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JEE Mains | PYQ

An inductor of self inductance \( 1 \, \text{H} \) is connected in series with a resistor of \( 100\pi \, \Omega \) and an ac supply of \( 100\pi \, \text{V} \), \( 50 \, \text{Hz} \). Maximum current flowing in the circuit is ________ \( \text{A} \).

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \left(\frac{R}{\sqrt{R^{2}+\omega^{2} L^{2}}}\right) \), where \( \omega \) is frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below:

An alternating current is given by \( I = I_A \sin \omega t + I_B \cos \omega t \). Then r.m.s current will be:

A series \( LCR \) circuit is connected to an alternating source of emf \( E \). The current amplitude at resonant frequency is \( I_0 \). If the value of resistance \( R \) becomes twice of its initial value then amplitude of current at resonance will be:

In a series LCR circuit, a resistor of \( 300 \, \Omega \), a capacitor of \( 25 \, \text{nF} \) and an inductor of \( 100 \, \text{mH} \) are used. For maximum current in the circuit, the angular frequency of the ac source is __________ \( \times 10^{4} \) radians \( \text{s}^{-1} \).

The electric field of an electromagnetic wave in free space is \( \vec{E} = 57 \cos \!\left[ 7.5 \times 10^{6} t - 5 \times 10^{-3}(3x + 4y) \right] (4\hat{i} - 3\hat{j}) \, \text{N} / \text{C} \). The associated magnetic field in Tesla is:

An alternating current is represented by the equation, \( i=100\sqrt{2}\sin(100\pi t) \) ampere. The RMS value of current and the frequency of the given alternating current are:

A plane electromagnetic wave propagates along the \( +x \) direction in free space. The components of the electric field, \( \vec{E} \) and magnetic field, \( \vec{B} \) vectors associated with the wave in Cartesian frame are:

An ac current is represented as \( i = 5\sqrt{2} + 10\cos\!\left(650\pi t + \frac{\pi}{6}\right)\ \text{Amp} \). The r.m.s value of the current is:

The magnetic field of an E.M. wave is given by \( \vec{B} = \left(\displaystyle \frac{\sqrt{3}}{2}\,\hat{i} + \frac{1}{2}\,\hat{j} \right) \, 30 \, \sin \left[ \omega \left(\displaystyle t - \frac{z}{c} \right) \right] \) (S.I. Units). The corresponding electric field in S.I. units is:

If an optical medium possesses a relative permeability of \( \frac{10}{\pi} \) and relative permittivity of \( \frac{1}{0.0885} \), then the velocity of light is greater in vacuum than that in this medium by _______ times.
\( (\mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \;, \; \varepsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \;, \; c = 3 \times 10^{8} \, \text{m/s} )\)

An inductor of reactance \( 100\,\Omega \), a capacitor of reactance \( 50\,\Omega \) and a resistor of resistance \( 50\,\Omega \) are connected in series with an AC source of \( 10 \, \text{V} \), \( 50 \, \text{Hz} \). Average power dissipated by the circuit is _____ \( \text{W} \).

The radiation exerted by a \( 450\, \text{W} \) light source on a perfectly surface placed at \( 2\, \text{m} \) away from it, is:

For ac circuit shown in figure, \( R = 100 \, \text{k}\Omega \) and \( C = 100 \, \text{pF} \) and the phase difference between \( V_m \) and \( (V_B - V_A) \) is \( 90^\circ \). The input signal frequency is \( 10^{x} \, \text{rad/sec} \), where ‘x’ is __________.

Arrange the following in the ascending order of wavelength \( \lambda \):
(A) Microwaves \( \left(\lambda_{1}\right) \)    (B) Ultraviolet rays \( \left(\lambda_{2}\right) \)    (C) Infrared rays \( \left(\lambda_{3}\right) \)    (D) X-rays \( \left(\lambda_{4}\right) \)
Choose the most appropriate answer from the options given below:

A plane electromagnetic wave of frequency \( 20 \, \text{MHz} \) travels in free space along the \( +x \) direction. At a particular point in space and time, the electric field vector of the wave is \( E_y = 9.3 \, \text{V m}^{-1} \). Then, the magnetic field vector of the wave at that point is:

A parallel plate capacitor of area \( A = 16 \, \text{cm}^2 \) and separation between the plates \( 10 \, \text{cm} \), is charged by a DC current Consider a hypothetical plane surface of area \( A_0 = 3.2 \, \text{cm}^2 \) inside the capacitor and parallel to the plates. At an instant, the current through the circuit is \( 6 \, \text{A} \). At the same instant the displacement current through \( A_0 \) is __________ \( \text{mA} \).