Alternating Current — JEE Main PYQs

In the circuit shown in the figure, the ratio of the quality factor and the band width is ____ s.

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

A series LCR circuit is connected to an AC source of $220\mathrm{V}$, $50\mathrm{Hz}$. 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 …

For the given figures, choose the correct options:

An inductor of inductance $2\mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}F$, where the value of $x$ is ______.
(Tak …

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

In a series LR circuit with $X_L=R$, power factor is $P_1$. If a capacitor of 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 :

If $R$, $X_L$, and $X_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

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

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

A series LCR circuit consists of $R=80\Omega$, $X_L=100\Omega$, and $X_C=40\Omega$. The input voltage is $2500\cos (100\pi t)$ V. The amplitude of current, in the circuit, is ______ A.

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 …

The equation of current in a purely inductive circuit is $5\sin \left(49\pi \mathrm{t}-30^{\circ }\right)$. If the inductance is 30 mH then the equation for the voltage across the inductor, will be :

Let $\pi =\frac{22}{7}$

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212\mathrm{rad}{\mathrm{s}}^{-1}$ and $232\mathrm{rad}{\mathrm{s}}^{-1}$. The value of resistance in the circuit is $\mathrm{R}=5\Omega$. Th …

A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

To light, a $50\mathrm{W},100\mathrm{V}$ lamp is connected, in series with a capacitor of capacitance $\frac{50}{\pi \sqrt{\mathrm{x}}}\mu \mathrm{F}$, with $200\mathrm{V},50\mathrm{Hz}$ AC source. The value of x will be ______.

To increase the resonant frequency in series LCR circuit,

The rms value of conduction current in a parallel plate capacitor is $6.9\mu \mathrm{A}$. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of $600\mathrm{rad}/\mathrm{s}$, will be :

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

A square wave of the modulating signal is shown in the figure. The carrier wave is given by $C(t)=5\sin (8\pi t)$ Volt. The modulation index is:

In a series LR circuit ${\mathrm{X}}_{\mathrm{L}}=\mathrm{R}$ and power factor of the circuit is ${\mathrm{P}}_1$. When capacitor with capacitance C such that ${\mathrm{X}}_{\mathrm{L}}={\mathrm{X}}_{\mathrm{C}}$ is put in series, the power factor becomes $P_2$. The ratio …

The effective current I in the given circuit at very high frequencies will be ______ A

In the given circuit, the magnitude of ${\mathrm{V}}_{\mathrm{L}}$ and ${\mathrm{V}}_{\mathrm{C}}$ are twice that of ${\mathrm{V}}_{\mathrm{R}}$. Given that $\mathrm{f}=50\mathrm{Hz}$, the inductance of the coil is $\frac{1}{\mathrm{K}\pi }\mathrm{mH}$. The value of K is

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

A telegraph line of length 100 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 ____ mH. ( …

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

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 cir …

A $110\mathrm{V},50\mathrm{Hz},\mathrm{AC}$ source is connected in the circuit (as shown in figure). The current through the resistance $55\Omega$, at resonance in the circuit, will be ____ A.

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

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

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

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

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 sta …

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

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

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

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance $\mathrm{R}=3\mathrm{k}\Omega$, an inductor of inductive reactances ${\mathrm{X}}_{\mathrm{L}}=250\pi \Omega$ and an unknown capacitor. The value of capacitance to maximize the average power s …

A resonance circuit having inductance and resistance $2\times 10^{-4}$ H and $6.28\Omega$ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ______.
[$\pi =3.14$]

A common transistor radio set requires 12 V (D.C) for its operation. The D.C source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C) on standard domestic A.C supply. The number of turns of secondary coil are 24, then the number of t …

In the given circuit the AC source has $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

AC voltage $\mathrm{V}(\mathrm{t})=20\sin \omega \mathrm{t}$ of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is $1{\mathrm{m}}^2$. The amplitude of the oscillating displacement current for the applied Ac volta …

In an LCR series circuit, an inductor 30 mH and a resistor $1\Omega$ are connected to an AC source of angular frequency $300\mathrm{rad}/\mathrm{s}$. The value of capacitance for which, the current leads the voltage by $45^{\circ }$ is …

A series LCR circuit is designed to resonate at an angular frequency ${\omega }_0=10^5\mathrm{rad}/\mathrm{s}$. The circuit draws 16 W power from 120 V source at resonance. The value of resistance ' R ' in the circuit is
____ $\Omega$.

For a series LCR circuit with $\mathrm{R}=100\Omega ,\mathrm{L}=0.5\mathrm{mH}$ and $\mathrm{C}=0.1\mathrm{pF}$ connected across $220\mathrm{V}-50\mathrm{Hz}$ AC supply, the phase angle between current and supplied voltage and the nature of the circuit is :

A seriesLCR circuit of $\mathrm{R}=5\Omega ,\mathrm{L}=20\mathrm{mH}$ and $\mathrm{C}=0.5\mu \mathrm{F}$ is connected across an AC supply of 250 V , having variable frequency. The power dissipated at resonance condition is ____ $\times 10^2\mathrm{W}$.

An ac circuit has an inductor and a resistor of resistance $R$ in series, such that $X_L=3R$. Now, a capacitor is added in series such that $X_C=2R$. The ratio of new power factor with the old power factor of the circuit is $\sqrt{5}:x$ The value of $x$ is ____.

The angular frequency of alternating current in a L-C- R circuit is $100\mathrm{rad}/\mathrm{s}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

A transmitting station releases waves of wavelength 960 m . A capacitor of $2.56\mu \mathrm{F}$ is used in the resonant circuit. The self inductance of coil necessary for resonance is ____ $\times 10^{-8}\mathrm{H}$.

In a circuit consisting of a capacitance and a generator with alternating emf ${\mathrm{E}}_{\mathrm{g}}={\mathrm{E}}_{{\mathrm{g}}_0}\sin \omega \mathrm{t},{\mathrm{V}}_{\mathrm{C}}$ and ${\mathrm{I}}_{\mathrm{C}}$ are the voltage and current. Correct phase diagram for such circuit is …

Match List - I with List - II :

List - I
(a) $\omega \mathrm{L}>\frac{1}{\omega \mathrm{C}}$
(b) $\omega \mathrm{L}=\frac{1}{\omega \mathrm{C}}$
(c) $\omega L<\frac{1}{\omega C}$
(d) Resonant frequency

List - II
(i) Current is in phase with emf
(ii) Current lags behind the appl …