The Reciprocity Theorem for AC network theorem can be stated as follows: For a linear network containing generators and impedances, the ration of a voltage V introduces in one loop to the current I produced in any other loop is the same as the ratio of voltage and current obtained if the position of voltage source V and the current measured are interchanged.
To illustrate the reciprocity theorem, let voltage V in figure 1(a) produced a current I3 in the branch having impedance Z3. In Figure 1(b), we just interchange the voltage source and ammeter. As per reciprocity theorem,
For better concept, here we are going to solve few examples.
Example 1. Verify the reciprocity theorem in the circuit 2(a)
Solution. In figure 2(a), at first we have to find the impedance of the circuit across the voltage source 10<900V.
Here, 4 ohm resistor is in series with -j4 ohm capacitor, similarly 1 ohm resistor is in series with j2 ohm indictor. These two branch are in parallel with each and in series with 5 ohm resistor as shown in figure. Now the combined impedance of the circuit is given by:
Example 2. Verify the reciprocity theorem in the circuit 2(b)
In Figure 2(b).
Zin, the impedance across the voltage source is
Thus I’2 in Figure 2 is same as I”2 in figure 3. This proves the reciprocity theorem.