7

,Atternati ng Current

= = ~_,-----~-~~ P_art-A (JEE Main)

6. In an a.c. circuit, voltage and current are given by :
V = 100 sin (100 t) V and
opic 1 -Alternating Current, Voltage
and Power
•••••••••P•••••
I = l 00 sin ( l 00 t + j' )rnA respectively.
The average power dissipated in one cycle is:
(S/' 1 MultiplP Chofr<' Question!; (Jan. 29, 2024 (11)1

An ac current is repres·ented as = 5✓2 + 10 (a) I0W (b) 2.5W (c) 25W (d) 5 W
t. 7. An alternating emfE = 440 sin l 00 7tt is applied to a circuit
cos ( 650nt + ~) Amp (April 7, 2025 (I)(
containing an inductance of ✓2 1-J. If an a.c. ammeter is
1t
The r.m.s value of the current is
connected in the circuit, itsreading will be :
(a) SOAmp (b) IOOAmp
·(July 29, 2022 (I)(
(c) I0Amp (d) 5✓ 2 Amp (a) 4.4A (b) 1.55A (c) 2.2A (d) 3.11 A
2. An alternating current is represented by the equation, 8. The equation of current in a purely inductive circuit is
i = 100✓2 sin(I001tt) ampere. The RMS value of current 5 sin (497rt- 300). Ifthe inductance is 30 mH then the equation

