Match List I with List II
| LIST I | LIST II | ||
| A. | Impedance of a series RLC circuit at resonance | I. | Voltage across L & C are \( 180^\circ \) out of phase. |
| B. | For a series LC circuit | II. | Current in L & C are \( 180^\circ \) out of phase |
| C. | For a parallel LC circuit | III. | Minimum |
| D. | Reactance of a capacitor in a DC circuit | IV. | Infinite |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-III, B-I, C-II, D-IV
In an inductor the voltage leads the current by \( 90^\circ \); in a capacitor it lags the current by \( 90^\circ \).
(A) Impedance of a series RLC circuit at resonance — this matches (III) Minimum. At resonance \( X_L = X_C \), so the reactances cancel and the impedance falls to its least value \( Z = R \).
\( \displaystyle Z = \sqrt{R^{2} + (X_L - X_C)^{2}} = R \)
(B) For a series LC circuit — this matches (I) Voltage across L & C are \( 180^\circ \) out of phase. In series the same current flows through both; \( V_L \) leads it by \( 90^\circ \) and \( V_C \) lags it by \( 90^\circ \), so the two voltages are opposite.
(C) For a parallel LC circuit — this matches (II) Current in L & C are \( 180^\circ \) out of phase. In parallel the same voltage acts across both; \( I_L \) lags it by \( 90^\circ \) and \( I_C \) leads it by \( 90^\circ \), so the two currents are opposite.
(D) Reactance of a capacitor in a DC circuit — this matches (IV) Infinite. For a steady (DC) supply \( \omega = 0 \), so the capacitive reactance becomes infinite and the capacitor blocks a steady current.
\( \displaystyle X_C = \frac{1}{\omega C} \rightarrow \infty \quad (\omega = 0) \)