Balanced Method

a measurement method based on compensation (balancing) of the voltage or electromotive force (emf) being measured by a voltage or emf produced across a known resistance by a current from an auxiliary source. The balanced method is used in measurements not only of electrical values (such as emf, voltage, current, or resistance) but also of other physical quantities (mechanical, light, and temperature), which are usually converted to electrical quantities before making measurements.

The balanced method is a version of the method of comparison with a standard. In this method the effect of the action of the quantities on the instrument is set to zero (an attempt is made to obtain a zero reading of the measuring instrument). The balanced method is distinguished by high accuracy; the accuracy depends on the sensitivity of the null instrument (null indicator), which controls the compensation, and on the precision of determination of the quantity necessary to compensate the quantity being measured.

The balanced method in a DC circuit functions as follows. The voltage U_x being measured (see Figure 1) is compensated by a voltage drop produced across a known resistor r by the current from an auxiliary source U_aux (the operating current I_op). The galvanometer G (the null instrument) is connected to the circuit of the voltages being compared by throwing a switch S to the right-hand position. When the voltages are compensated, no current flows through the galvanometer, and hence no current flow occurs in the circuit of the voltage U_x being measured. This is an important advantage of the balanced method as compared to other methods, since it is possible to measure the total emf value of the source U_x; in addition, the results of measurements made by the method are not affected by the resistance of connecting wires and the galvanometer. The operating current is established by means of a standard cell E_N of known emf, compensating this emf by the voltage drop across the resistor R (the switch S is now in its left-hand position). The value of the voltage U_x is determined by the formula U_x = E_N · r/R, where r is the resistor across which the voltage drop is compensated by U_x.

Figure 1. Diagram of an emf balancer with a standard cell: (U_aux) auxiliary voltage source, (R) calibrated resistor, (r_reg) regulating resistor, (E_y) standard cell, (I_op operating current, (G) galvanometer, (S) switch, (U_x) voltage being measured

To measure the current strength I_x by the balanced method, the current is passed through a known resistor R₀ and the voltage drop across the resistor I_xR₀ is measured. The resistance R₀ is connected in place of the voltage source U_z shown in Figure 1. To measure power it is necessary to measure voltage and current alternately. To measure resistance the unknown resistor is connected in series with a known resistor in an auxiliary circuit; the voltage drop across the two resistors is then compared. Electrical measuring instruments based on the balanced method are called potentiometers or electrical measurement compensators. The balanced method can also be used to measure AC values; however, the accuracy is lower. The balanced method is widely used in automatic control and regulation.