A complex voltage E is applied to the ladder network of Figure 7.31. Show that the (complex) mesh currents I_k satisfy the equations

Show that

satisfies (7.20) provided that cosh θ = 1 – 1/2 LCω². Note that this equation yields two values for u, so that in general I_k may be written as

where A and B are independent of k. Using the special equations for I₀ and I_n, obtain the values of A and B and prove that

Lojl- - (1 - 1) = E Lojl, + Co j Lojl- - (1k - Ik+1) + Co j Co j Co -(1-1-1) = 0 (k = 1,..., N 1) (7.20) -(In-1-In) = 0 -