An electric appliance unit includes an appliance and a plug-in battery pack. The appliance has an appliance housing carrying an electric switch accommodated in a switch housing and including first electric contacts. The battery pack includes second electric contacts for engaging the first electric contacts. A first guiding arrangement guides and preliminarily centers the battery pack relative to the switch housing along a first insertion path extending to a first position to effect a coarse alignment of the first and second electric contacts upon reaching the first position. The first guiding arrangement includes a first guide component carried by the battery pack and cooperating, along the first insertion path, with a second guide component in the appliance housing. A second guiding arrangement guides and finely centers the battery pack relative to the switch housing along a second insertion path extending from the first position to a second position to effect a precise alignment of the first and second electric contacts with one another along the second insertion path. The second guiding arrangement includes a third guide component carried by the battery pack and cooperating, along the second insertion path, with a fourth guide component on the switch housing.