and the frequency of the given alternating current are·

[April 4, 2025 (1)1
for the voltage across the inductor, will be : ( Let 7t = ~2 )
(a) 100✓2 A, lOOHz (b) 1Jl. A, IOOHz (July 28, 2022 (1)1
(a) l.47sin(497tt-30°) (b) l.47sin(497tt+60° )
(c) lOOA,S0Hz (d) 50✓ 2 A,50Hz (c) 23.1 sin(497tt-30°) (d) 23.l sin(497tt+60°)
3. An electric bulb rated as 100 W-220 Vis connected to an ac 9. A direct current of 4 A and an alternating current of peak
source of rms voltage 220 V. The peak value of current value 4 A flow through resistance of 3 n and 2 n
through the bulb is : respectively. The ratio of heat produced in the two
(April 3, 2025 (II)) resistances in same interval oftime will be :
(a) 0.64A (b) 0.45A (c) 2.2A (d) 0.32A (July 27, 2022 (I)]
4.
An alternating current is given by (a) 3:2 (b) 3:1 (c) 3:4 (d) 4:3
1= IA sin ffit + 1 cos ffit. l 0. The current flowing through an ac circuit is given by
8
l)ie r.m.s. current will be (Jan. 24, 2025 (I)( I= 5sin (1201tl)A
How long will the current take to reach the peak value starting
(a) ✓Ii_+ I~ (b)
,jii_ +I~ from zero? (June 27, 2022 (I)J
2 I I I
(a) 60 s (b) ros (c) 120 s (d) 240 s
(c) ~ 11A +Isl
s.
V~ (d) ✓2 11. A resistance of 40Q is connected to a source of alternating
current rated 22~ V, 50 ~- Find the time taken by the current
An altemati I • . . to change from its maximum value to rms value:
a pure! _n~ VO tage V(t) = 220 sm 100 ntvolt 1sapphedto
10 ri
s
resi tive load of 50 n. The time taken for the current (June 24, 2022 (1)1
se om halfof the peak value to the peak value is: (a) 2.5rns (b) 1._25rns (c) 2.5's (d) 0.25s
12. An AC c111:ent _is given by I = I I sin (l)t + I COS(l)t. A hot wire
(a) 5 ms (Jan. 30, 2024 (JI)] ammeter will give a reading. 2
(b) 3.3ms (c) 7.2ms (d) 2.2ms (March 17, 2021 (I), Feb 26, 2021 (I) SJ
 ""'Ill
a146 M4NMW
la) /1; + 1
~--i-1-
2
(b)
11 + 12
✓2 [L0~:~1
1 +I, fif=jf 21. The alternating current is given by
~-ri" ~~
(c) (d)
I:\. An alternating voltage V(t) = 220 sin 1OOnt volt is applied to
i ={J42 sin(~ t )+ 1o}A
a purely resisuve load of500. The time taken for the current The r.m.s. value of this current is ____ A.
to rise from halfofthe peak value to the peak value is: l"A. Aug. 27, 2121 Ill(
II \pnl 2019 II
(a) Sms (b) 2.2ms
(c) 7.2 ms (d) 3.3 ms --------------·····
14. A sinusoidal voltage V(t) =100 sin (SOOt) is applied across a Topic 2-AC Circuit, LCR Circuit and
pure inductance ofl = 0.02 H. The current through the coil Power Factor
IS: IOnlia• ,\pril ll, 10141
(a) 10 cos (500 t) (b) - IO cos (500t)
(c) 10sin(500t) (d) -10sin(500t) @ I • ,1u1ti11ll· ( hoitt• Qrn ...tion-.
I c; In an a.c. circuit the voltage applied is E = £ 0 sin (J)/. The
22. Given below arc two statements: one is labelled as Aswrtioa
resulting current in the circuit is I= 10 sin ( wr-%) . The (A) and the other is labelled as Reason (R).
power consumption in the circuit is given by 120011 Assertion (A) : Choke coil is simply a coil having a largt
r:: £ I inductance but a small resistance. Choke coils are uscd with
(a) p = ,JJ.Eofo (b) P = 120 fluorescent mercury-tube finings. lfhousehold elcctricpo,,.'CI'
is directly connected to a mercury tube, the tube will be
Eolo damaged.
(c) P=-zero (d) P = - Reason (R) : By using the choke coil, the voltage across the
2
16. In a uniform magnetic field of induction Ba wire in the form ( R \
of a semicircle of radius r rotates about the diameter of the
circle with an angular frequency (J). The axis of rotation is
l
tube is reduced by a factor ✓R2 +(J)2 L2 J• where co is
perpendicular to the field. If the total resistance ofthe circuit frequency of the supply across resistor R and inductor L. If
is R. the mean power generated per period of rotation is the choke coil were not used, the voltage across the resiSIU
(2004( would be the same as the applied voltage.
In the light of the above statements, choose the lllOSI
(a) (Bnrw)
2 (Bnr 2w)2 appropriate answer from the options given below:
(b) SR
2R )Jan. 19, 2t2S {I)(
2 2 2 (a) Both (A) and (R) are true but (R) is not the cxma
(c) Bw ~> (d) (Bnrw ) explanation of(A).
2R SR (b) (A) is false but (R) is true.
Alternating current can not be measured by D.C. ammeter (c) Both (A) and (R) are true and (R) is the coma
because (20041 explanation of(A).
(a) Average value of current for complete cycle is zero (d) (A) is true but (R) is false.
(b) A.C. Changes direction 23. A series LCR circuit is connected to an alternating scui:c
(c) A.C. can not pass through D.C. Ammeter ofemfE. The current amplitude at resonant frequencyisfo.lf
the value of resistance R becomes twice of its initial value
(d) D.C. Ammeter will get damaged.
then amplitude ofcurrent at resonance will be
® ·? 1 .\1111..ri1•\al111,(l1w-.t1011•
)Jan. 22, 202S (llij

I lo
18. An alternating emfE = I 10✓2 sin IOOt volt is applied to a (a) lo (b) ; (c) .Ji (d) 2fo
capacitor of2µF, therms value of current in the circuit is- 24. A bulb and a capacitor are connected in series across auc
- - mA. supply. A dielectric is then placed between theplatesofthc
capacitor. The glow of the bulb: )April 9, 2124 (I~
(Aprll 8, 2024 (11)1
(a) increases (b) remainssame
19. A alternating current at any instant is given by (c) becomes zero (d) decreases
25. A LCR circuit is at resonance for a capacitorC, inductanceL
i =[ 6+ ✓56sin(1oom
+~)]A. The rms value of the and resistance R. Now the value of resistance is halved
keeping all other parameters same. The current amplitudell
current is___ A. (April 4, 1024 (1)1 resonance will be now: (April 8, 202~ llM
20. As shown in the figure an inductorofinductance200 mH is (a) zero (b) double
connected to an AC source of emf220 V and frequency 50 (c) same (d) halved
Hz. The instantaneous voltage ofthe source is OVwhen the 26. A coil of negligible resistance is connected in sericswith90
n resistor across 120 V, 60 Hz supply. Avoltmetemads36V
peak value of current is ✓lta
A. The value of a is across resistance. Inductance ofthe coil is:
(April 8, lOl~ 11111
(Juno 2◄, 2022 {1)1
(a) 0.76H (b) 2.86H (c) 0.286H (d) 0.91H
 Alternating Current

