Learn Hardcore Korean: bang jeonguga gapjagi nagaseo bame chaegeul mos ilgeosseoyo. - The room’s light bulb suddenly went out, so I couldn’t read at night.

Breakdown of bang jeonguga gapjagi nagaseo bame chaegeul mos ilgeosseoyo.

Why is it 방 전구가 instead of 방의 전구가?

In Korean, two nouns are often placed directly next to each other without 의 when the relationship is obvious.

방 전구 = the room bulb / the bulb in the room
방의 전구 is also possible, but it sounds more explicit or a little less conversational

So 방 전구가 is a natural compressed way to say the bulb in the room.

What is the particle 가 doing in 전구가, and why is there 을 in 책을?

They mark different grammatical roles in the two parts of the sentence.

전구가: 가 marks the subject of the first clause
→ the bulb is the thing that went out
책을: 을 marks the object of the second clause
→ the book is the thing that the speaker couldn’t read

Even though it is one sentence, it contains two linked clauses, so each clause can have its own marker.

What does 나가다 mean here? I thought it meant to go out or to leave.

Here, 나가다 is being used in a very common idiomatic way.

With things like lights, electricity, or appliances, 나가다 can mean:

So 전구가 나가다 means the light bulb went out or burned out.
It does not mean the bulb physically left the room.