Match List – I with List – II.
| List - I | List - II | ||
|---|---|---|---|
| (A) | Purely resistive AC circuit | (I) | No power dissipation |
| (B) | Purely inductive or capacitive AC circuit | (II) | Power is dissipated only in Resistor |
| (C) | LCR series AC circuit | (III) | Maximum power dissipation |
| (D) | Power dissipated at resonance in LCR series circuit | (IV) | Power is dissipated in L and C |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(II), (D)-(III)
The average power in an AC circuit is \( P = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi \), where \( \phi \) is the phase angle between voltage and current, and \( \cos\phi \) is the power factor. Only a resistor dissipates energy; an ideal inductor or capacitor stores energy and returns it.
(A) Purely resistive AC circuit — this matches (III) Maximum power dissipation. Voltage and current are in phase, \( \phi = 0 \), so \( \cos\phi = 1 \) and the power takes its largest possible value.
(B) Purely inductive or capacitive AC circuit — this matches (I) No power dissipation. Current and voltage differ in phase by \( 90^\circ \), so \( \cos\phi = 0 \) and the average power over a cycle is zero. (IV) is wrong, because L and C do not dissipate energy.
(C) LCR series AC circuit — this matches (II) Power is dissipated only in Resistor. The inductor and capacitor only exchange energy with the source, so the power is \( I_{\mathrm{rms}}^{2}R \).
(D) Power dissipated at resonance in LCR series circuit — this matches (III) Maximum power dissipation. At resonance \( X_L = X_C \), so \( Z = R \) is the least possible, the current is the largest and \( \phi = 0 \).
Note: A similar question was also asked in CUET (UG) 2023 on 30-05-2023 (Slot 1) and on 26-05-2023 (Slot 1).
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… Case (i) Resistive circuit: … In that case \( \phi = 0,\ \cos\phi = 1 \). There is maximum power dissipation. Case (ii) Purely inductive or capacitive circuit: … Therefore, \( \cos\phi = 0 \), and no power is dissipated even though a current is flowing in the circuit. … Case (iii) LCR series circuit: … Even in such cases, power is dissipated only in the resistor. Case (iv) Power dissipated at resonance in LCR circuit: … That is, maximum power is dissipated in a circuit (through R) at resonance.”