27. Given below are two statements:

32. An AC voltage V = 20 sin 200rrt is applied to a series LCR
Statement I : In an LCR series circuit, current is maximum at
resonance.
Statement 11 : Current in a purely resistive circuit can never
circuit which drives a current I • IOsin ( 2OOn1 + f). The
be less than that in a series LCR circuit when connected to average power dissipated is:
same voltage source. )Ju. JI 2024 (11)1
In the light of the above statements, choose the correct (a) 21.6W (b) 200W (c) 173.2\V (d) SOW
from the options given below:
)April 6, 2024 (I)) 33. A series L. R circuit connected with an ac source E
(a) Statement I is true but Statement II is false
(b) Statement I is false but Statement n is true I
= (25 sin I 000 t) V has a power factor of ✓2 • Ifthe source of
(c) Both Statement I and Statement II arc true
(d) Both Statement I and Statement II are false emfis changed to E = (20 sin 2000 t) V, the new power factor
28. A series LCR circuit is subjected to an AC signal of200 V, 50 ofthe circuit wiU be:
Hz. If the voltage across the inductor (L= 10 mH) is 31.4 V, )Joo. JO. 2024 (1)1
then the current in this circuit is _ _ __ I I I I
)April 5, 2024 (ll)J (a) ✓2 (b) Ji (c) Js (d) ./7
(a) 68A (b) 63A (c) JOA (d) IOmA 34. Given below are two statements :
29. In an ac circuit, the instantaneous current is zero, when the
Statement I : An AC circuit undergoes electrical resonance
instantaneous voltage is maximum. In this case, the source
may be connected to : . ifit contains either a capacitor or an inductor.
Statement II : An AC circuit containing a pure capacitor or
(April 4, 2024 (I))
A. pure inductor. a pure inductor consumes high power due to its non-zero
R pure capacitor. power factor. )April IJ. 2023 (11)1
C pure resistor. In the light ofabove statements, choose the correct answer
D. combination ofan inductor and capacitor. from the options given below :
Choose the correct answer from the options given below: (a) Both Statement I and Statement II arc false
(a) A, Band Conly (b) B, C and Donly (b) Statement I is true but Statement TI is false
(c) A and B only (d) A, Band D only (c) Both Statement I and Siatement U are true
30. Match List I with List II (d) Statement I is false but Statement II is true
List- I List - II 35. 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.
A. Purely capacitive circuit L Ir Statement II : In a series LCR circuit, the value of power

r
factor at resonance is one. )April 12. 2023 (IJI
~v In the light ofgiven statements, choose the most appropriate

~
answer from the options given below:
(a) Statement I is incorrect but Statement II is true
• p,,,,,,;,,,o;we;,ru;, (b) Both Statement I and Statement 11 are false
(c) Statement I is correct but Statement U is false

L,
(d) Both Statement I and Statement II are true
36. As per the given graph choose the correct reprCSC'lltation
for curve A and curve B. )April 11, 2023 (1)1
c LCR=i~.,,=.,u m. {Where Xo = reactance of pure capacitive circuit connected
with A.C. source
XL= reactance ofpure inductive circuit connected with A.C.
source

