The battery E charges the capacitor to certain potential V, after which the flow of current in C and R₃ stops and continues only in the circuit through R₁ and R₂. When the current in the capacitor circuit stops there will be no fall of potential in resistance R₃ and the capacitor's p.d. must equal that between points a and b, i.e. the fall of potential in resistance R₂. Ohm's law gives us that the current
I = E/(R₁ + R₂)
This current creates a p.d. at the ends of resistance R₂, i.e. between points a and b, of
V = IR₂ = ER₂/(R₁ + R₂)
And this is the potential to which the capacitor C will be charged.