I have a cyclic electric circuit with N knots and constant resistances $$R_i = 1/N$$.
EDIT:
I calculated the incidence matrix B and the conducting matrix C: $$ B = \matrix{(-1, 1, 0, 0, ..., 0) ; (0, -1, 1, 0, ..., 0) ; (0, 0, -1, 1, 0, ..., 0) ; ... ; (1, 0, ..., 0, -1) }$$ and $$C = diag(N, ..., N)$$.
In addition, I know that $$ b = (u, 0, 0, ..., 0)^T$$
Now, how does $$(x_1, ..., x_N)$$ look like if the following equation has to be true? $$ B^T \times C \times B \times x = B^T \times C \times b$$
Thanks for any help!