236 ELECTRICAL APPARATUS ever, from which the direct current, ?"o, is derived by reversal, must go through zero twice during each period, thus must have the shape shown as i in Fig. 76, that is, must abruptly reverse. If, however, the supply circuit contains any self-inductance—and every circuit contains some inductance—the current can not change instantly, but only gradually, the slower, the higher the inductance, and the actual current in the supply circuit assumes FIG. 77.—Differential current on rectifier on inductive load. a shape like that shown in dotted lines in Fig. 76. Thus the cur- rent in the alternating part and that in the rectified part of the circuit can not be the same, but a difference must exist, as shown as i1 in Fig. 77. This current, if, passes between the two parts AC FIG. 78.—Rectifier with A.C. and D.C. shunt resistance for inductive load of the circuit, as arc at the rectifier brushes, and causes the recti- fying commutator to spark, if there is any appreciable inductance in the circuit. The intensity of the sparking current depends on the inductance of the rectified circuit, its duration on that of the alternating supply circuit. By providing a byepath for this differential current, if, the sparking is mitigated, and thereby the amount of power, which can be rectified, increased. This is done by shunting a non-inductive resistance across the rectified circuit, r0, or across the alternating circuit, r, or both, as shown in Fig. 78. If this resistance is low, it consumes considerable power and finally increases sparking