Electrical Engineering ⇒ Topic : Compensation theorem

COMPENSATION THEOREM

The compensation theorem is particularly useful for the following purposes:

To calculate the sensitivity of a bridge network.

To analyse those networks where the values of the branch elements are varied and for studying the effect of tolerance on such values.

This theorem is stated as follows

"if a change, say ΔR, is made in the resistance of any branch of a network when the current was originally I, then the change of current at any other point in the network may be calculated by assuming that an e.m.f.I ΔR has been introduced into the changed branch while all other sources have their e.m.fs. suppressed and are represented by their internal resistances only

Compensation Theorem

The compensation theorem can be stated as follows.

                For a given set of circuit conditions, any resistance R in a network carrying a current I can be replaced, in the same network by a voltage generator of zero internal resistance having a terminal voltage E = + IR.

             This theorem can be proved as follows. Consider a network as shown in Fig. 1 (a), in which a resistance R is carrying a current I. The rest of the network is symbolised by a box. The voltage drop across R is IR and acts from b to a. Now introduce two voltage source, of equal magnitude (IR) and opposite signs,as shown in Fig. 1 (b). There is no change in the current due to the introduction of the two voltage sources which are connected in series with R. The potential difference between a and c is zero (Fig. 1 (b)). In Fig. 1 (c), the points a and c are short-circuited and there is no potential difference between these two points; and R is replaced by E = IR. Compensation theorem is useful for calculating the out of balance current in the detector in a bridge circuit, when an element in one of the arms of the bridge changes by a small value.

                                                     Figure (1)  Circuit to illustrate compensation theorem