(a) An ideal single-phase two-winding transformer with turns ratio \(a_{t}=\) \(N_{1} / N_{2}\) is connected with a series impedance \(Z_{2}\) across winding 2 . If one wants to replace \(Z_{2}\), with a series impedance \(Z_{1}\) across winding 1 and keep the terminal behavior of the two circuits to be identical, find \(Z_{1}\) in terms of \(Z_{2}\).

(b) Would the above result be true if instead of a series impedance there is a shunt impedance?

(c) Can one refer a ladder network on the secondary (2) side to the primary (1) side simply by multiplying every impendance by \(a_{t}^{2}\) ?