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 impedance a$\_$t$^2?$