Dependence of saturation current in photoelectric tube on the time taken by the electron to reach the opposite plate? The kinetic energy of an electron in a photoelectric tube increases with increase in the applied voltage across the plates of the tube, thus the velocity of the electrons also increases. Accordingly the time taken by the electron to reach the opposite plate should be less and so the current in the external circuit should increase as $i=\frac{dp}{dt}$ and so current is inversely proportional to time.But this is not the case as the value of saturation current remains the same.Why is the value not depending on the time taken by the electron to reach the opposite plate?
 A: The current in any circuit is given by i= dq/dt. q being the charge of the carriers not dp/dt. Increasing the voltage will only increase the kinetic energy of the electrons coming out but not the current because the number of electrons available is the same(unless you are varying the intensity of the light which is creating the effect).
But if their is air, it should resist the electron flow a little. Hence you might see a voltage dependence. But that possibly wouldn't be ohmic.
A: The saturation current is the same because the RATE of charge flow per unit time is the same. Shorter time, smaller charge flow.
The charge is not fixed. The amount of photoelectrons emitted is maxed. So all that are emitted are being collected   
A: The rate determining step is not the time taken by the electrons to reach the opposite plate. What I mean is, the electrons that are emitted reach the opposite plate almost instantaneously. Assuming constant electric field between plates $E$ and charge of electron $e$ and mass $m$  and distance between plates $x$. Time $t$ taken to reach the opposite plates for an electron starting from rest is $$T=\frac{\sqrt {2xm}}{\sqrt{eE}}$$
The $m/e$ ratio for electrons is so small that we can assume $T=0$. Thus even if  the $E$ field is increased ,after a certain limit, the effect would be negligible. The crucial step that determines the current is the number of electrons that are emitted which is solely dependent on intensity of light.
