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Resistor, inductor and unknown capacitor on a 50 Hz supply with voltage and current in phase: find the capacitance

The same question, asked 3 times: 15 May 2023 S2*, 26 Apr 2025 S1*, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    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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  2. Question 2

    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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  3. Question 3

    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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