The cathode of a photoelectric cell is changed such that the work function changes from W₁ to W₂ (W₂ > W₁). If the currents before and after change are I₁ and I₂, all other conditions unchanged, then (assuming hf> W₂)

I₁ = I₂   

As long as Energy of photon hf> W(Work Function), photoelectron will be emitted i.e the work function has no effect on the current. So, work function does not play any role here. Further, the photo-electric current is proportional to intensity of light. Here, there is no change in the intensity of light. Hence I₁ = I_­2.