Jag var utmattad på toppen.

Word by word:

• Jag = I
• var = was (past tense of är / is, from the verb vara, to be)
• utmattad = exhausted
• på = on / at
• toppen = the top / the summit

So the sentence is literally something like I was exhausted at/on the top.

Var is the past tense of vara (to be).

• Jag är utmattad = I am exhausted
• Jag var utmattad = I was exhausted

So if the situation happened in the past, Swedish uses var, just like English uses was.

Utmattad is an adjective. It describes a state or condition: exhausted.

In this sentence, it comes after the verb var, so it works as a predicative adjective:

• Jag var trött = I was tired
• Jag var utmattad = I was exhausted

It is describing jag.

Swedish adjectives change form depending on what they describe.

For predicative use after vara, the common forms are:

• common gender singular: utmattad
• neuter singular: utmattat
• plural: utmattade

Examples:

• Mannen var utmattad. = The man was exhausted.
• Barnet var utmattat. = The child was exhausted.
• De var utmattade. = They were exhausted.

With jag, you normally use utmattad in a sentence like this.

På toppen means at the top or on the summit, depending on context.

If the sentence is about climbing a mountain, hill, tower, or similar place, på toppen means being at the highest point.

So the idea is:

• Jag var utmattad på toppen = I was exhausted at the top / on the summit

Swedish often uses på for positions on surfaces or at elevated points, including the top of something.

That is why på toppen is natural.

A few examples:

• på bordet = on the table
• på berget = on the mountain
• på toppen = at/on the top

English may prefer at the top in many cases, but Swedish commonly uses på here.

Toppen is the definite form of topp, so it means the top.

• en topp = a top / a peak
• toppen = the top / the summit

So:

• på en topp = on a peak / on a top
• på toppen = at the top / on the summit

The sentence uses the definite form because it refers to a specific top.

Yes, but it changes the meaning slightly.

• på toppen = at the top / on the summit
  This usually means a specific top, often the top of something already known from context.
• på en topp = on a peak / on one peak
  This sounds less specific and more indefinite.

So if you mean when I reached the top, på toppen is the natural choice.

Yes. Swedish allows different word orders depending on emphasis.

The basic sentence is:

• Jag var utmattad på toppen.

You can also say:

• På toppen var jag utmattad.

That version puts more focus on på toppen.

But remember an important rule in Swedish: the finite verb usually stays in the second position in main clauses. So if you move på toppen to the front, var still comes second:

• På toppen var jag utmattad.

Not:

• På toppen jag var utmattad.

Yes. Utmattad is much stronger than trött.

• trött = tired
• utmattad = exhausted
• helt utmattad = completely exhausted

So this sentence suggests a fairly intense level of tiredness, not just mild fatigue.

Yes, it is a natural sentence, especially in a context like hiking or climbing.

That said, depending on context, a Swede might also say:

• Jag var helt slut på toppen. = I was completely wiped out at the top.
• Jag var väldigt trött på toppen. = I was very tired at the top.
• Jag var utmattad när jag kom upp på toppen. = I was exhausted when I got up to the top.

Your original sentence is grammatically correct and natural.

A rough guide for an English speaker:

• Jag ≈ yahg or sometimes closer to yag
• var ≈ vahr
• utmattad ≈ oot-MAT-tad
• på ≈ paw
• toppen ≈ TOP-pen

A more important point than perfect imitation is the rhythm:

• Jag var utmattad på toppen

Stress falls especially on:

• -matt- in utmattad
• top- in toppen

It can be both, depending on context.

Physical:

• Vi stod på toppen av berget. = We stood on the top of the mountain.

Abstract:

• Hon är på toppen av sin karriär. = She is at the top of her career.

In your sentence, though, the most natural reading is physical: being exhausted at the top of something, such as a mountain or hill.

You would usually say:

• Jag var utmattad på toppen av berget.

Here:

• på toppen = at the top
• av berget = of the mountain

So toppen av berget means the top of the mountain.