eeokeoneul kyeon chaero jamdeureosseoyo.

-ㄴ/은 채로 means while remaining in that state or with something left as it is.

So 에어컨을 켠 채로 means with the air conditioner left on.

In this sentence, the idea is:

• first, the speaker turned the air conditioner on
• then, without changing that state, the speaker fell asleep

It is very similar to English expressions like:

• with the air conditioner on
• while leaving the air conditioner on

Because 켠 is the adnominal form that shows a completed action resulting in a current state.

The base verb is 켜다 (to turn on).

Here is the difference:

• 켜는 = turning on / present-type modifier
• 켠 = turned on / already on

Since the air conditioner was already on at the time the speaker fell asleep, 켠 채로 is the natural form.

So:

• 에어컨을 켜는 채로 would sound wrong or unnatural here
• 에어컨을 켠 채로 = with the air conditioner turned on

Because 켜다 is a transitive verb, so it takes an object.

• 에어컨을 켜다 = to turn on the air conditioner

Here, 에어컨 is the thing being turned on, so it gets 을.

Even though the whole phrase becomes 에어컨을 켠 채로, the object marking stays because 에어컨 still belongs to the verb 켜다.

잠들었어요 comes from 잠들다, which means to fall asleep.

잤어요 comes from 자다, which means to sleep.

So the difference is:

• 잠들었어요 = focuses on the moment or event of falling asleep
• 잤어요 = focuses more generally on sleeping

In this sentence, 잠들었어요 suggests:

• the speaker ended up falling asleep
• possibly unintentionally
• while the air conditioner was still on

That is why it sounds very natural here. It often has the feeling of I dozed off or I ended up falling asleep.

They are similar, but not exactly the same.

• 에어컨을 켜고 잠들었어요 = I turned on the air conditioner and fell asleep
• 에어컨을 켠 채로 잠들었어요 = I fell asleep with the air conditioner left on

The -고 form mainly links actions in sequence:

1. turn it on
2. fall asleep

The 채로 form emphasizes the state being maintained:

• the air conditioner stayed on
• that unchanged state matters

So if you specifically want to highlight it was left on, 채로 is a better choice.

켜 놓고 and 켠 채로 are close, but the nuance is a little different.

• 켜 놓고 means turn on and leave it that way / have it on
• 켠 채로 means in the state of being on

A simple way to think about it:

• 켜 놓고 highlights the action of setting it up and leaving it
• 켠 채로 highlights the unchanged state during the next event

In everyday Korean, both can work in similar situations.
But 켠 채로 잠들었어요 sounds especially natural when you want to emphasize that the speaker fell asleep without turning it off.

Yes. Korean often leaves out the subject when it is obvious from context.

So 에어컨을 켠 채로 잠들었어요 does not explicitly say I, he, she, or they.

Depending on context, it could mean:

• I fell asleep with the air conditioner on
• He/She fell asleep with the air conditioner on
• They fell asleep with the air conditioner on

In many real conversations, the subject is understood and does not need to be stated.

It is the polite informal style, often called 해요체.

• 잠들었어요 = polite and natural for everyday conversation
• plain form: 잠들었어
• formal style: 잠들었습니다

So this sentence is suitable for:

• normal conversation
• talking politely to someone you do not speak casually with
• most everyday situations

It is not extremely formal, but it is polite.

Often, yes.

Because the sentence uses 잠들었어요 and 켠 채로, it can sound like:

• the speaker unintentionally fell asleep
• the air conditioner was left on
• this may have been undesirable or careless

The sentence itself does not explicitly say regret, but in many contexts it can carry that feeling.

For example, it can sound like:

• Oops, I fell asleep with the air conditioner on
• I ended up falling asleep without turning it off

That nuance depends on context and tone, but many learners notice it, and they are not imagining it.