C

In the photoelectric effect, the emitted photoelectric current (photoelectron emission rate) does not depend on the frequency of the incident photons as long as that frequency is greater than the threshold frequency (u > v th). Rather, it is primarily dependent on the intensity of the incident beam, which relates to the number of photons striking the surface per unit time. Thus, increasing the frequency, while maintaining it above the threshold frequency, does not increase the current but can increase the energy of the emitted electrons. Therefore, the correct answer is C.