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Resonance in a series LCR circuit: find L, C or the frequency

This type of question, asked 10 times: 2021 Paper 17, 2021 Paper 18, 28 Jun 2022, 29 Jun 2022, 25 Jan 2023, 29 Jan 2023, 6 Apr 2024, 23 Jan 2025, 23 Jan 2026 S1, 5 Apr 2026 S2. All 10 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 17

    8
    A 100Ω100\Omega resistance, a 0.1μF0.1\mu F capacitor and an inductor are connected in series across a 250 V250\text{ }V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz60\text{ }Hz.

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  2. Question 2

    2021 Paper 18

    8
    A series LCR circuit driven by 300 V300\text{ }V at a frequency of 50 Hz50\text{ }Hz contains a resistance R=3kΩR = 3k\Omega, an inductor of inductive reactance XL=250πΩX_{L}= 250\pi\Omega and an unknown capacitor. The value of capacitance to maximize the average power should be : (Take π2=10\pi^{2}= 10)

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  3. Question 3

    28 Jun 2022

    30
    A telegraph line of length 100 km100\text{ }km has a capacity of 0.01μFkm\frac{0.01\mu F}{km} and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ____\_\_\_\_ mHmH. (take π=10\pi=\sqrt{10})

  4. Question 4

    29 Jun 2022

    120
    An inductor of 0.5mH0.5mH, a capacitor of 200μF200\mu F and a resistor of 2Ω2\Omega are connected in series with a 220 V220\text{ }V ac source. If the current is in phase with the emf, the frequency of ac source will be _×102 Hz\_ \times10^{2}\text{ }Hz.

  5. Question 5

    25 Jan 2023

    26
    An LCR series circuit of capacitance 62.5nF62.5nF and resistance of 50Ω50\Omega, is connected to an A.C. source of frequency 2.0kHz2.0kHz. For maximum value of amplitude of current in circuit, the value of inductance is___ mHmH. (Take π2=10\pi^{2}= 10)

  6. Question 6

    29 Jan 2023

    117
    An inductor of inductance 2μH2\mu H is connected in series with a resistance, a variable capacitor and an ACAC source of frequency 7kHz7kHz. 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 π=227\pi =\frac{22}{7} )

  7. Question 7

    6 Apr 2024

    112
    For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5nF2.5nF. If resistance of 200Ω200\Omega and 100mH100mH inductor is being used in the given circuit. The frequency of ac source is ____ ×103 Hz\times10^{3}\text{ }Hz. (given π2=10\pi^{2}= 10 )

  8. Question 8

    23 Jan 2025

    100
    In a series LCR circuit, a resistor of 300Ω300\Omega, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____\_\_\_\_\_ ×104\times10^{4} radians s  −1\ ^{- 1}.

  9. Question 9

    23 Jan 2026 S1

    23
    Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for V=5sin⁡(100t)V = 5\sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor ( C ) used is ____\_\_\_\_ μF\mu F.

  10. Question 10

    5 Apr 2026 S2

    23
    A series LCR circuit with R =20Ω, L=1.6H= 20\Omega,\text{ }L = 1.6H and C=40μ FC = 40\mu\text{ }F is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ____\_\_\_\_ Ω\Omega.