In Star Trek, The Original Series, what is the maximum number of photon torpedoes that the Enterprise NCC-1701 can hold?
According to the semi-canon Mr Scott's Guide to the Enterprise, the "photorp" complement of the NCC-1701 Enterprise is 20 x Morris Magtronic FP-4 photonic torpedoes.
Since Mr Scott doesn't explain that this has changed post-refit, we can reasonably assume that it also applies to the original NCC-1701 as well as the refit version seen in the film series.
Most deck plans that I have seen indicates 40 photorps. The magazines are on decks 10 and 11 which is located in the Dorsal (neck) section. They are divided into two racks on each deck (four total) with each rack holding 10 photorps(total of 40).