In "Romeo and Juliet" the exposition gives way to the rising action/problem when Romeo learns from the Nurse that Juliet is a Capulet in Act I, Scene V:
Is she a Capulet?/O dear account! my life is my foe's debt (112).
Romeo has fallen in love with the child of his family's mortal enemy, Capulet. Then, too, Juliet contributes to this problem by asking the Nurse to learn the name of Romeo. To the Nurse's answer that he is a Montague, "the only son of your great enemy" (132), Juliet reacts:
My only love sprung from my only hate!/Too early seen unknown, and known too late!/Prodigious birth of love it is to me,/That I must love a loathed enemy (133-136).
In the rhyming couplet of love that Juliet speaks, Shakespeare also introduces the theme of intractable fate. Elizabethan audiences would quickly recognize this reference to the inevitability of a tragic ending.
Most people try and argue that the first half of Romeo and Juliet is a rising action leading up to the death of Mercutio. I actually don't think this is at all logical, as part of the point is that a rising action builds up suspense towards a climactic event. And there isn't any suspense built towards Mercutio's death - the whole point of it is that it is an absolute, unexpected, tragic, shocking accident.
Act 1, though, does have a clear rising action, which is the build up of anticipation towards the Capulet party. Everyone's talking about it, and it is, of course, the moment where Romeo and Juliet meet each other for the first time.
Here's the evidence:
Benvolio promises, at the end of the first scene, to make Romeo forget about Rosaline, with whom he is in love:
I'll pay that doctrine, or else die in debt.
Capulet, in the next scene, announces...
This night I hold an old accustom'd feast,
Whereto I have invited many a guest...
and after Peter has told Benvolio about it, he advises Romeo to attend the feast:
Go thither, and with unattainted eye
Compare her face with some that I shall show,
And I will make thee think thy swan a crow.
Next scene. Lady C wants Juliet to go:
What say you? Can you love the gentleman?
This night you shall behold him at our feast.
Read o'er the volume of young Paris’ face...
Next scene, Romeo fears that
Some consequence, yet hanging in the stars,
Shall bitterly begin his fearful date
With this night's revels...