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EFFECT OF THE SELF AND MUTUAL INDUCTANCE OF THE FIXED AND
The self-inductance of the fixed coils of the wattmeter employed in these measurements is 0.075 millihenry, of the auxiliary coil 0.111 millihenry, and the mutual inductance of the two is 0.072 millihenry. At a frequency of 120, p = 754, and the reactance of the auxiliary coil is 0.083 ohm. This is wholly negligible in its effect upon the magnitude or phase of the compensation current ig. The self-inductance of the fixed coil has no appreciable effect upon the magnitude or phase of the main current in. The mutual inductance between the coils, however, may have an appreciable effect upon the magnitude of the compensation current is in the auxiliary coil, provided the electromotive force e, on the compensation circuit is small. Thus, the back e. m. f. in this circuit, due to the current i, in the fixed coil, is pMin, and this is equal to 0.16 volt when i;= 3 amperes and p= 754. In methods 4 and 5, eg was usually 45 to 70 volts, and hence the correction y due to mutual inductance is only one or two units in the last decimal place of the values given for cos $, in Tables IV and V. In method 3, however, eg was smaller and the correction is 5 to 6 in the last decimal place of the values of cos , in Table III.
The expression for cos , in which the mutual inductance of the fixed and auxiliary coils is taken into account, is
There is also a slight correction d to be made in method 3, for the potential current in, which also passes through rz; that is, the resultant of i, and in passes through rg. This makes a slightly larger current and shifts the phase a little. The shifting of the phase, however, does no appreciable harm. The correction y can be made insignificant by increasing r, and using an auxiliary condenser of correspondingly smaller capacity, while the correction ở is reduced to an insignificant quantity by baving the potential current i, sufficiently small in comparison with ij. In fact, it is easy under most circumstances to eliminate the three corrections B, y, by properly proportioning the coils,
leaving only a small correction a to be applied, due to the resistance of the fixed coils and connections.
METHOD 4.-SHUNT ON POTENTIAL CIRCUIT.
In this case, fig. 7, the compensation current i, is shunted off from iz, the resistance r, being in the potential circuit through the moving
Fig. 7.-Connections for Method 4. coil instead of the main circuit as in method 3. The compensation current is thus in phase with i,, but by reversing the terminals of the compensation coil it has the same effect as though it were opposite in phase. Thus, fig. 6 represents this method also. Therefore, since
METHOD 5. USING A TRANSFORMER FOR THE COMPENSATION CURRENT.
In this case the high potential winding of a transformer is joined across the terminals A B of the circuit, fig. 8, and thu low potential
coil supplies the current i, to the compensation coil through a resistance R . This current is opposite in pbase to in, as in methods 3 and 4.
ZR, The small electromotive force e, may be determined by the ratio of transformation, or by direct measurement. It is very convenient to put a voltmeter on the secondary of the transfornier and measure ez directly, and then get E by multiplying by the ratio of transformation. Some of the results obtained by this method are given in Table V.
The transformer used here is the potential transformer wbich was employed to get the voltage on the main condenser circuit. In these experiments it had a ratio of about 14, and hence, for 90 volts on the secondary there was 1,260 on the primary. The secondary consisted of two equal coils, and the compensation coil was joined to the terminals of one of them. The slight current used (about a hundredth of an ampere) did not alter the ratio of transformation of the transformer.
METHOD 6. SHUNT ON MAIN CIRCUIT.
This method corresponds to method 4, but the condenser is placed in the moving coil circuit, fig. 9, and a portion of i, is shunted off into
FIG. 10.-Phase diagram for Method 6. the compensation coil. Thus, i, is opposite in phase to i, and is combined with i, so that the resultant of i, and is, o C, is 90° different in phase from i, fig. 10.
This method is especially adapted to small condensers, where the current 1, is very small and in can be increased above its usual value.
Table V.-RESULTS BY METHOD V.
(E=1,260 volts=voltage on the condensers. e=4ā volts=voltage on the compensation circuit.]
This corresponds to method 5, where the transformer is used as a source of is, but as in method 6, the condenser under test is placed in the moving coil circuit. In order to bring the compensation current 90° out of phase with iz, with which it is combined, an auxiliary con
FIG. 11.-Connections for method 7. denser C, is placed in the i, circuit instead of a resistance, fig. 11. The phases are shown in fig. 10. Thus:
E iz=p Czez
R_PC,R cos ,