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.
Which equivalent circuits are dual ?
Norton-Thevenin
Thevenin and Norton are duals of one another — option 3 — and they are the only pair in the list that could be, since the other three items are not equivalent circuits at all.
What duality means here. Two circuits are duals when one is obtained from the other by exchanging every quantity for its counterpart:
| Thevenin | Norton |
|---|---|
| Voltage source VTH | Current source IN |
| In series with RTH | In parallel with RN |
| Open-circuit voltage | Short-circuit current |
Voltage ↔ current, series ↔ parallel, open ↔ short. That is precisely the dual transformation, and the two forms describe the same network:
\(I_{N}=\dfrac{V_{TH}}{R_{TH}},\qquad R_{N}=R_{TH}\)
Both present identical behaviour at the terminals, so no external measurement can distinguish them — which is what makes them equivalent as well as dual.
Why the other options fail. Superposition, Tellegen's theorem and Millman's theorem are analytical methods, not equivalent circuits. Superposition is a procedure for decomposing a multi-source problem. Tellegen's theorem is a conservation statement, \(\sum v_{k}i_{k}=0\), depending only on a network's topology and holding for linear and non-linear elements alike. Millman's theorem — as the passage itself notes — is an extension of Thevenin's and Norton's to several parallel sources, giving
\(V=\dfrac{\sum V_{k}G_{k}}{\sum G_{k}}\)
which makes it a special case rather than a dual.
Why the duality is useful in practice. Each form suits a different question. The Thevenin form makes voltage division and the effect of a series load immediate; the Norton form makes current division and parallel combination immediate. Being free to convert between them is what makes source transformation a standard simplification step — a voltage source with a series resistance can be replaced by a current source with a parallel one at will, and the network collapsed further.
Hence, the dual equivalent circuits are Norton and Thevenin.
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
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 ?
Consider the networks shown in the following figures (a) and (b) :
The above networks are :
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
