The photovoltaic effect of a background beam do not affect the spatial-charge field in a photovoltaic crystal with a constant external applied field, but has an effect on the current density in the crystal.If the crystal is connected with an external circuit which includes a resistor and a constant voltage source, the photovoltaic effect of the background beam will affect the full width at half maximum of the solitons, even switch the bright solitons, to the dark solitons, or vice versa.