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Reactance needed in series with a lamp or resistor from the voltage across it

This type of question, asked 2 times: 27 Jul 2022, 8 Apr 2024. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    27 Jul 2022

    24
    To light, a 50 W,100 V50\text{ }W,100\text{ }V lamp is connected, in series with a capacitor of capacitance 50πxμF\frac{50}{\pi\sqrt{x}}\mu F, with 200 V,50 Hz200\text{ }V,50\text{ }Hz AC source. The value of xx will be

  2. Question 2

    8 Apr 2024

    105
    A coil of negligible resistance is connected in series with 90Ω90\Omega resistor across 120 V,60 Hz120\text{ }V,60\text{ }Hz supply. A voltmeter reads 36 V36\text{ }V across resistance. Inductance of the coil is:

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