Alternating Current — JEE Main PYQs

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for $V=5\sin (100t)$. The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $\mu$F.

For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\frac{\alpha }{10}$. The value of $\alpha$ is

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t/T)$. The r.m.s current for the period $t=0$ to $t=T$ is ______

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______ .
( $\pi =3.14$ )

The figure given below shows an LCR series circuit with two switches ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$. When switch ${\mathrm{S}}_1$ is closed keeping ${\mathrm{S}}_2$ open, the phase difference $(\varphi )$ between the current and source voltage is $30^{\circ }$ and phase differe …

An inductor of 10 mH, capacitor of $0.1\mu \mathrm{F}$ and a resistor of $100\Omega$ are connected in series across an a.c power supply $220\mathrm{V},70\mathrm{Hz}$. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacit …

An a.c. source of angular frequency $\omega$ is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to $\omega /4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resist …

A series LCR circuit with R $=20\Omega ,\mathrm{L}=1.6\mathrm{H}$ and $\mathrm{C}=40\mu \mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ______ $\Omega$.

A LCR series circuit driven with ${\mathrm{E}}_{\mathrm{rms}}=90\mathrm{V}$ at frequency ${\mathrm{f}}_{\mathrm{d}}=30\mathrm{Hz}$ has resistance $\mathrm{R}=80\Omega$, an inductance with inductive reactance ${\mathrm{X}}_{\mathrm{L}}=20.0\Omega$ and capacitance with capacitive r …

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is ${\mathrm{I}}_0$. 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 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is $\_\_\_\_$ $\times 10^4$ radians ${\mathrm{s}}^{-1}$.

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 elect …

An alternating current is given by
$\mathrm{I}={\mathrm{I}}_{\mathrm{A}}\sin \omega \mathrm{t}+{\mathrm{I}}_{\mathrm{B}}\cos \omega \mathrm{t}$.
The r.m.s. current will be :-

An electric bulb rated as $100\text{W}-220\text{V}$ is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:

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

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 V , 50 Hz . Average power dissipated by the circuit is ______ W.

An ac current is represented as

$i=5\sqrt{2}+10\cos \left(650\pi t+\frac{\pi }{6}\right)$ Amp

The r.m.s value of the current is

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

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF . If resistance of $200\Omega$ and 100 mH inductor is being used in the given circuit. The frequency of ac source is $\_\_\_\_$ $\times 10^3\mathrm{Hz}$. (gi …

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to :
A. pure inductor.
B. pure capacitor.
C. pure resistor.
D. combination of an inductor and capacitor.

Choose the correct answer from the o …

A alternating current at any instant is given by $\mathrm{i}=\left[6+\sqrt{56}\sin \left(100\pi \mathrm{t}+\frac{\pi }{3}\right)\right]$ A. The rms value of the current is ____ A.

A series LCR circuit is subjected to an AC signal of $200\mathrm{V},50\mathrm{Hz}$. If the voltage across the inductor $(\mathrm{L}=10\mathrm{mH})$ is 31.4 V , then the current in this circuit is ______ :

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of $12\mu \mathrm{F}$. The maximum displacement current between the plates of the capacitor is nearly:

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $20\mu \mathrm{F}$ is ______ V.

Given below are two statements :

Statement I: In an LCR series circuit, current is maximum at resonance.

Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above st …

When a dc voltage of 100 V is applied to an inductor, a dc current of 5A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be $20\sqrt{3}\Omega$. The power dissipated in the circuit is ______ W.

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

A coil of negligible resistance is connected in series with $90\Omega$ resistor across $120\mathrm{V},60\mathrm{Hz}$ supply. A voltmeter reads 36 V across resistance. Inductance of the coil is :

An alternating emf $\mathrm{E}=110\sqrt{2}\sin 100\mathrm{t}$ volt is applied to a capacitor of $2\mu \mathrm{F}$, the rms value of current in the circuit is ______ mA.

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

A capacitor of reactance $4\sqrt{3}\Omega$ and a resistor of resistance $4\Omega$ are connected in series with an ac source of peak value $8\sqrt{2}\mathrm{V}$. The power dissipation in the circuit is ____ W.

Primary side of a transformer is connected to $230\mathrm{V},50\mathrm{Hz}$ supply. Turns ratio of primary to secondary winding is $10:1$. Load resistance connected to secondary side is $46\Omega$. The power consumed in it is :

A series $LCR$ circuit with $L=\frac{100}{\pi }\mathrm{mH}$, $C=\frac{10^{-3}}{\pi }\mathrm{F}$ and $\mathrm{R}=10\Omega$, is connected across an ac source of $220\mathrm{V}$, $50\mathrm{Hz}$ supply. The power factor of the circuit would be ____.

In an a.c. circuit, voltage and current are given by : $V=100\sin (100t)$ V and $I=100\sin \left(100t+\frac{\pi }{3}\right)$ mA respectively.
The average power dissipated in one cycle is :

A transformer has an efficiency of $80\%$ and works at 10 V and 4 kW. If the secondary voltage is 240 V, then the current in the secondary coil is :

A parallel plate capacitor has a capacitance $\mathrm{C}=200\mathrm{pF}$. It is connected to 230 V ac supply with an angular frequency $300\mathrm{rad}/\mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

In series LCR circuit, the capacitance is changed from C to 4 C . To keep the resonance frequency unchanged, the new inductance should be :

An alternating voltage $\mathrm{V}(\mathrm{t})=220\sin 100\pi \mathrm{t}$ volt is applied to a purely resistive load of $50\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A and its efficiency is $90\%$. The windin …

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistance shown in shown in figure. The output voltage ( ${\mathrm{V}}_0$ ) is :

A series L,R circuit connected with an ac source $\mathrm{E}=(25\sin 1000\mathrm{t})\mathrm{V}$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $\mathrm{E}=(20\sin 2000$ t)V, the new power factor of the circuit will be :

An AC voltage $V=20\sin 200\pi t$ is applied to a series LCR circuit which drives a current $I=10\sin \left(200\pi t+\frac{\pi }{3}\right)$. The average power dissipated is:

A series combination of resistor of resistance 100 $\Omega$, inductor of inductance 1 H and capacitor of capacitance $6.25\mu \mathrm{F}$ is connected to an ac source. The quality factor of the circuit will be ____.

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

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 d …

As per the given graph choose the correct representation for curve A and curve B.
{Where ${\mathrm{X}}_{\mathrm{C}}=$ reactance of pure capacitive circuit connected with A.C. source
XL $=$ reactance of pure inductive circuit connected with A.C. source
$\mathrm{R}=$ impedance of pur …

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 re …

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 l …

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (Rs) re …

A series LCR circuit is connected to an ac source of 220 V, 50 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 …