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Resonance condition: capacitance, inductance or frequency for maximum current

This type of question, asked 10 times: 4 May 2023 S1, 15 May 2023 S2, 16 May 2023 S2, 20 Apr 2025 S2, 22 Apr 2025 S1, 26 Apr 2025 S1, 13 Apr 2026 S1, 16 Apr 2026 S2, 12 May 2026 S1, 13 May 2026 S1. All 10 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    33
    An inductor of inductance 2 μH2\,\mu\text{H} is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz. The value of capacitance for which maximum current is drawn into the circuit is 1x F\frac{1}{x}\,\text{F}, where the value of xx is (Take π2=10\pi^2 = 10)

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  2. Question 2

    15 May 2023 S2

    16
    A resistor of 50 Ω50\,\Omega, inductor of self inductance 3π2 H\frac{3}{\pi^2}\text{ H} and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz. When the voltage and current are in phase, the value of capacitance is (nearly)

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  3. Question 3

    16 May 2023 S2

    11
    An inductance of 2 mH, a condenser of 20 μF20\,\mu\text{F} and a resistance of 50 Ω50\,\Omega are connected in series to an a.c. source. The reactance of inductor and condenser are same. The reactance of either of them will be

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  4. Question 4

    20 Apr 2025 S2

    15
    An a.c. e.m.f. of peak value =230 V= 230\text{ }V and frequency 50 Hz is connected to a circuit with R=11.5Ω, L=2.5HR = 11.5\Omega,\text{ }L = 2.5H and a capacitor all in series. The value of capacitance is ' CC ' for the current in the circuit to be maximum. The value of C and maximum current are respectively ( π2=10\pi^{2}= 10 ).

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  5. Question 5

    22 Apr 2025 S1

    40
    An a.c. e.m.f. of peak value 230 V and frequency 50 Hz is connected to a circuit with R=11.5Ω, L=2.5HR = 11.5\Omega,\text{ }L = 2.5H and a capacitor all in series. The value of capacitance is ' CC ' for the current in the circuit to be maximum. The value of ' CC ' and maximum current are respectively ( π2=10\pi^{2}= 10 )

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  6. Question 6

    26 Apr 2025 S1

    20
    A resistor of 5.Ω5.\Omega, inductor of self inductance (2π2)H\left( \frac{2}{\pi^{2}} \right)H and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V,50 Hz100\text{ }V,50\text{ }Hz supply. When the voltage and current are in phase, the value of capacitance is

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  7. Question 7

    13 Apr 2026 S1

    139
    A resistor of 100 Ω\Omega, inductor of self inductance (4π2)\left(\dfrac{4}{\pi^2}\right) H and a capacitor of unknown capacity are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the value of capacity is

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  8. Question 8

    16 Apr 2026 S2

    139
    An inductor of inductance 2 μH2\ \mu\mathrm{H} is connected in series with a resistance, a variable capacitor and an a.c. source of 10 kHz. The value of capacitance for which maximum current is drawn in to the circuit is 1x\dfrac{1}{x} F, where the value of x is (Take π2=10\pi^2 = 10)

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  9. Question 9

    12 May 2026 S1

    140
    In a series LCR circuit, the inductance L=20L = 20 mH, capacitor C=2 μFC = 2\ \mu\mathrm{F} and resistance R=100R = 100 ohm. The frequency at which resonance occurs is

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  10. Question 10

    13 May 2026 S1

    137
    What is the value of inductance L for which the current is maximum in series LCR circuit with C=10 μC = 10\ \muF and ω=1000\omega = 1000/s ?

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