The work function of a certain metal is $\frac{\mathrm{hc}}{{\mathrm{\lambda }}_0}.$ When a monochromatic light of wavelength $\mathrm{\lambda } < {\mathrm{\lambda }}_0$ is  incident such that the plate gains a total power $\mathrm{P}$. If the efficiency of photoelectric emission is $\mathrm{\eta }\%$ and all the emitted photoelectrons are captured by a hollow conducting sphere of radius $\mathrm{R}$ already charged to potential $\mathrm{V}$, then neglecting any interaction between plate and the sphere, expression of potential of the sphere at time $\mathrm{t}$ is