På audiografens oppfølgingstime kommer det an på om høreapparatbatteriet er nytt.

Here på means at, not on in the physical English sense.

• På audiografens oppfølgingstime = at the audiologist’s follow-up appointment
• In Norwegian, på is often used for events, appointments, meetings, classes, and similar situations.

So this is a very natural use:

• på skolen = at school
• på jobb = at work
• på møte = at a meeting
• på timen = at the appointment / during the lesson

Audiografens is the genitive form of audiografen.

Breakdown:

• audiograf = audiologist / hearing specialist
• audiografen = the audiologist
• audiografens = the audiologist’s

So:

• audiografens oppfølgingstime = the audiologist’s follow-up appointment

The -s is the usual Norwegian possessive ending, similar to English ’s.

Because Norwegian normally writes compound nouns as one word.

Here:

• oppfølging = follow-up
• time = hour, lesson, appointment

Together:

• oppfølgingstime = follow-up appointment

This is very typical in Norwegian. English often separates these words, but Norwegian usually combines them:

• høreapparat = hearing aid
• sykehuslege = hospital doctor
• arbeidsdag = workday

Not usually. In this context, time means appointment.

Norwegian time can mean:

• hour
• lesson/class period
• appointment

So in healthcare contexts:

• jeg har time hos legen = I have an appointment with the doctor

That is the meaning here.

Kommer det an på is an idiomatic expression meaning depends on.

So:

• det kommer an på = it depends
• det kommer an på om ... = it depends on whether ...

You should learn this as a fixed phrase, because the literal meanings of the individual words are not very helpful here.

Examples:

• Det kommer an på været. = It depends on the weather.
• Det kommer an på hva du vil. = It depends on what you want.

The det is part of the fixed expression det kommer an på.

In English we also say it depends, where it does not refer to a concrete thing. Norwegian works similarly here:

• Det kommer an på ... = It depends on ...

So even though det may feel vague, it is required in this expression.

Because Norwegian has verb-second word order in main clauses.

The sentence starts with another element:

• På audiografens oppfølgingstime = at the audiologist’s follow-up appointment

When that comes first, the finite verb must come second:

• På audiografens oppfølgingstime kommer det an på ...

If there were no opening phrase, you would say:

• Det kommer an på om høreapparatbatteriet er nytt.

So the fronted phrase causes inversion:

• Det kommer ...
• På audiografens oppfølgingstime kommer det ...

Here om means whether, not if in the conditional sense.

• det kommer an på om ... = it depends on whether ...
• hvis usually means if in a condition

So in this sentence, om is the correct choice because the meaning is whether the battery is new, not a condition like if this happens, then...

Compare:

• Jeg vet ikke om han kommer. = I don’t know whether he is coming.
• Hvis han kommer, blir jeg glad. = If he comes, I’ll be happy.

Again, this is a Norwegian compound noun.

Breakdown:

• høreapparat = hearing aid
• batteri = battery
• høreapparatbatteri = hearing-aid battery
• høreapparatbatteriet = the hearing-aid battery

Norwegian strongly prefers compounds like this instead of separate words.

Because the sentence is talking about a specific battery, not just any battery.

• et batteri = a battery
• batteriet = the battery

Since the context is the hearing aid being discussed, Norwegian naturally uses the definite form:

• høreapparatbatteriet = the hearing aid battery

English sometimes uses the where Norwegian uses a definite ending on the noun itself.

Because batteri is a neuter noun:

• et batteri

The adjective ny must agree with the noun:

• en ny stol = a new chair
• et nytt batteri = a new battery

In the sentence, the adjective comes after er, but it still agrees with the noun:

• batteriet er nytt = the battery is new

So nytt is the neuter form of ny.

Because this adjective is predicative, not attributive.

Compare:

Attributive adjective: before the noun

• det nye batteriet = the new battery

Predicative adjective: after a verb like er

• batteriet er nytt = the battery is new

In predicative position, Norwegian uses the form that agrees with gender/number, not the definite adjective pattern.

So:

• det nye batteriet = the new battery
• batteriet er nytt = the battery is new

Not always exactly, depending on the healthcare system, but for a learner it is often close enough to understand it as a hearing specialist / audiologist.

In real usage, professional titles can differ somewhat between countries, so the translation may not be perfectly one-to-one. But in this sentence, the important point is that it refers to the specialist handling hearing and hearing aids.

Yes. A simpler version could be:

• Det kommer an på om høreapparatbatteriet er nytt.
  = It depends on whether the hearing aid battery is new.

The original sentence adds the setting:

• På audiografens oppfølgingstime = at the audiologist’s follow-up appointment

So the full sentence is just more specific about when/in what context this matters.

A word-for-word style breakdown is:

• På = at
• audiografens = the audiologist’s
• oppfølgingstime = follow-up appointment
• kommer = comes
• det = it
• an på = on / depends on
• om = whether
• høreapparatbatteriet = the hearing-aid battery
• er = is
• nytt = new

A more natural English rendering is:

• At the audiologist’s follow-up appointment, it depends on whether the hearing aid battery is new.

So the main things to notice are:

1. Norwegian compounds are written as one word.
2. det kommer an på is an idiom meaning it depends.
3. The adjective nytt agrees with the neuter noun batteri.