Alternating Current JEE Main PYQs, 2020 to 2025

An ac current is represented as

$i=5 \sqrt{2}+10 \cos \left(650 \pi t+\frac{\pi}{6}\right) A m p$

The r.m.s value of the current is

An inductor of self inductance 1 H is connected in series with a resistor of $100 \pi$ ohm and an ac supply of $100 \pi$ volt, 50 Hz . Maximum current flowing in the circuit is _________ A.

In a series LCR circuit, a resistor of $300 \Omega$, 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 _________ $\times 10^4$ radians $\mathrm{s}^{-1}$

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

A series LCR circuit with $$\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}$$ and $\mathrm{R}=10 \Omega$, is connected across an ac source of $220 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The power factor of the circuit would be ________.