1. Use AC circuit phase relations

For a series $LCR$ circuit, the net reactance is $X = X_L - X_C = \omega L - \frac{1}{\omega C}.$

• If $X_L > X_C$, the circuit is inductive.
• If $X_L < X_C$, the circuit is capacitive.
• If $X_L = X_C$, the circuit is at resonance.

Also:

• In an inductive circuit, current lags behind emf.
• In a capacitive circuit, current leads the emf.
• At resonance, impedance is minimum, so maximum current occurs.
• At resonance, current and emf are in phase.

2. Match each item

(a) $\omega L > \dfrac{1}{\omega C}$

This means $X_L > X_C$, so the circuit is inductive. Hence, current lags behind the applied emf.

So, $(a) \to (ii)$

(b) $\omega L = \dfrac{1}{\omega C}$

This is the resonance condition. At resonance, current is in phase with emf.

So, $(b) \to (i)$

(c) $\omega L < \dfrac{1}{\omega C}$

This means $X_C > X_L$, so the circuit is capacitive. Hence, current leads the emf.

So, $(c) \to (iv)$

(d) Resonant frequency

At resonant frequency, impedance is minimum and current is maximum.

So, $(d) \to (iii)$

3. Final matching

The correct matching is: $a(ii),\ b(i),\ c(iv),\ d(iii)$

This corresponds to Option A.

4. Comparison with stored answer

Stored correct answer = A

Our derived answer = A

Hence, the answer agrees with the stored answer.