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.
Find out which of the following statements is wrong ? The principle of superposition is useful for
substituting sources by their shunt impedances.
A deactivated source is replaced by its internal impedance, and the word "shunt" misdescribes what happens — option 2 is the wrong statement.
What actually replaces each source.
| Source | Ideal case | Practical source |
|---|---|---|
| Voltage | Short circuit | Its series internal resistance |
| Current | Open circuit | Its shunt internal resistance |
The distinction the statement blurs is that only a current source carries its internal impedance in shunt. A practical voltage source is modelled as an ideal source with resistance in series, so deactivating it leaves that series resistance in the circuit — not a shunt element. Applying the word "shunt" to sources in general is therefore wrong for half of them, and it is wrong for the half the statement is most likely to be read as covering.
Why the other three statements are sound.
Option 1 — linearity test. Superposition is linearity, restated for circuits. A system obeys it if and only if it is linear, so checking whether responses to separate excitations add is a valid test. This is exactly how a network containing a suspected non-linear element is diagnosed.
Option 3 — V-I relationships. Currents and voltages are the quantities superposition applies to, precisely because they are related linearly by Ohm's law and Kirchhoff's laws. The contrast is with power, which is quadratic and to which superposition never applies:
\(\left(I_{1}+I_{2}\right)^{2}R\neq I_{1}^{2}R+I_{2}^{2}R\)
— the cross term \(2I_{1}I_{2}R\) is what is lost.
Option 4 — one source at a time. That is the method itself: activate one source, deactivate all the others, compute the response, repeat, and add the results algebraically. Its value is that it converts one difficult multi-source problem into several easy single-source ones, and the sign of each contribution is handled automatically by the algebra.
The practical caution that follows from all this: after superposing to find the total current or voltage, any power must be computed from that total, never by adding the powers found in the individual passes.
Hence, the wrong statement is that superposition substitutes sources by their shunt impedances.
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 :
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
