For an ac circuit, consider the following statements and select the correct statements only:
(A) For a series LCR circuit, the power factor is unity at resonance.
(B) For purely inductive circuit, average power dissipation is zero.
(C) For L-R circuit, the phase difference between the current and voltage is zero.
(D) For a resonant series LCR circuit, voltage and current are in same phase.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
In an ac circuit the average power is \( P = V_{\mathrm{rms}} I_{\mathrm{rms}} \cos\phi \), where \( \phi \) is the phase difference between voltage and current and \( \cos\phi \) is the power factor.
\( \displaystyle \tan\phi = \frac{X_L - X_C}{R} \)
(A) For a series LCR circuit, the power factor is unity at resonance. — Correct. At resonance \( X_L = X_C \), so \( \tan\phi = 0 \), \( \phi = 0 \) and \( \cos\phi = 1 \).
(B) For purely inductive circuit, average power dissipation is zero. — Correct. The current lags the voltage by 90°, so \( \cos\phi = \cos 90^\circ = 0 \). The inductor stores energy for a quarter cycle and returns it in the next.
(C) For L-R circuit, the phase difference between the current and voltage is zero. — Incorrect. With \( X_C = 0 \), \( \tan\phi = \omega L/R \), which is not zero; the current lags the voltage by an angle between 0 and 90°.
(D) For a resonant series LCR circuit, voltage and current are in same phase. — Correct. At resonance the impedance is purely resistive (Z = R), so \( \phi = 0 \).
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… So, the average power dissipated depends not only on the voltage and current but also on the cosine of the phase angle \( \phi \) between them. The quantity cos\( \phi \) is called the power factor.”
Power in AC Circuit: The Power Factor – “… Case (ii) Purely inductive or capacitive circuit: If the circuit contains only an inductor or capacitor, we know that the phase difference between voltage and current is \( \pi/2 \). Therefore, cos \( \phi \) = 0, and no power is dissipated even though a current is flowing in the circuit.”
Power in AC Circuit: The Power Factor – “… So, \( \phi \) may be non-zero in a RL or RC or RCL circuit.”
Power in AC Circuit: The Power Factor – “… Case (iv) Power dissipated at resonance in LCR circuit: At resonance Xc – XL = 0, and \( \phi \) = 0. Therefore, cosφ = 1 and P = I2Z = I2R.”