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Power factor or phase of a series LCR circuit from R, XL and XC

This type of question, asked 7 times: 2021 Paper 10, 25 Jun 2022, 25 Jan 2023, 27 Jan 2024, 24 Jan 2026 S1, 4 Apr 2026 S1, 6 Apr 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 10

    12
    In a series LCRLCR circuit, the inductive reactance (XL)\left( X_{L} \right) is 10Ω10\Omega and the capacitive reactance (XC)\left( X_{C} \right) is 4Ω4\Omega. The resistance (R) in the circuit is 6Ω6\Omega. The power factor of the circuit is:

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  2. Question 2

    25 Jun 2022

    102
    A sinusoidal voltage V(t)=210sin⁡3000tV(t) = 210\sin3000t volt is applied to a series LCR circuit in which L=10L = 10 mH,C=25μFmH,C = 25\mu F and R=100ΩR = 100\Omega. The phase difference (Φ)(\Phi) between the applied voltage and resultant current will be :

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  3. Question 3

    25 Jan 2023

    116
    A series LCR circuit is connected to an AC source of 220 V,50 Hz220\text{ }V,50\text{ }Hz. The circuit contains a resistance == 80Ω80\Omega, an inductor of inductive reactance XL=70ΩX_{L}= 70\Omega, and a capacitor of capacitive reactance XC=130ΩX_{C}= 130\Omega. The power factor of circuit is x10\frac{x}{10}. The value of xx is:

  4. Question 4

    27 Jan 2024

    120
    A series LCR circuit with L=100πmH,C=10−3πFL =\frac{100}{\pi}mH,C =\frac{10^{- 3}}{\pi}F and R=10ΩR = 10\Omega, is connected across an ac source of 220 V,50 Hz220\text{ }V,50\text{ }Hz supply. The power factor of the circuit would be______

  5. Question 5

    24 Jan 2026 S1

    9
    For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is α10\frac{\alpha}{10}. The value of α\alpha is ____\_\_\_\_

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  6. Question 6

    4 Apr 2026 S1

    25
    An inductor of 10 mH , capacitor of 0.1μ F0.1\mu\text{ }F and a resistor of 100Ω100\Omega are connected in series aross an a.c power supply 220 V,70 Hz220\text{ }V,70\text{ }Hz. The power factor of the given circuit is 0.5 . The difference in the inductive reactance and capacitance reactance is 3αΩ\sqrt{3}\alpha\Omega. The value of α\alpha is ____\_\_\_\_ .

  7. Question 7

    6 Apr 2026 S1

    20
    A LCR series circuit driven with Erms=90 VE_{rms}= 90\text{ }V at frequency fd=30 Hzf_{d}= 30\text{ }Hz has resistance R=80ΩR = 80\Omega, an inductance with inductive reactance XL=20.0ΩX_{L}= 20.0\Omega and capacitance with capacitive reactance XC=80.0ΩX_{C}= 80.0\Omega. The power factor of the circuit is ____\_\_\_\_ .

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