Whenever an alternating pressure is impressed on a circuit, part of it is spent in overcoming the resistance, and the rest goes to balance the reverse pressure due to self-induction.
The total pressure applied to the circuit is known as the impressed pressure, as distinguished from that portion of it called the active pressure which is used to overcome the resistance, and that portion called the self-induction pressure used to balance the reverse pressure of self-induction.
The intensity of the reverse pressure induced in a circuit due to self-induction is proportional to the rate of change in the current strength.
Thus a current, changing at the rate of one ampere per second, in flowing through a coil having a coefficient of self-induction of one henry, will induce a reverse pressure of one volt.
Ques. Describe how the rate of change in current strength varies, and how this affects the reverse pressure.
Ans. The alternating current varies from zero to maximum strength in one-quarter period, that is, in one-quarter revolution of the generating loop or 90° as represented by the sine curve in fig. 1,307. Now, during, say, the first 10 degrees of rotation (from 0 to A), the current jumps from zero value to A', or 4 amperes, according to the scale; during some intermediate 10 degrees of the quarter revolution, as from B to C, the current increases from B' to C' or 2½ amperes, and during another 10 degrees as from D to E, at the end of one-quarter revolution where the sine curve reaches its amplitude, it rises and falls ½ ampere. It is thus seen that the rate of change varies from a maximum when the current is least, to zero when the current is at its maximum. Accordingly, the reverse pressure of self-induction being proportional to the rate of change in the current strength, is greatest when the current is at zero value, and zero when the current is at its maximum.
Fig. 1,307.—Sine curve showing that the rate of change in the strength of an alternating current is greatest when the current is least, and zero when the current is at a maximum. This is evident from the diagram, since during say the first 10° as OA, the current increases 4 amperes; during BC, 2½ amperes; during DE it rises and falls ½ ampere. The reverse pressure of self-induction being proportional to the rate of change of the current, is a maximum when the current is zero, and zero when the current is a maximum, giving a phase difference of 90° between reverse pressure of self-induction and current.
This relation is shown by curves in fig. 1,308, and it should be noted that the reverse pressure and current are 90° apart in phase. For this reason many alternating current problems may be solved graphically by the use of right angle triangles, the sides, drawn to some arbitrary scale, to represent the quantities involved, such as resistance, reactance, impedance, etc.