The transformer is a static device which works on AC. The windings of the transformer are having the resistance and inductance which actually contributes the impedance and controls the current drawn on A.C. In D.C. only the contribution of current is because of resistance and not impedance. The resistance is less this will cause the heavy current in the Windings and will cause the burning out of the winding. Therefore the transformer should never be connected on D.C., secondly the current in D.C. has the constant magnitude resulting the constant flux. Only in the initial stage the current, causes the rate of change of current, hence results the rate of change of flux, and inducing voltage. But after that there is no rate of change of flux, so there will not be any voltage induced. So the transformer cannot work on D.C.