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A circuit element \( X \) when connected to an a.c. supply of peak voltage \( 100\,V \) gives a peak current of \( 5\,A \) which is in phase with the voltage. A second element \( Y \) when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by \( \dfrac{\pi}{2} \). If \( X \) and \( Y \) are connected in series to the same supply, what will be the rms value of the current in ampere?

A telegraph line of length \( 100 \, \mathrm{km} \) has a capacity of \( 0.01 \, \mu \mathrm{F}/\mathrm{km} \) and it carries an alternating current at \( 0.5 \) kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ________ \( \mathrm{mH} \). (if \( \pi = \sqrt{10} \) ).

Light wave traveling in air along \( x \)-direction is given by \( E_y = 540\sin \pi \times 10^4(x-ct)\,\text{V m}^{-1} \). Then, the peak value of magnetic field of wave will be: (Given \( c=3\times 10^8 \,\text{ms}^{-1} \))

Given below are two statements:
Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement-II: In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below:

An AC source is connected to an inductance of \( 100 \, \text{mH} \), a capacitance of \( 100 \, \mu \text{F} \) and a resistance of \( 120 \, \Omega \) as shown in figure. The time in which the resistance having a thermal capacity \( 2 \, \text{J}/^\circ\text{C} \) will get heated by \( 16^\circ \text{C} \) is ______ \( \text{s} \).

A resistance of \( 40 \, \Omega \) is connected to a source of alternating current rated \( 220 \, \text{V} \), \( 50 \, \text{Hz} \). Find the time taken by the current to change from its maximum value to the rms value:

In the given circuit, the magnitude of \( V_L \) and \( V_C \) are twice that of \( V_R \). Given that \( f = 50 \, \text{Hz} \), the inductance of the coil is \( \dfrac{1}{K \pi} \, \text{mH} \). The value of \( K \) is __________.

As shown in the figure an inductor of inductance \( 200 \, \text{mH} \) is connected to an AC source of emf \( 220 \, \text{V} \) and frequency \( 50 \, \text{Hz} \). The instantaneous voltage of the source is \( 0 \, \text{V} \) when the peak value of current is \( \frac{\sqrt{a}}{\pi} \, \text{A} \). The value of \( a \) is ________.

If wattless current flows in the AC circuit, then the circuit is:

An alternating emf \( E = 440\sin 100\pi t \) is applied to a circuit containing an inductance of \( \dfrac{\sqrt{2}}{\pi} \, \text{H} \). If an a.c. ammeter is connected in the circuit, its reading will be:

In a series LR circuit \( X_L = R \) and power factor of the circuit is \( P_1 \). When capacitor with capacitance \( C \) such that \( X_L = X_C \) is put in series, the power factor becomes \( P_2 \). Then ratio \( \dfrac{P_1}{P_2} \) is:

The current flowing through an ac circuit is given by \( I = 5 \sin (120\pi t) \, \text{A} \)
How long will the current take to reach the peak value starting from zero?

To light, a \( 50 \, \text{W} \), \( 100 \, \text{V} \) lamp is connected, in series with a capacitor of capacitance \( \dfrac{50}{\pi \sqrt{x}} \, \mu \text{F} \), with \( 200 \, \text{V} \), \( 50 \, \text{HZ} \) AC source. The value of \( x \) will be ______.

To increase the resonant frequency in series LCR circuit.

A direct current of \( 4 \, \text{A} \) and an alternating current of peak value \( 4 \, \text{A} \) flow through resistance of \( 3 \, \Omega \) and \( 2 \, \Omega \) respectively. The ratio of heat produced in the two resistance in same interval of time will be:

A \( 72 \, \Omega \) galvanometer is shunted by a resistance of \( 8 \, \Omega \). The percentage of the total current which passes through the galvanometer is:

A \( 220 \, \text{V}, 50 \, \text{Hz} \) AC source is connected to a \( 25 \, \text{V}, 5 \, \text{W} \) lamp and an additional resistance \( R \) in series (as shown in figure) to run the lamp at its peak brightness, then the value of \( R \) (in ohm) will be ______.

In a series LCR circuit, the inductance, capacitance and resistance are \( L = 100 \, \text{mH} \), \( C = 100 \, \mu \text{F} \) and \( R = 10 \, \Omega \) respectively. They are connected to an AC source of voltage \( 220 \, \text{V} \) and frequency of \( 50 \, \text{Hz} \). The approximate value of current in the circuit will be __________ \( \text{A} \).

The frequencies at which the current amplitude in an \( LCR \) series circuit becomes \( \dfrac{1}{\sqrt{2}} \) times its maximum value, are \( 212 \, \text{rad s}^{-1} \) and \( 232 \, \text{rad s}^{-1} \). The value of resistance in the circuit is \( R = 5 \, \Omega \). The self inductance in the circuit is __________ \( \text{mH} \).

The equation of current in a purely inductive circuit is \( 5 \sin(49\pi t - 30^\circ) \). If the inductance is \( 30 \, \text{mH} \) then the equation for the voltage across the inductor, will be:
{Let \( \pi = \dfrac{22}{7} \)}

For a series LCR circuit, \( I \) vs \( \omega \) curve is shown:
(a) To the left of \( \omega_r \), the circuit is mainly capacitive
(b) To the left of \( \omega_r \), the circuit is mainly inductive
(c) At \( \omega_r \), impedance of the circuit is equal to the resistance of the circuit
(d) At \( \omega_r \), impedance of the circuit is \( 0 \).

Choose the most appropriate answer from the options given below:

An inductor of \( 0.5 \, \text{mH} \), a capacitor of \( 200 \, \mu\text{F} \) and a resistor of \( 2 \, \Omega \) are connected in series with a \( 220 \, \text{V} \) ac source. If the current is in phase with the emf, the frequency of ac source will be ______ \( \times 10^{2} \, \text{Hz} \).

A sinusoidal voltage \( V(t) = 210\sin(3000t) \) volt is applied to a series LCR circuit in which \( L = 10\,\text{mH} \), \( C = 25\,\mu\text{F} \) and \( R = 100\,\Omega \). The phase difference \( (\phi) \) between the applied voltage and resultant current will be:

A series LCR circuit has \( L = 0.01 \, \text{H} , \ R = 10 \, \Omega \) and \( C = 1 \, \mu \text{F} \) and it is connected to ac voltage of amplitude \( (V_m) \) \( 50 \, \text{V} \). At frequency \( 60 \% \) lower than resonant frequency, the amplitude of current will be approximately:

A \( 100 \,\mathrm{V} \), \( 50 \,\mathrm{Hz} \), AC source is connected in the circuit (as shown in figure). The current through the resistance \( 55 \,\Omega \), at resonance in the circuit, will be __________ \( \mathrm{A} \).

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JEE Main 2022 25th July Morning Shift

To increase the resonant frequency in series LCR circuit.