \ # / / \ \ # c--d e--f # \ \ / / # \ g / # \ | / # \|/ # h (0V) # # By symmetry, c, d, e, and f are all at 1/2V, so the c-d and e-f # resistors carry no current and can be ignored. Then the a-c-h path # has resistance 2 and current 1/2. The a-f-h path likewise. Then # b-d-g and b-e-g each have resistance 2, so the b-(d,e)-g diamond is # two two-ohm resistors in parallel and thus has resistance 1. Then # a-b-(d,e)-g-h is three one-ohm resistors in series and thus has # resistance 3. Then the whole network is two two-ohm and one # three-ohm resistors in parallel, giving it resistance # 1/((1/2)+(1/2)+(1/3)), or 3/4. # # Total current is thus 4/3, with 1/2 passing through a-f-h and 1/2 # through a-c-h and the remaining 1/3 through a-b-(d,e)-g-h: a-b and # g-h carry 1/3 and b-d-g and b-e-g carry half that, or 1/6. V a 1 R a b 1 R a c 1 R a f 1 R b d 1 R b e 1 R c d 1 R e f 1 R d g 1 R e g 1 R g h 1 R c h 1 R f h 1 V h 0