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 principle of superposition is the property of
combined property of additivity and homogeneity of linear n/w s
Linearity has two separate requirements, and superposition needs both — option 3.
| Property | Statement | Meaning |
|---|---|---|
| Additivity | \(f(x_{1}+x_{2})=f(x_{1})+f(x_{2})\) | Responses to separate causes add |
| Homogeneity | \(f(kx)=k\,f(x)\) | Scaling the cause scales the effect |
Together they give the general form
\(f\left(a x_{1}+b x_{2}\right)=a\,f(x_{1})+b\,f(x_{2})\)
which is exactly what superposition asserts: the total response equals the sum of the responses to each source acting alone, each taken at its own strength.
Why neither property alone is enough. They are genuinely independent, and a function can possess one without the other.
Homogeneous but not additive. The relation \(y=x_{1}x_{2}/(x_{1}+x_{2})\) scales correctly with a common factor but does not decompose into separate contributions.
Additive but not homogeneous. Pathological additive functions exist that fail to scale for irrational multipliers. In circuit terms the point is simpler: a network with a constant offset, \(y=mx+c\), is affine rather than linear — it satisfies neither condition, since \(f(0)\neq0\). Superposition would give the wrong answer for it, which is why an independent source must be deactivated rather than merely ignored.
Where superposition fails, and why. It applies to currents and voltages but never to power, because power is quadratic:
\(P=I^{2}R\quad\Rightarrow\quad \left(I_{1}+I_{2}\right)^{2}R\neq I_{1}^{2}R+I_{2}^{2}R\)
The cross term \(2I_{1}I_{2}R\) is exactly what homogeneity forbids. Powers must therefore be computed from the total current, after superposition has been applied. Diodes, transistors in their non-linear range and saturating magnetics are excluded for the same reason.
Why option 4 is a distractor of a different kind. Associativity is a property of an operation — how terms may be grouped — not of a system's response. It has no bearing on whether a network's responses may be superposed.
Hence, superposition is the combined property of additivity and homogeneity.
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
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
