Consider the networks shown in the following figures (a) and (b) : The above networks are :
Reciprocal network of each other
To determine the relationship between the two given networks in figures (a) and (b), let's analyze the properties that define reciprocal networks.
A reciprocal network is one where the transfer impedance is symmetric, meaning that if you apply a voltage in one direction and observe the resulting current, you'll get the same result if you swap the positions of the voltage and current sources. Mathematically, this condition is represented as:
\(Z_{12} = Z_{21}\)
In figure (a), the input is provided by a source \(V_1 = V_S\), leading to current \(I_1\) entering the network and \(I_2\) exiting it at the far side. Likewise, in figure (b), the roles of input and output are reversed which means:
- The source is now \(V_2 = V_S\), leading to a new current \(I'_1\) in place of \(I_2\) from the first figure.
By checking whether these configurations give equivalent responses from the network, if the transfer functions across both configurations are equal or symmetric, the networks are reciprocal.
According to the properties of reciprocal networks and the explained figures, the circuit configurations ensure that:
\(Z_{12} = Z_{21}\)
Therefore, the correct answer is that the given networks are Reciprocal network of each other. This is supported by the symmetry in their configurations as they sustain the reciprocal property by swapping source and output.
Similar Questions
Read the passage and answer the questions that follow based on your understanding of the passage :
General methods of n/w analysis become laborious and time consuming for large and complex network. For such situations the solution is network theorems. Besides, the other features of n/w theorems are (A) they are applicable to a useful and fairly wide class of networks, (B) their conclusions are simple and (C) they sometimes provide good physical insight into the problems.
The maximum power transfer implies that the load impedance must be the complex conjugate of the source impedance. The superposition theorem is valid for any linear, time invariant or time varying. It is useful in circuit analysis when the n/w has large number of sources. Thevenin's or Norton's theorem is applicable to any number of time invariant or time varying n/w. It is useful when only one part of the n/w is varying, while the other part remains constant. Thevenin's equivalent ckt is the voltage source equivalent at the terminals concerned. Millman's theorem is the extension of Thevenin's or Norton's theorem for a number of Current or Voltage sources respectively. The substitution theorem is applicable to any network and can be applied to a branch which is not coupled to other branches of the network. Tellegen's theorem is applicable to any lumped n/w regardless of the type of elements, which may be linear or non-linear, time varying or time invariant.
The Thevenin's equivalent across AB is
Which equivalent circuits are dual ?
For the n/w, find RTH
The principle of superposition is the property of
In Thevenin equivalent circuit which is incorrect :
Find out which of the following statements is wrong ?
The principle of superposition is useful for
Read the following statements regarding Thevenin’s equivalent circuit :
(a) The Thevenin’s voltage is calculated across the short circuit terminals.
(b) The Thevenin’s voltage is calculated at the open circuit terminals.
(c) The connection in the circuit is open if any voltage source is present.
(d) The connection in the circuit is shorted if any voltage source is present.
Which of the above statements are incorrect ?
Match the following :
List - I List - II (a) Superposition Theorem (i) Ratio between V and I is constant in different loops (b) Maximum Power Transfer Theorem (ii) Ideal current source with parallel Resistor (c) Norton's Theorem (iii) Load impedance is a complex conjugate (d) Reciprocity Theorem (iv) Not valid to Power of the circuit Codes :
Find the value of i using the above circuit by making use of the superposition theorem.
Important Questions from Network Theorems
Which of the following statements is true?
- Which of the following is essential for reciprocity theorem to be applicable?
A linear element satisfies the property (ies) of:
Superposition theorem is only applicable for determining ____ only.
KVL gives the law of conservation of
