Charges on dust grains immersed in a plasma may vary as a consequence of plasma currents falling onto their surface. Such charge variations might lead to many collective phenomena in the dusty plasma. We have written a set of multifluid equations that describe the charge dynamics of the dust particles self-consistently, i.e., as a consequence of loss in the electron and ion number densities. Various collective phenomena related with dust- and ion-acoustic modes are then studied in the context of these equations. Consistency of the results with previous work and aspects arising due to the present self-consistent charge dynamics are discussed.