In an electrical circuit \(R,\) \(L,\) \(C\) and an \(\mathrm{AB}\) voltage source are all connected in series. When \(L\) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \(\tan^{-1}\sqrt{3}\). If instead, \(C\) is removed from the circuit, the phase difference is again \(\tan^{-1}\sqrt{3}\). The power factor of the circuit is:

1. \(1 / 2 \) 2. \(1 / \sqrt{2} \)
3. \(1 \) 4. \(\sqrt{3} / 2\)

Subtopic:  Power factor |
 81%
From NCERT
AIPMT - 2012
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An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)

Subtopic:  Power factor |
 54%
From NCERT
NEET - 2018
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An AC source rated \(100~\text{V}\) (rms) supplies a current of \(10~\text{A}\) (rms) to a circuit. The average power delivered by the source:

(a) must be \(1000~\text{W}\).
(b) may be \(1000~\text{W}\).
(c) may be greater than \(1000~\text{W}\).
(d) may be less than \(1000~\text{W}\).
Choose the correct option:
1. (a) only
2. (b), (c)
3. (b), (d)
4. (a), (d)

Subtopic:  Power factor |
 62%
From NCERT
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The maximum power is dissipated for an AC in a/an:
1. resistive circuit 2. \({LC}\) circuit
3. inductive circuit 4. capacitive circuit
Subtopic:  Power factor |
 72%
From NCERT
NEET - 2023
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An AC source given by \(V=V_m\sin(\omega t)\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
1. \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)

2. \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)

3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)

4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)

Subtopic:  Power factor |
From NCERT
NEET - 2022
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The instantaneous values of alternating current and voltages in a circuit are given as,
\(i=\frac{1}{\sqrt{2}}\sin\left(100\pi t \right )~\text{Ampere}\)
\(e=\frac{1}{\sqrt{2}}\sin\left(100\pi t+\pi /3 \right)~\text{Volt}\)
What is the average power consumed by the circuit in watts?
1. \( \frac{\sqrt{3}}{4} \) 2. \( \frac{1}{2} \)
3. \( \frac{1}{8} \) 4. \( \frac{1}{4}\)
Subtopic:  Power factor |
 75%
From NCERT
AIPMT - 2012
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For a series \(\mathrm{LCR}\) circuit, the power loss at resonance is:
1. \(\frac{V^2}{\left[\omega L-\frac{1}{\omega C}\right]}\)

2. \( \mathrm{I}^2 \mathrm{~L} \omega \)

3. \(I^2 R\)

4. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)

Subtopic:  Power factor |
 79%
From NCERT
AIPMT - 2002
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