D. LCR series circuit

"' vl R = impedance ofpure resistive circuit connected with AC.
source
Z = Impedance ofthe LCR series circuit}
~I
Choose the correct answer from the options given below: lrnp«lancc
)April 4, 2024 (Ill) Curve 8
(a) A-1, B-IY, C-DI, D-II (b) A-N, B-I, C-DI, D-Il
(c) A-IY, B-I, C-11, D-m (d) A-1, B-IY, C-II, D-IlJ
31. In series LCR circuit, the capacitance is changed from C to
4C. To keep the resonance frequency unchanged, the new f(H:)
inductance should be: )Ftb. 1, 2~24 (Ill (a) A=Xc,B=R (b) A=XL,B=Z
I (c) A= Xe, B = Xi_ (d) A=xi:,B=R
(a) reduced by - L (b) increased by 2L 37. Given below are two statements:
4
Statement I: Maximum power is dissipated in a circuit
3 containing an inductor, a capacitor and a resistor connected
(c) reduced by- L (d) increased by 4L in series with an AC source, when resonance occurs.
4
g148 wµ,n11,w
'-tit~m,·nt \I : Maximum power is dissipated in D circuit 43. A coil ofinductance I Hand resistance 100 0 is connected
containing pure resistor due to zero phase difference between 10 a b.111eryof6V. Determine approximately.
cUITcnt and voltage. !July 29, 2021 (I)!
\n the light ofthe above statements. choo;c the com:ct ans\\\.'f (a) The time elapsed before the current acquires halfofits
ftool the ~lims gi= below: \ \pril 10. 202~ \Ill steady - state value
(11) Statement 1is false but Statement II is true (b) The energy stored in the magnetic field associated 11ith
(b) S1a1cmcn1 I is true but Statement II is false the coil at an instant 15 ms after the circuit is switched
(c) Both Statement I and S1a1cmcn1 II arc true on. (Given ln2 = 0.693, e-312 = 0.25)
(d) Both Statement I and Statement 11 arc false (a) t=IOms;U=2mJ (b) t=lOms;U=lmJ
JR. A capacitor of capacitance 150.0 µF is connected lo an (c) t=7ms;U=lmJ (d) t=7ms;U=2mJ
alternating source ofemf given by E= 36 sin(\20m) V. The .i~. A circuit element X when connected to an a.c. supply of
maximum value ofcurrent in the circuit is approximately equal peak voltage I00 V gives a peak current of 5A which is in
to: \.\pril 6, 2023 \llll
phase with ~he voltage. Asecond clement Y when connectcd
\ to the same a.c. supply also gives the same value of peak
(a) 2A (b) ✓2 A (c) ✓2A (d) 2✓2A . lt

JI), An alternating voltage source V= 260 sin (628t) is connected

2°
current which lags behind the voltage by lfX and Yart
across a -pure inductor of 5 mH. Inductive rcactancc in the connected in series to the same supply, what will be therms
circuit is: !Jan. 31. 2023 (Ill\ value of the current in ampere? IJuty 29,lOll(lhl
(a) 3.14n (b) 6.28n (c) o.sn (d) 0.31&n 10 s 5
40. 1n a series LR circuit with XL= R. power factor is P1. If a • (a) ✓2 (b) ✓2 (c) 5✓2 (d) 2
capacitor of capacitance C with Xe = XL is added to the
45 Aseries LCRcircuit has L= 0.01 H, R= lO!landC•l !If
cirt11it the powtr factor becomes P2' The ratio ofPI to P2will • and ii is connected to ac voltage of amplitudc(V.,)SOY.At
be: \Jan. 3Q, 1023 (1\1 frequency 60% lower than resonant frequency, the amplitude
(a) I: 3 (b) 1: ✓ 2 (c) l: 1 (d) l: 2 ofcurrent will be approximately:
!Jul) 27, 2011 (lhl
4 \. ln the given circuit, rms value of current (lrrns) through the (a) 466mA(b) 312mA (c) 238mA (d) l'KimA
resistor Ris: IJan. 30, 2023 (!Ill
.i6. In a series LR circuit XL= Rand power factor ofthe circuit is

L':J
P1' When capacitor with capacitance C such that
XL= Xe is put in series, the power factor becomes Pr Tbe
. P, . !July 26, 1011 (Ill
rallO - 1s:
P2
v,.. -1oo./iv
I ✓3
(d) 2: I
(a) 2A
l
(b) ✓2 A (c) 20 A (d) 2✓2A
(a) 2 (b) ✓2 (c) ✓2
47. To increase the resonant frequency in series LCR circui~
.u. For the gi,•en figures, choose the correct options: lJul~ lS, 2022 (Ill
400 IJan. 29, 2023 (II)\ (a) source frequency should be increased

