Reciprocity Theorem with Examples

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Reciprocity Theorem

Reciprocity Theorem: This theorem is applicable to only linear, passive and bilateral networks, that is, the network with R, L, C, so the network with RLC is called reciprocal network

Reciprocity Theorem

Defenition


In a linear, passive and bilateral networks, the ratio of response to the excitation is always constant; even if
the sources are interchanged from input to the output terminals .

Reciprocity Theorem
Reciprocity Theorem

Receiprocity condition with sources interchanged for input to output terminals.

Reciprocity Theorem equation
Reciprocity Theorem equation

Note:

  1. This theorem is applicable to only linear, passive and bilateral networks, that is, the network with R, L, C
    so the network with RLC is called reciprocal network.
  2. The presence of the controlled sources in the network makes it linear, active and bilateral. Hence, reciprocity theorem is not applicable. So, these networks are called non-reciprocal networks.

Problem: Question 1

Q : The network shown in the following figure is a linear passive and bilateral network. Use the data given in Fig. (a) and apply the principle of reciprocity and superposition to determine current ix
in Fig. (b).

Reciprocity Theorem circuit theorem
Reciprocity Theorem circuit theorem

Solution

Solution: By applying the homogeneity property to Fig. (a), we get circuit given in Fig. (c).

homogeneity property
fig: Applying homogeneity property

On applying reciprocity property to Fig. (c), we get circuit in Fig. (d).

applying reciprocity property
applying reciprocity property

Fig. (b) = Fig. (c) + Fig. (d)

ix1= i x1 + ix2
= 8−4 = 4 A

Question 2:

Determine the value of ix in the given circuits.

Reciprocity Theorem-problem
Reciprocity Theorem-problem

Solution

Solution: By applying homogenity property to Fig. (c) in Problem 2, we get Fig. (e).

Reciprocity Theorem-problem solution
Reciprocity Theorem-problem solution

Figure (b) = Figure (f) + Figure (d) = ix
= −24 − 4

= −28 A

Electrical Circuit Theorems

  1. Substitution Theorem & Examples
  2. Reciprocity Theorem with Examples
  3. Duality Theorem in Electrical circuits

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