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We are beginning siman 37. The Chayei Adam writes that on Motzai Yom Tov, both when going into Chol Hamoed and when going back to the regular week, we add atah chonantanu just like Motzai Shabbos. Although one would have thought that the Chayei Adam would next state that similarly, one makes havdalah on a kos on Motzai Yom Tov just as they do on Motzai Shabbos, he does not mention anything about the kos. The Shulchan Aruch makes this omission as well. Both the Chayei Adam and Shulchan Aruch continue and write that on Motzai Yom Tov, we do not use a neir. The Mishnah Berurah points out that there is clearly an omission in the Shulchan Aruch regarding use of a kos, but there is no question that one makes havdalah on a kos just as they do on Motzai Shabbos.
We have learned (shiur S247) that the purpose of the neir on Motzai Shabbos is to remind us of the creation of fire by Adam Harishon on Motzai Shabbos. Additionally, since it is assur to make fire on Shabbos, there is an element of newness to making fire on Motzai Shabbos, which again serves as a reminder to the fire of Adam Harishon on Motzai Shabbos. One is allowed to use fire on Yom Tov, so the neir does not recall the newness of fire of Adam Harishon. Therefore, no bracha is made on a neir on Motzai Yom Tov.
A person does not make a bracha on besamim either. The Mishnah Berurah suggests that we know the purpose of besamim is to help a person recover somewhat from the loss of the neshama yeseirah. The concept of neshama yeseirah is only written in conjunction with Shabbos, and does not apply to Yom Tov, so there is no need to help the person. The Chayei Adam suggests that the simcha of Yom Tov gives a person enough strength that the simcha extends after Yom Tov is over, so there is no need for the besamim.
The bracha on the kos is the same on Yom Tov as it is on Shabbos. There is a slight difference in that the minhag is not to recite the pesukim of hinei keil of the beginning of havdalah. Additionally, on Motzai Shabbos there is a minhag to overflow the kos of havdalah, as a siman tov of overflowing goodness for the upcoming week. This is only relevant to Motzai Shabbos, so this minhag does not apply to Motzai Yom Tov.
Summary
- One recites atah chonantanu and havdalah on a kos on Motzai Yom Tov just as they do on Motzai Shabbos. However, the pesukim of hinei keil, and the bracha on neir and besamim are omitted.
- There is no need to overfill the kos on Motzai Yom Tov.