All models of the Zulu require batteries or power to work.
There are 5 types of them.
Zulu: straight cord, battery powered, dual GA plugs
Zulu P: straight cord, installed panel powered, single LEMO plug (same plug a Bose headset uses)
Zulu C: coil cord, battery powered, single U-174 plug
Zulu CP: coil cord, panel powered, single LEMO plug (same plug a Bose headset uses)
Zulu CD: coil cord, battery powered, dual GA plugs
I see that there are three with coil cords.
In the 182 you do not want the Zulu C, that U174 plug is for helicopters.
The Zulu CP is if you have the panel set up to provide power to the unit. This is an extra box that would be needed to be installed. If your plane is a rental I doubt you have this type of box and connector unit.
The Zulu CD has the coil cord and the two plugs that most GA aircraft have. It also has the ANR unit that is attached to the cords and requires batteries.
Which model do you actually have?