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Power factor of a series circuit from R and the reactances or impedance (cos phi = R/Z)

This type of question, asked 10 times: 10 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S1, 19 Apr 2025 S2, 22 Apr 2025 S1, 25 Apr 2025 S1, 13 Apr 2026 S2, 15 Apr 2026 S1, 18 Apr 2026 S1, 13 May 2026 S2. All 10 questions below, oldest first.

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  1. Question 1

    10 May 2024 S1

    11
    In a series LR circuit XL=RX_L=R, power factor is P1P_1. If a capacitor with XC=XLX_C=X_L is added, power factor becomes P2P_2. The ratio P1:P2P_1:P_2 will be

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  2. Question 2

    14 May 2024 S2

    9
    The power factor of an R-L circuit is 12\frac{1}{\sqrt{2}}. If the frequency of AC is doubled the power factor will now be

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  3. Question 3

    19 Apr 2025 S1

    8
    A series LCR circuit is connected to an a.c. source of 230 V,50 Hz230\text{ }V,50\text{ }Hz. The circuit contains resistance of 80Ω80\Omega an inductor having inductive reactance 70Ω70\Omega and a capacitor of capacitive reactance 130Ω130\Omega. The power factor of the circuit is x . The value of x is

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  4. Question 4

    19 Apr 2025 S2

    47
    An a.c. source is applied to a series LR circuit with XL=3RX_{L}= 3R and power factor is X1X_{1}. Now a capacitor with Xc=RX_{c}=R is added in series to LRLR circuit and the power factor is X2X_{2}. The ratio X1X_{1} to X2X_{2} is

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  5. Question 5

    22 Apr 2025 S1

    32
    When alternating current is passed through L−RL-R series circuit, the power factor is 32\frac{\sqrt{3}}{2} and R=50ΩR = 50\Omega, then the value of L is [cos⁡π6=32,sin⁡π6=12,tan⁡π6=13]\left\lbrack \cos\frac{\pi}{6}=\frac{\sqrt{3}}{2},\sin\frac{\pi}{6}=\frac{1}{2},\tan\frac{\pi}{6}=\frac{1}{\sqrt{3}} \right\rbrack

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  6. Question 6

    25 Apr 2025 S1

    38
    The power factor of a CR circuit is 12\frac{1}{\sqrt{2}}, If the frequency of a.c. signal is halved, then the power factor of the circuit will become

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  7. Question 7

    13 Apr 2026 S2

    139
    In a series LR circuit with XL=RX_L = R. Power factor is P1P_1. If a capacitor of capacitance CC with Xc=XLX_c = X_L is added to the circuit the power factor becomes P2P_2. The ratio of P1P_1 to P2P_2 will be :

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  8. Question 8

    15 Apr 2026 S1

    137
    A series LCR circuit is connected to an a.c. source of 220220 V, 5050 Hz. The circuit contains a resistance R=80 ΩR = 80\,\Omega, an inductor of inductive reactance 70 Ω70\,\Omega and capacitor of capacitive reactance 130 Ω130\,\Omega. The power factor of the circuit is x10\dfrac{x}{10}. The value of x is

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  9. Question 9

    18 Apr 2026 S1

    138
    An a.c. source is applied to a series LR circuit with XL=3RX_L = 3R and power factor is X1X_1. Now a capacitor with Xc=RX_c = R is added in series to LR circuit and power factor is X2X_2. The ratio X1X_1 to X2X_2 is

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  10. Question 10

    13 May 2026 S2

    138
    In an a.c. circuit, if the power factor changes from 0.50.5 to 0.250.25 then the increase in impedance is

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