The four bridges pair with their four uses in the order printed: a-i, b-ii, c-iii, d-iv — option 1.

Maxwell against Hay — the distinction the question turns on. Both measure inductance by balancing an unknown coil against a standard capacitor, which is convenient because capacitors are far easier to make accurately than inductors. The difference is where the capacitor sits.

Maxwell's bridge uses a capacitor in parallel with a resistor. Its balance gives

\(L_{x}=R_{2}R_{3}C_{1},\qquad R_{x}=\dfrac{R_{2}R_{3}}{R_{1}}\)

For a high-Q coil, \(R_{1}\) would have to be impractically large, so the method suits medium Q.

Hay's bridge puts the capacitor in series with its resistor instead, which makes the required resistance small for a high-Q coil — exactly the opposite dependence. Its balance carries a \(1/Q^{2}\) correction term that becomes negligible above Q = 10, so the two bridges divide the range between them.

c — why Schering is the precision capacitance bridge. It measures not only capacitance but the dissipation factor \(D=\tan\delta=\omega C R\), which is the quantity that matters when testing insulation, cables and high-voltage bushings for deterioration. Its balance is independent of frequency, and it works at high voltage — both essential for that application.

d — Wien for frequency. Its balance condition depends on frequency,

\(f=\dfrac{1}{2\pi RC}\)

so with known R and C the balance point measures the source frequency — and the same network, used as the positive-feedback arm of an amplifier, generates that frequency in the Wien-bridge oscillator.

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