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For the given figures, choose the correct options:

An LCR series circuit of capacitance \( 62.5 \, \text{nF} \) and resistance of \( 50 \, \Omega \), is connected to an A.C. source of frequency \( 2.0 \, \text{kHz} \). For maximum value of amplitude of current in circuit, the value of inductance is ______________ \( \text{mH} \). (Take \( \pi^{2} = 10 \))

Which of the following Maxwell’s equation is valid for time varying conditions but not valid for static conditions:

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

In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ \( \text{s} \).

A capacitor of capacitance \( 150.0 \, \mu \text{F} \) is connected to an alternating source of emf given by \( E = 36 \sin(120 \pi t) \, \text{V} \). The maximum value of current in the circuit is approximately equal to:

The waves emitted when a metal target is bombarded with high energy electrons are:

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

A series combination of resistor of resistance \( 100 \, \Omega \), inductor of inductance \( 1 \, \text{H} \) and capacitor of capacitance \( 6.25 \, \mu \text{F} \) if connected to an ac source. The quality factor of the circuit will be ________.

Given below are two statements:
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statement, choose the correct answer from the potions given below:

An alternating voltage source \( V = 260 \sin(628 t) \) is connected across a pure inductor of \( 5 \, \text{mH} \). Inductive reactance in the circuit is:

The energy density associated with electric field \( \vec{E} \) and magnetic field \( \vec{B} \) of an electromagnetic wave in free space is given by ( \( \varepsilon_{0} \) – permittivity of free space, \( \mu_{0} \) – permeability of free space)

As per the given graph, choose the correct representation for curve A and curve B.
{Where \( X_C \) = reactance of pure capacitive circuit connected with A.C. source
\( X_L \) = reactance of pure inductive circuit connected with A.C. source
\( R \) = impedance of pure resistive circuit connected with A.C. source.
\( Z \) = Impedance of the LCR series circuit}

Given below are two statements:
Statement I: When the frequency of an A.C source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.
Statement II: In a series LCR circuit, the value of power factor at resonance is one.
In the light of given statements, choose the most appropriate answer from the options given below.

Match List I with List II:

Choose the correct answer from the options given below:

As per the given figure, if \( \frac{dI}{dt} = -1 \, \text{A/s} \) then the value of \( V_{AB} \) at this instant will be _______ \( \text{V} \).

An ideal transformer with purely resistive load operates at \( 12 \, \text{kV} \) on the primary side. It supplies electrical energy to a number of nearby houses at \( 120 \, \text{V} \). The average rate of energy consumption in the houses served by the transformer is \( 60 \, \text{kW} \). The value of resistive load \( (R_s) \) required in the secondary circuit will be \( \text{m}\Omega \).

Given below are two statements:
Statement I: An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of above statements, choose the correct answer from the options given below:

In a series LR circuit with \( X_{L} = R \), power factor is \( P_{1} \). If a capacitance \( C \) with \( X_{C} = X_{L} \) is added to the circuit the power factor becomes \( P_{2} \). The ratio of \( P_{1} \) to \( P_{2} \) will be:

A series LCR circuit is connected to an AC source of \( 220 \, \text{V} \), \( 50 \, \text{Hz} \). The circuit contains a resistance \( R = 80 \, \Omega \), an inductor of inductive reactance \( X_L = 70 \, \Omega \) and a capacitor of capacitive reactance \( X_C = 130 \, \Omega \). The power factor of circuit is \( \dfrac{x}{10} \). The value of \( x \) is:

In the given circuit, rms value of current \( (I_{\mathrm{rms}}) \) through the resistor \( R \) is:

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JEE Main 2023 30th Jan Morning Shift

As per the given figure, if \( \frac{dI}{dt} = -1 \, \text{A/s} \) then the value of \( V_{AB} \) at this instant will be _______ \( \text{V} \).