The charge transport and photogeneration in solar cells based on the low bandgap-conjugated polymer, poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b; 3,4-b']dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) and fullerenes is studied. The efficiency of the solar cells is limited by a relatively low fill factor, which contradicts the observed good and balanced charge transport in these blends. Intensity dependent measurements display a recombination limited photocurrent, characterized by a square root dependence on effective applied voltage, a linear dependence on light intensity and a constant saturation voltage. Numerical simulations show that the origin of the recombination limited photocurrent stems from the short lifetime of the bound electron-hole pairs at the donon/acceptor interface.