# Test case (all resistors one-ohm): # # +---/\/\/---a---------------/\/\/---------------+ # | | | # 1V--e---+ +---/\/\/---d---/\/\/---b---/\/\/---+---gnd--0V # | | # +---------/\/\/---------c---------/\/\/---------+ # # The equivalent resistance is easy to work out in this case. The # gnd-c-e path has resistance 2; the gnd-b-d-a path has resistance 3, # so the gnd-a effective resistance is 1/((1/1)+(1/3))=1/(4/3)=3/4, # giving the gnd-e path through a a resistance of 7/4. Then the total # resistance is 1/((4/7)+(1/2))=1/((8/14)+(7/14))=1/(15/14)=14/15. # # Total current is thus 15/14. gnd-c and c-e carry 1/2 each, with a-e # carrying the other 8/14=4/7; of this 4/7, gnd-a carries three times # what gnd-b-d-a carries, so the currents are 3/7 for gnd-a and 1/7 # for gnd-b, b-d, and d-a. V gnd 0 R gnd a 1 R gnd b 1 R gnd c 1 R a d 1 R b d 1 R a e 1 R c e 1 V e 1