Abstract :
Ratio of voltages may be taken by the balance method with enitire accuracy, if the detector is either self-excited or excited in phase with I2, by keeping RD= R1 R2/R1+R2. If this value is even approximately maintained, errors are negligible. With excitation in phase with E1 or I1, the errors are of a similar order of magnitude, but the equations involved are much more complicated, and the exact errors are much more difficult to determine. With excitation in phase with E2, the errors are never reduced to zero; but where the phase angle ?? is 2 deg. or less, the error in ratio is only about 0.06 per cent if RD is kept equal to or greater than the value in the above formula. This amount is negligible for ordinary purposes. For phase angle, with any of the above connections, a result may be obtained by keeping RD equal to the value given above, and doubling the angle obtained by direct calculation. It is, however, subject to considerable error if RD varies, and correction is impracticable; therefore it is better to use some method which does not involve these errors, as for instance, the two-dynamometer method. It should be noted that the above results are calculated for sine wave voltage. With a distorted voltage wave, or with slightly differing waves, harmonic currents flow in the detector which greatly complicate the theory. The actual additional errors caused by this are in general negligible for practical work.