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Power factor or current of an LR or RC circuit when the frequency changes

This type of question, asked 2 times: 30 Jan 2024, 5 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    30 Jan 2024

    20
    A series L, R circuit connected with an ac source E=(25sin⁡1000t)VE = (25\sin1000t)V has a power factor of 12\frac{1}{\sqrt{2}}. If the source of emf is changed to E=(20sin⁡2000E = (20\sin2000 t)Vt)V, the new power factor of the circuit will be :

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  2. Question 2

    5 Apr 2026 S1

    19
    An a.c. source of angular frequency ω\omega is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to ω/4\omega/4, (keeping the voltage unchanged) the current is found to be I/3I/3. The ratio of resistance to reactance at frequency ω\omega is

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