Match the following, if $X_{\text{L}}$ and $X_{\text{C}}$ are inductive and capacitive reactances respectively:
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Remember the "CIVIL" mnemonic:
In a Capacitor, I (current) leads V (voltage).
In an Lnductor (inductor), V leads I (current lags).
At resonance ($X_{\text{L}} = X_{\text{C}}$), they are in phase.
Step 1: Think in terms of limiting pure circuits instead of the formula. A pure inductor makes voltage lead current by $90^\circ$, and a pure capacitor makes current lead voltage by $90^\circ$. An LCR circuit's behaviour sits between these two extremes depending on which reactance wins. Step 2: Compare $X_L$ and $X_C$ case by case. When $X_L = X_C$, the two opposite phase pulls cancel exactly, so the circuit behaves purely resistively (voltage and current in phase, resonance). When $X_L \lt X_C$, the capacitive pull dominates and the circuit behaves capacitively. When $X_L \gt X_C$, the inductive pull dominates and the circuit behaves inductively. Step 3: Match to the given labels. This gives A (equal reactances) to the resonance/resistive case, B (capacitive dominance) to the capacitive case, and C (inductive dominance) to the inductive case. \[ \boxed{\text{A-I, B-III, C-II}} \]
