Two of the pairings are definitions and carry the rest: a-ii, b-i, c-iii, d-iv — option 2.

Reciprocity against symmetry — the distinction the question tests. They are different conditions and are easily confused.

Reciprocity, \(Z_{12}=Z_{21}\), says the transfer works equally in both directions: a source at port 1 producing a given response at port 2 would produce the same response at port 1 if source and measurement were interchanged. Every network built only from R, L, C and transformers is reciprocal; devices containing dependent sources — transistors, gyrators, circulators — are not.

Symmetry, \(Z_{11}=Z_{22}\), says the two ports look alike from outside: the network is electrically identical whichever end it is entered from. A T-network with equal series arms is symmetric; one with unequal arms is still reciprocal but not symmetric. So symmetry implies reciprocity, but not the reverse.

b — where the h₁₂ expression comes from. The hybrid parameter \(h_{12}\) is the reverse voltage ratio measured with port 1 open:

\(h_{12}=\dfrac{V_{1}}{V_{2}}\bigg|_{I_{1}=0}\)

Setting \(I_{1}=0\) in the Z equations gives \(V_{1}=Z_{12}I_{2}\) and \(V_{2}=Z_{22}I_{2}\), so the current cancels and

\(h_{12}=\dfrac{Z_{12}}{Z_{22}}\)

c — identifying the parameter set by its units. A matrix whose entries are all resistances in ohms can only be an impedance matrix, since

\([V]=[Z][I]\)

requires the coefficients to carry the dimensions of ohms. A Y matrix would hold siemens, and an h matrix is hybrid precisely because its four entries have four different dimensions — ohms, dimensionless, dimensionless, siemens — so a uniform matrix cannot be one.

The particular matrix shown, with all four entries equal, describes a network satisfying both conditions at once: \(Z_{12}=Z_{21}\) and \(Z_{11}=Z_{22}\), so it is reciprocal and symmetric — a single shunt resistance R between the two ports.

Hence, the correct code is a-ii, b-i, c-iii, d-iv.