CJ
(b) another resistance should be added in series with tllc
first resistance.
(c) another capacitor should be added in series with die
first capacitor.
(cl) the source frequency should be decreased.
48. When you walk through a metal detector carrying amclll
400 object in your pocket, it raises an alarm. This phenCIIICIICI
works on fJ uly 25, 2121 (1111
(a)· Electromagnetic induction
(b) Resonance in ac circuits
(c) Mutual induc1ion in ac circuits
(d) interference of electromagnetic waves
220 V.SOHz
(b) 49. For aseries LCR circuit, I vs ro curve is shown:
lJ une 29, ltll (Ill
(a) Therms current in circuit (b) can never be larger than
that in(a) (a) To the left of ro,, the circuit is mainlycapaciti\'C.
(b) Therms C1mcn1 in figure (a) is always equal to that in
figure (b) (b) To the left of ro,, the circuit is mainly inducti\'C.
(c) Therms current in circuit (b) can be larger than that in
(a) (c) At ro,, impedance ofthe circuit is cqualtothcresislllce
(d) At resonance, current in (b) is less than that in (a) of the circuit.
(d) At (J),, impedance oflhe circuit is 0.
 Alternating Current
.,.~~
1 'moxr-··------ I

pclow:
COr

Choose the most appropriate a~swer fr~m the options given

. ILVc
1c)

I
fv;v
(a) (a) and (d) only (b) (b) and (d) only
(c) (a) and (c) only (d) (b) and (c) only (•)~~)~
50. lfwattlcss current flows in the AC circuit, then the circuit
is !Juno 25, 2022 (I)]
(a) Purely Resistive circuit (b) Purely Inductive circuit c
(c) LCR series circuit

f*
(d) RC series circuit only
51. A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied toa rot

series LCR circuit in which L = 10 mH, C = 25 µF and (c) (d)

