SELF

86

S.B. Karavashkin and O.N. Karavashkina

Denote l some fixed location of probe in the gap of core, so that - L l L  and L = 16 mm . Understanding that the experiment has been conducted with the sinusoidal current, we can represent the emf induced in each winding as a harmonic function of time and probe location in the gap. Assuming that experimentally the amplitude and phase of emf excited in each winding varies along the gap linearly, we yield at

,

(where U_1a0 = 5 V    in accordance with conditions of conducted experiment), the value of inductive emf will be

;

;

U_2max , _2max  are maximal values of amplitude and phase of emf induced in the probe when the probe was located near the boundary abutting on the inducing side of the primary loop; and  U_2min ,  _2min   are the minimal values of amplitude and phase of emf induced in the probe, when the probe was located near the boundary opposing to the inducing side of primary loop.

To record the similar relationship for the emf induced in the probe by loop c, we have additionally to take into consideration few factors. First, variation along the gap of the amplitude and phase of induction excited by loop c is directed as opposite to the variation of inductive emf excited by loop a. Second, we should take into account the phase of primary windings that proceeds by different connection of winding c. And third, we should account, how changes the amplitude of voltage across the winding c, which proportionally changed the amplitude of emf induced by this winding. Two last requirements are accounted by introduced coefficient  k ,     - 1 k 1  affecting the amplitude but not the phase of emf induced in the probe by winding c. The first requirement is satisfied by way of some transformation of expressions (8) and (9). With this, we can record that at

,

(where, by the condition of experiment, U_1cmax = 5 V) the expression for emf of induction excited by winding c will be the following:

;

;

In (12) and (13) we intentionally retained the values U_2max , U_2min , _2max , _2min ,  that we used in (8) and (9), since the experimental circuit was symmetrical at the conditions at which we measured the indicated parameters. Now, keeping in mind (7) and (10), we can return to the diagram in Fig. 21 and build on this principle the diagrams of summed inductive emfs at inequal voltages across the primary windings.

The general expression describing the variation of combined inductive emf can be recorded so:

It is understood that in (14) the anti-phase connection of primary windings will correspond to the positive values of k, and connection in phase will correspond to the negative values of k.

To determine in (14) the resulting amplitude and phase of induced emf, rearrange the right-hand part of this expression so: