1
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

A series LCR circuit is connected to an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$. The circuit contain a resistance $$\mathrm{R}=100 ~\Omega$$ and an inductor of inductive reactance $$\mathrm{X}_{\mathrm{L}}=79.6 ~\Omega$$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $$\mu \mathrm{F}$$.

2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
A series $\mathrm{LCR}$ circuit consists of $\mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega$, and $\mathrm{X}_{\mathrm{C}}=40 \Omega$. The input

voltage is 2500 $\cos (100 \pi \mathrm{t}) \mathrm{V}$. The amplitude of current, in the circuit, is _________ A.
3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

An inductor of $$0.5 ~\mathrm{mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and resistance of $$20 ~\Omega$$ are connected in series with a $$220 \mathrm{~V}$$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $$\sqrt{x}$$ A. The value of $$x$$ is ___________

4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
In an ac generator, a rectangular coil of 100 turns each having area $14 \times 10^{-2} \mathrm{~m}^{2}$ is rotated at $360 ~\mathrm{rev} / \mathrm{min}$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0 \mathrm{~T}$. The maximum value of the emf produced will be ________ $V$.

$\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$