# Solved papers for JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा JEE PYQ-Alternating Current

### done JEE PYQ-Alternating Current Total Questions - 36

• question_answer1) The power factor of an AC circuit having resistance R and inductance L (connected in series) and an angular velocity co is [AIEEE 2002]

A)
$\frac{R}{\omega L}$

B)
$\frac{R}{{{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}})}^{1/2}}}$

C)
$\frac{\omega L}{R}$

D)
$\frac{R}{{{({{R}^{2}}-{{\omega }^{2}}{{L}^{2}})}^{1/2}}}$

• question_answer2) In an oscillating LC circuit, the maximum charge on the capacitor is 0. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is [AIEEE 2003]

A)
$Q/2$

B)
$Q/\sqrt{3}$

C)
$Q/\sqrt{2}$

D)
Q

• question_answer3) Alternating current cannot be measured by DC ammeter because                     [AIEEE 2004]

A)
AC cannot pass through DC ammeter

B)
AC changes direction

C)
average value of current for complete cycle is zero

D)
DC ammeter will get damaged

• question_answer4) In an LCR series AC circuit, the voltage across each of the components. L, C and R is 50 V. The voltage across the LC combination will be                                          [AIEEE 2004]

A)
$50V$

B)
$50\sqrt{2}V$

C)
$100V$

D)
0

• question_answer5) In an LCR circuit, capacitance is changed from C to 2 C. For the resonant frequency to remain unchanged, the inductance should be changed from L to                     [AIEEE 2004]

A)
4L

B)
2L

C)
L/2

D)
L/4

• question_answer6) The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of                                  [AIEEE 2005]

A)
$4\mu F$

B)
$8\mu F$

C)
$1\mu F$

D)
$2\mu F$

• question_answer7) A circuit has a resistance of$12\,\Omega$and an impedance of$15\,\Omega$. The power factor of the circuit will be                          [AIEEE 2005]

A)
0.8

B)
0.4

C)
1.25

D)
0.125

• question_answer8) The phase difference between the alternating current and emf is$\pi /2$. Which of the following cannot be the constituent of the circuit?                                              [AIEEE 2005]

A)
C alone

B)
R, L

C)
L, C

D)
L alone

• question_answer9) In a series resonant LCR circuit, .the voltage across R is 100 V and$R=1k\,\Omega$. With $C=2\mu F$ The resonant frequency$\omega$is 200 rad/s. At resonance, the voltage across L is        [AIEEE 2006]

A)
$2.5\times {{10}^{-2}}V$

B)
$40\,V$

C)
$250\,V$

D)
$4\times {{10}^{-3}}\,V$

• question_answer10) In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency cd in a magnetic field B. The maximum value of emf generated in the coil is  [AIEEE 2006]

A)
$NABR\,\omega$

B)
$NAB$

C)
$NABR$

D)
$NAB\,\omega$

• question_answer11) In an AC circuit, the voltage applied is$cos\text{ }\alpha$ $1/\sqrt{3}$The resulting current in the circuit is$1/\sqrt{2}$. The power consumption in the circuit is given by                     [AIEEE 2007]

A)
${{x}^{2}}={{y}^{2}}+xy\frac{dy}{dx}$

B)
p=zero

C)
${{x}^{2}}={{y}^{2}}+3xy\frac{dy}{dx}$

D)
${{y}^{2}}={{x}^{2}}+2xy\frac{dy}{dx}$

• question_answer12) In a series LCR circuit$R=200\,\,\Omega$and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by$30{}^\circ$. On taking out the inductor from the circuit the current leads the voltage by 30°. The power dissipated in the LCR circuit is -                       [AIEEE 2010]

A)
242 W

B)
305 W

C)
210 W

D)
Zero W

• question_answer13)  In an LCR circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220V and 100 Hz is connected to it as shown?       [JEE ONLINE 07-05-2012]

A)
800V,8 A

B)
110V.1.1 A

C)
300V, 3 A

D)
220V, 2.2 A

• question_answer14)  In the circuit shown here, the voltage across Land C are respectively300 V and 400 V. The voltage E of the ac source is:                                                      [JEE ONLINE 09-04-2013]

A)
400 Volt

B)
500 Volt

C)
100      Volt

D)
700 Volt

• question_answer15)  An LCR circuit as shown in the figure is connected to voltage source ${{\operatorname{V}}_{\operatorname{ac}}}$ whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is:    [JEE ONLINE 22-04-2013]

