🌟 When you combine these two sentences.

집에 오다 + 공부를 하다
Come

home + study

You may choose the conjunction 'and'
'and' is usually translated as '그리고' or '그래서'

So, we can say
A. 나는 집에 와요 그리고 공부를 해요.(Present)
B. 나는 집에 왔어요 그래서 공부를 했어요.(Past)

Many Korean conjunction often combine verbs as conjunctive particles. These can be said

A-1. 나는 집에 오고 공부를 해요"(Present)
B-1. 나는 집에 와서 공부를 했어요"(Past)

Now a difference in meaning arise.

At A-1. The sentences states only 'sequence of time' '집에 오다' and '공부를 하다' don't have any causal connection. Just saying 'I'm studying after I come home.

But at B-1. Two verbs must be The two verb should be operated in the same place. Because conjunction '-아/어서(그래서) is used to refer to causality. This sentence can be translated as 'I came home and studied (at home)'

📝In summary

👍Simply referring to the sequence of time, use the conjunction '-고(그리고).
✌Refer to the causal relationship of motion (Occurs in the same place), use '-아/어서(그래서)

P.S. I didn't intend to explain it so dry, but I couldn't help it. I still hope it helps someone.😉