Match the following : Codes :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
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
Each phrase in List-II states the single most characteristic fact about its theorem.
(a) Superposition → (iv) not valid for power. The theorem says that in a linear network the response to several sources is the sum of the responses to each acting alone. It works for voltage and current because they are linear in the sources, but power goes as the square of them:
\(P=\left(I_{1}+I_{2}\right)^{2}R\ \ne\ I_{1}^{2}R+I_{2}^{2}R\)
The cross term \(2I_{1}I_{2}R\) is what superposition throws away, so powers must never be added this way — always superpose the currents first and compute the power from the total.
(b) Maximum power transfer → (iii) load is a complex conjugate. For an AC source of internal impedance \(Z_{S}=R_{S}+jX_{S}\), the maximum power reaches the load when
\(Z_{L}=Z_{S}^{*}=R_{S}-jX_{S}\)
The conjugate cancels the reactance so the circuit is purely resistive, and the equal resistances then split the source voltage evenly. The transfer efficiency at that point is only 50 %, which is why the condition is used in signal and communication circuits but never in power distribution.
(c) Norton → (ii) ideal current source with a parallel resistor. Norton's equivalent is the dual of Thevenin's, with \(I_{N}=\dfrac{V_{Th}}{R_{Th}}\) and the same resistance moved from series to parallel.
(d) Reciprocity → (i) the ratio of V to I is constant when source and response are interchanged. In a linear, passive, bilateral network, a source in one branch producing a response in another gives exactly the same ratio if the two are swapped — the transfer impedance is unchanged. The theorem fails as soon as a dependent source, a transistor or any non-bilateral element is present.
| Theorem | Key fact | Code |
|---|---|---|
| Superposition | Linear quantities only | (iv) |
| Max power transfer | Conjugate match | (iii) |
| Norton | Current source with shunt R | (ii) |
| Reciprocity | Transfer ratio unchanged | (i) |
The order (iv), (iii), (ii), (i) is option 3.
Hence, the correct match is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).
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