Transient current measurements in dielectrics are generally interpreted using two simplifying hypotheses: (i) the applied voltage is a step function; (ii) the ammeter can be neglected in the circuit. To test the validity of these hypotheses, transient currents and charges have been simulated on a microcomputer, supposing a source of time constant tau not=0, and taking into account the ammeter. The system equations apply to a dielectric with Debye relaxation (time constant tau 0) and ohmic conductivity. It has been shown that a step function can profitably be substituted for the effective voltage, for every t>10 tau and under the condition tau << tau 0. It is concluded that experimental measures can be interpreted through the simplified circuit model, only for about t>10 tau m and under the two conditions: theta =C/(cx infinity +C) near 1, and tau m<< tau 0.