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LR circuit power factor before and after a capacitor is added in series: ratio of power factors

The same question, asked 4 times: 10 May 2024 S1*, 19 Apr 2025 S2, 13 Apr 2026 S2*, 18 Apr 2026 S1. Every wording 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

    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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  3. Question 3

    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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  4. Question 4

    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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