Match List - I with List - II.
| List - I | List - II | ||
| (A) | Resistive circuit | (I) | No power dissipation |
| (B) | Purely capacitive or inductive circuit | (II) | Maximum power dissipation as \( X_L = X_C \) |
| (C) | Series L-C-R circuit | (III) | Power dissipated only in the resistor |
| (D) | Series L-C-R circuit at resonance | (IV) | Maximum power dissipation |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
The average power in an a.c. circuit is
\( \displaystyle P = V_{\mathrm{rms}}\,I_{\mathrm{rms}}\cos\phi \)
where \( \cos\phi = R/Z \) is the power factor. Only a resistor turns electrical energy into heat; an ideal inductor or capacitor stores energy and gives it back every cycle.
(A) Resistive circuit — this matches (IV) Maximum power dissipation. Here \( \phi = 0 \) and the power factor is 1, its largest value, so \( P = V_{\mathrm{rms}} I_{\mathrm{rms}} \).
(B) Purely capacitive or inductive circuit — this matches (I) No power dissipation. The current and voltage differ in phase by \( 90^\circ \), so \( \cos\phi = 0 \) and the average power is zero; such a current is called a wattless current.
(C) Series L-C-R circuit — this matches (III) Power dissipated only in the resistor. The inductor and capacitor take no average power, so all the power is used in \( R \), \( P = I_{\mathrm{rms}}^{2}R \).
(D) Series L-C-R circuit at resonance — this matches (II) Maximum power dissipation as \( X_L = X_C \). At resonance the reactances cancel, \( Z = R \) is the smallest and the current is the largest, so the power taken by the circuit is the maximum.
Note: A similar question was also asked in CUET (UG) 2023 on 09-06-2023 (Slot 3) and on 30-05-2023 (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: At resonance \( X_C - X_L = 0 \), and \( \phi = 0 \). … That is, maximum power is dissipated in a circuit (through R) at resonance.”