A)
902 Hz

B)
143 Hz

C)
23 Hz

D)
345 Hz

• question_answer16) In a series L-C-R circuit, $\text{C}=\text{1}{{0}^{-11}}$ Farad, $\text{L}=\text{1}{{0}^{-5}}$ Henry and $\text{R}=100$ Ohm, when a constant D.C. voltage E is applied to the circuit, the capacitor acquires a charge $\text{1}{{\text{0}}^{-9}}\operatorname{C}.$ The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage ${{\operatorname{E}}_{0}}$ is equal to the constant D.C voltage E. At resonance the peak value of the charge acquired by the capacitor will be: [JEE ONLINE 22-04-2013]

A)
${{10}^{-15}}\operatorname{C}$

B)
${{10}^{-6}}\operatorname{C}$

C)
${{10}^{-10}}\operatorname{C}$

D)
${{10}^{-8}}\operatorname{C}$

• question_answer17) When resonance is produced in series LCR circuit, then which of the following is not correct?                   [JEE ONLINE 25-04-2013]

A)
Current in the circuit is in phase with the applied voltage.

B)
Inductive and capacitive reactances are equal.

C)
If R reduced, the voltage across capacitor will increase.

D)
Impedance of circuit is maximum.

• question_answer18) A series LR circuit is connected to an ac source of frequency $\omega$ and the inductive reactance is equal to $2R.$ A capacitance of capacitive reactance equal to R is added in series with L and R The ratio of the new power factor to the old one is:                     [JEE ONLINE 25-04-2013]

A)
$\sqrt{\frac{2}{3}}$

B)
$\sqrt{\frac{2}{5}}$

C)
$\sqrt{\frac{3}{2}}$

D)
$\sqrt{\frac{5}{2}}$

• question_answer19) When the rms voltages ${{V}_{L}},{{V}_{C}}$and ${{V}_{R}}$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio ${{V}_{L}}:{{V}_{C}}:{{V}_{R}}=1:2:3.$If the rms voltage of the AC sources is 100 V, the ${{V}_{R}}$ is close to:[JEE ONLINE 09-04-2014]

A)
50 V

B)
70 V

C)
90 V

D)
100 V

• question_answer20)  For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in:                        [JEE MAIN 11-04-2015]

A)
series with C and has a magnitude$\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.$

B)
series with C and has a magnitude$\frac{C}{({{\omega }^{2}}LC-1)}.$

C)
parallel with C and has a magnitude$\frac{C}{({{\omega }^{2}}LC-1)}.$

D)
parallel with C and has a magnitude$\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.$

• question_answer21) The AC voltage across a resistance can be measured using a:        [JEE MAIN 11-04-2015]

A)
potentiometer

B)
moving coil galvanometer

C)
moving magnet galvanometer

D)
hot wire voltmeter

• question_answer22) An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:- [JEE MAIN - I 3-4-2016]

A)
0.065 H

B)
80 H

C)
0.08 H

D)
0.044 H

• question_answer23) A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that $R=5\Omega ,\,L=25\,mH$ and $C=1000\,\mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be-                     [JEE Online 09-04-2017]

A)
$10\,\Omega$ and ${{\tan }^{-1}}\,\left( \frac{5}{3} \right)$

B)
$7\,\Omega$ and ${{45}^{\text{o}}}$

C)
$7\,\Omega$ and ${{\tan }^{-1}}\left( \frac{5}{3} \right)$

D)
$10\,\Omega \,$ and ${{\tan }^{-1}}\,\left( \frac{8}{3} \right)$

• question_answer24) For an RLC circuit driven with voltage of amplitude ${{\text{v}}_{m}}$ and frequency ${{\omega }_{0}}\text{=}\frac{\text{1}}{\sqrt{\text{LC}}}$ the current exibits resonance. The quality factor, Q is given by :    [JEE Main Online 08-04-2018]

A)
$\frac{R}{({{\omega }_{o}}C)}$

B)
$\frac{CR}{{{\omega }_{o}}}$

C)
$\frac{{{\omega }_{o}}L}{R}$

D)
$\frac{{{\omega }_{o}}R}{L}$

• question_answer25)  In an a.c. circuit, the instantaneous e.m.f. and current are given by $\text{e=100 sin 30 t}$ $\text{i=20 sin }\left( 30t-\frac{\pi }{4} \right)$ In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively: [JEE Main Online 08-04-2018]

