**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 I_{3} in the branch having impedance Z_{3}. In Figure 1(b), we just interchange the voltage source and ammeter. As per reciprocity theorem,

i.e.,

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<90^{0}V.

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:

Therefore,

And

### Example 2. Verify the reciprocity theorem in the circuit 2(b)

In Figure 2(b).

Z_{in}, the impedance across the voltage source is

Therefore,

This gives

Thus I’_{2} in Figure 2 is same as I”_{2} in figure 3. This proves the reciprocity theorem.