Match List I with List II.
| List - I | List - II |
| (A) Resistive Circuit | (I) No power dissipation |
| (B) Purely inductive or capacitive circuit | (II) Maximum power dissipation because \( X_L = X_C \) |
| (C) LCR series circuit | (III) Power dissipated only in resistor |
| (D) Power dissipated at resonance in LCR circuit | (IV) Maximum power dissipation |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
The average power in an ac circuit is
\( \displaystyle P = V_{\mathrm{rms}}\,I_{\mathrm{rms}}\cos\phi \)
where \( \phi \) is the phase difference between voltage and current and \( \cos\phi \) is the power factor.
(A) Resistive Circuit — this matches (IV) Maximum power dissipation. Voltage and current are in phase, \( \phi = 0 \), so \( \cos\phi = 1 \) and the power factor is the largest possible.
(B) Purely inductive or capacitive circuit — this matches (I) No power dissipation. The current is \( 90^\circ \) out of phase with the voltage, so \( \cos\phi = 0 \); such a current is called wattless current.
(C) LCR series circuit — this matches (III) Power dissipated only in resistor. The inductor and the capacitor store energy and give it back each cycle; only the resistor turns electrical energy into heat, \( P = I_{\mathrm{rms}}^{2}R \).
(D) Power dissipated at resonance in LCR circuit — this matches (II) Maximum power dissipation because \( X_L = X_C \). At resonance the reactances cancel, the impedance falls to \( R \), \( \cos\phi = 1 \) and the current, and so the power, is the largest.
Note: A similar question was also asked in CUET (UG) 2023 on 09-06-2023 (Slot 3) and on 26-05-2023 (Slot 1).
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… Case (i) Resistive circuit: If the circuit contains only pure R, it is called resistive. 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: At resonance \( X_c - X_L = 0 \), and \( \phi = 0 \). Therefore, \( \cos\phi = 1 \) and \( P = I^{2}Z = I^{2}R \). That is, maximum power is dissipated in a circuit (through R) at resonance.”