A)
$\frac{50}{\sqrt{2}},0$

B)
$50,\,\,0$

C)
$50,\,\,10$

D)
$\frac{1000}{\sqrt{2}},\,\,10$

• question_answer26) A series AC circuit containing an inductor$\left( 20\text{ }mH \right)$, a capacitor $\left( 120\text{ }\mu F \right)$ and a resistor $\left( 60\text{ }\Omega \right)$ is driven by an AC source of$24\text{ }V/50\text{ }Hz$. The energy dissipated in the circuit in 60 s is: [JEE Main 09-Jan-2019 Evening]

A)
$5.65\text{ }\times \text{ }{{10}^{2}}J$

B)
$2.26\text{ }\times {{10}^{3}}J$

C)
$5.17\text{ }\times \text{ }{{10}^{2}}\,J~$

D)
$3.39\text{ }\times \text{ }{{10}^{3}}\,J$

• question_answer27)  In the given circuit, $C=\frac{\sqrt{3}}{2}\mu F,{{R}_{2}}=20\Omega ,$and${{R}_{1}}=10\Omega .$Current in $L-{{R}_{1}}$path is ${{I}_{1}}$and in $C-{{R}_{2}}$ path it is ${{I}_{2}}.$The voltage of A.C source is given by, $V=200\sqrt{2}\sin (100t)$volts. The phase difference between ${{I}_{1}}$ and ${{I}_{2}}$is                                  [JEE Main 12-Jan-2019 Evening]

A)
0

B)
$30{}^\circ$

C)
$90{}^\circ$

D)
None of these

• question_answer28) Let l, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{l}{rcv}$in SI units will be-                      [JEE Main 12-Jan-2019 Evening]

A)
$[L{{A}^{-2}}]$

B)
$[L{{T}^{2}}]$

C)
$[{{A}^{-1}}]$

D)
$[LTA]$

• question_answer29) An alternating voltage $\text{v}(t)=220\sin 100\pi t$ volt is applied to a purely resistance load of $50\Omega .$. The time taken for the current to rise from half of the peak value to the peak value is : [JEE Main 8-4-2019 Morning]

A)
2.2 ms

B)
5 ms

C)
3.3 ms

D)
7.2 ms

• question_answer30) A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring mass damped oscillator having damping constant b the correct equivalence would be [JEE MAIN Held on 07-01-2020 Morning]

A)
$L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b$

B)
$L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m$

C)
$L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}$

D)
$L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b$

• question_answer31) A particle of mass m and charge q has an initial velocity $\vec{v}={{v}_{0}}\hat{j}$. If an electric field $\vec{E}={{E}_{0}}\hat{i}$ and magnetic field $\vec{B}={{B}_{0}}\hat{i}$act on the particle, its speed will double after a time: [JEE MAIN Held on 07-01-2020 Evening]

A)
$\frac{3\,m{{v}_{0}}}{q{{E}_{0}}}$

B)
$\frac{\sqrt{3\,}m{{v}_{0}}}{q{{E}_{0}}}$

C)
$\frac{2\,m{{v}_{0}}}{q{{E}_{0}}}$

D)
None of these

• question_answer32) A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at [JEE MAIN Held on 07-01-2020 Evening]

A)
2.5 s and 7.5 s

B)
5.0 s and 7.5 s

C)
2.5 s and 5.0 s

D)
5.0 s and 10.0 s

• question_answer33)  At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is [JEE MAIN Held On 08-01-2020 Morning]

A)
$48\,\mu V$

B)
$36\text{ }\mu V$

C)
$56\text{ }\mu V$

D)
$28\text{ }\mu V$

• question_answer34)  As shown in the figure, a battery of emf E is connected to an inductor L and resistance R in series. The switch is closed at$t=0$. The total charge that flows from the battery, between t = 0 and $t={{t}_{C}}$(${{t}_{C}}$ is the time constant of the circuit) is: [JEE MAIN Held on 08-01-2020 Evening]

A)
$\frac{EL}{{{R}^{2}}}$

B)
$\frac{ER}{e{{L}^{2}}}$

C)
$\frac{EL}{{{R}^{2}}}\left( 1-\frac{1}{e} \right)$

D)
$\frac{EL}{e{{R}^{2}}}$

• question_answer35) In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be _______ [JEE MAIN Held on 09-01-2020 Morning]

• question_answer36) In LC circuit the inductance $L=40\,mH$ and capacitance $C=100\,\mu F.$ If a voltage $V(t)=10\,\sin (314\,\,t)$ is applied to the circuit, the current in the circuit is given as [JEE MAIN Held on 09-01-2020 Evening]

A)
$0.52\,\,\sin \,\,314\,\,t$

B)
$5.2\,\cos \,\,314\,t$

C)
$10\,\cos \,\,314\,t$

D)
$0.52\,\,\cos \,\,314\,t$