Learn Hardcore German: Die Batterie ist geladen.

In German every noun has a grammatical gender (masculine, feminine or neuter). Batterie is feminine, so it takes the definite article die in the nominative case (subject position).

Why is the verb ist singular? Shouldn’t it agree with Batterie?

It does agree: Batterie is singular, and ist is the third-person-singular form of sein (to be). If you had a plural subject, e.g. Die Batterien, you would use sind (they are).

What form is geladen—is it an adjective or part of a passive construction?

Here geladen is the past participle of laden (to charge). In the sentence Die Batterie ist geladen it works like an adjective, describing the state of the battery (“charged”). Grammatically this is called a “stative passive” or “Zustandspassiv.”

How do I say “to charge” in German, and how do I form its past participle?

The verb is laden (pronounced [ˈlaːdən]). Its past participle is geladen. You form it by adding the ge- prefix and the -en ending, as with most strong verbs:

Infinitive: laden
Präteritum: lud
Partizip II: geladen

Can I invert the sentence to make it a question?

Yes. For a yes/no question, swap the verb and subject:

Statement: Die Batterie ist geladen.
Question: Ist die Batterie geladen?

How do I say “not charged” or “uncharged”?

You simply place nicht before the participle:

Die Batterie ist nicht geladen.
If you want “discharged” in the sense of “empty,” you can also use entladen (to discharge) and say:
Die Batterie ist entladen.

Are there any synonyms for geladen in this context?

In everyday use, geladen or aufgeladen (also meaning “charged”) are most common. For example:

aufgeladen emphasizes that you actively charged something (e.g. a phone).
geladen by itself often describes the current state (e.g. a battery in a remote control).