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Question: What do we do about lighting a havdala candle on Motza’ei Shabbat when it is also Yom Tov?

Answer: Lighting candles is one of the things that is forbidden on Shabbat but permitted on Yom Tov. Although the main permission given by the Torah is in regard to using fire to enable the preparation of food for Yom Tov, this dispensation applies to other needs of the day, including needs of mitzvot (Beitza 12a). We should recall that there is a rabbinic prohibition to create new fire, and it is permitted only to transfer fire from an existing source (Shulchan Aruch, Orach Chayim 502:1).
On the other hand, one may not even transfer a fire for a light that does not have a clear use (Shulchan Aruch ibid. 514:5, based on the Rosh, Beitza 2:22). It is not always easy to draw the line between a valid use and an invalid one. It is permitted to light candles in shul. The Mishna Berura (ad loc. 31) says that this is permitted even during the day, when the congregants can manage without its light because it still brings appropriate honor to the shul. The Mishna Berura (ibid. 30) also says that candles that are customarily lit at a brit milah may be lit on Yom Tov. (See the Tzitz Eliezer (VI, 10), who says that one may light a yahrtzeit candle on Yom Tov, if necessary, because the minhag to light it to show respect for the deceased is sufficient justification.)
One would think that regarding a havdala candle, where Chazal instituted the practice of making a beracha on it, one can certainly light the candle by transferring it from an existing flame, even though the practice is less than an outright obligation (Shulchan Aruch, ibid. 298:1). However, the issue is that it is not an absolute obligation to have the customary, braided candle of many wicks. Rather the gemara (Pesachim 103b) classifies having a "torch" (i.e., more than one wick) as the choice manner of performing the mitzva. Rav Shlomo Zalman Orbach was apparently unsure whether fulfilling the mitzva in the preferred way warrants transferring a fire from a simple candle (Shemirat Shabbat K’hilchata 62:(31)). One should also realize that if he lights his customary havdala candle, he will not be able to extinguish the flame, as doing so to preserve the candle for future use is not a positive use that is permitted on Yom Tov.
Therefore, the preferred system of making the beracha on the flame on Yom Tov is to take the two candles that were lit as the Yom Tov candles and put them together so that their flames become interconnected (Shemirat Shabbat K’hilchata 62:18). That way one has the torch effect without having to light extra candles to do so. In cases where one cannot put the two candles together, one can light a match or two so that he can put the flames together, as we should rely on the approach that fulfilling the mitzva in its standard way justifies lighting an additional light. Again, one should let the matches or candles go out themselves and not extinguish them.
The Tzitz Eliezer (XIV, 42) actually feels that one should light a new candle(s) and not use the ones lit for the honor of Yom Tov. This is because of the halacha that a havdala candle is supposed to be something that was lit to give light, not for honor (Shulchan Aruch, Orach Chayim 298:12). The Pri Megadim even adds that if the candle was lit both for honor and for light, it is still not valid. The Tzitz Eliezer demonstrates that Shabbat and Yom Tov candles are done both for light and for honor and, therefore, they are problematic. However, the Biur Halacha (ad loc.) says that the Pri Megadim’s view is not clearly accepted and the Shemirat Shabbat K’hilchata (62:(30)) says that the main purpose of the Yom Tov candles is to give light, even in an era where there are electric lights to provide the majority of the illumination.
In summary, while it is legitimate to light special candles for havdala when it is Yom Tov on Motza’ei Shabbat, the most suggested approach is to take two existing candles and put them together to form a "torch" upon which to make the beracha.