I
R = 100 n. The phase ,difference (<J>) between the applied
voltage and resultant current will be : !June 25, 2022 (ll)J 57. What happens to the inductive reactance and the current in
(a) tan-1 (0.17) (b) tan-1 (9.46) a purely inductive circuit ifthe frequency is halved?
(c) tan-1 (0.30) (d) tan-• (13.33) [Marcil 17. 2021 (11)1
52. Given below are two statements : (a) Inductive reactance will be doubled and current will be
Statement-I : The reactance of an ac circuit is zero. It is
halved
possible that the circuit contains a capacitor and an inductor.
(b) Both, inducting rcactance and current will be doubled
Slatement-H : In ac circuit, the average power delivered by
the source never becomes zero. (c) Inductive rcactance will be halved and current will be
In the light of the above statements, choose the correct doubled
answer from the options given below : !June 24, 2022 (11)1 (d) Both, inductive rcactancc and current will be halved
(a) Both Statement I and Statement II are true. 58. An LCR circuit contains resistance of 110 n and a supply of
{b) Both Statement I and Statement II are false. 220 Vat 300 rad/s angular frequency. Ifonly capacitance is
(c) Statement I is true but Statement II in false. removed from the circuit, current lags behind the voltage by
(d) Statement I is false but Statement II is true. 45°. Ifon the other hand, only inductor is removed the current
53. In an ac circuit, an inductor, a capacitor and a resistor are leads by 45° with the applied voltage. The rrns current flowing
connected in series with XL= R = Xe. Impedance of this in the circuit will be )Fob. 25, 2021 (II) 20 IO SI
circuit is: !Au~. JI, 2021 (1)1
(a) I.SA (b) IA (c) 2A (d) 2.5A
(a) 2R2 (b) Zero (c) R (d) R,fi, 59. A series L-R circuit is connected to a battery ofemf V. Ifthe
54. Aseries LCR circuit driven by 300 Vat a frequency ofSO Hz circuit is switched on at t = 0, then the time at which the
contains a resistance R.= 3 kn, an inductor of inductive
reactance X = 250 110 and an unknown capacitor. The value
energy stored in the inductor reaches ( ;) times of its
ofcapacitan~ to maximize the average power should be: (Take
~ = I0) JAug. 26, 2021 (I))
(a) 4µF (b) 2SµF
maximum value, is : (S•p. 04, 2020 (IIJI
(c) 400µF (d) 4-0µF
ss. In the given circuit the AC sour~ has ro .= 100 rad s·•. L ( M,✓ n J
Considering the inductor and capac1t~ to~ ideal, what will (a) -In
R n-1
L 1n(
(b) "'i. ~
,J;; +IJ
be the current I flowing through the c1rcmt?
!Aug. 26, 2021 (IJ)J
L ( ,✓n )
IOOµF 1000 (c) -In T,;;i
R n+I
L
(d) R.ln (.Jn-lJ
T
60. A 7S0 Hz, 20 V (rms) source is connected to a resistance of
100 n, an inductance of0.1803 Hand a capacitance of
10 µFall in series. The time in which the resistance (heat
capacity2 Jl"C)will get heated by 10°C. (assume no loss of
heat to the surroundings) is close to: (Sop. OJ, 2020 (Ill
(a) 418 s (b) 245 s (c) 365 s (d) 348 s
200V 61. An inductance coi I has a reactance of I00 n. When an AC
(a) 5.9A (b) 4.24A (c) 0.94A (d) 6A signal offrequcncy 1000 Hz is applied to the coil, the applied
S6. In a circuit consisting of a ca~citance and a generator voltage leads the current by 45°. The self-inductance ofthe
with alternating emf E, = E., sin ~I, V c and le are the coil is : IS.p. 02. 2020 (11)1
voltage and current. Correct pliasor diagram for such circuit (a) I.Ix I0-2 H (b) I.Ix 10-1 H
is: )JUI) 22, 202 t (I l)j
(c) S.S>< 10-'H (d) 6.7>< I0-7 H
al.SO
MPitfii+W
112 Consider the LR circuit shov.11 in the figure. Ifthe switch Sis
closed at t = 0 then the amount ofcharge that passes through
L
In theabovecircuit,C= ~ µF, R2 =2on, L= ! Hand
the battery between t = 0 and I= R is : Ill \pril 2019 (till R1= ion. Current in L.R1path is 11 and in C-Ripathit isli-
The voltage of A.C source is given by, V = 200Ji sin (100
2.1EL EL L R
(a) ,il (b) 2.7 R2 i ~ t) volts. The phase difference between I and 1 is:
I 2
I12 Jan. 201' 11111
7.3EL EL ~i--W (a) (If' (b) 30° (c) W' (d) 0
(c) 7 (d) 7 .3R2 E S 68. In the circuit shown,
R
63. A coil of self inductance 10 mH and resistance 0.1 n is
connected through a switch to a battery ofinternal resistance
0.9 n. After the switch is closed, the time taken for the current
to attain 80% ofthe saturation value is s,
{take/nS=l.6) 110 \prll20t9(11)1
(a) 0.324s (b) 0.103s ---11 ,,.-s,
(c) 0.002 s (d) 0.016s t
64. A20 Henry inductor coil is connected to a IO ohm resistance the switch S1 is closed at time t = Oand the switch S2 is
in series as shown in figure. The time at which rate of kept open. At some later time (t0), the switch S1 is~ed
dissipation ofenergy (Joule's heat) across resistance is equal and S2 is closed. the behaviour ofthe current I as a funcooi
to the rate at which magnetic energy is stored in the inductor, of time 't' is given by: 111 Jan. 2019 (IIJI
is: II April 2019 (Ill I
2 I i 10 n
(a) hi2 (b) ln2
2
Eo20H (a) (b)
(c) 2 In 2 (d) In 2
65. A circuit connected to an ac source of emf e = e0sin( IOOt) lo lo

1t
with I in seconds, gives a phase difference of
4 between
the emfe and current i. Which ofthe following circuits will
exhibit this? 18 April20l9 (11)1 (c) (d)
(a) RLcircuitwithR= I kn and L= \0mH
(b) RL circuit with R= I kn and L = I mH
(c) RCcircuitwithR= I knandC= I µF
lo ..
69. A series AC circuit containing an inductor (20 mH), 1
(d) RC circuit with R= l knandC= 10 µF. capacitor (120 µF) and a resistor (60 Q) is driven by ■
66. In the figure shown, a circuit contains two identical resistors AC source of 24 V/50 Hz. The energy dissipated in~
with resistance R = 5 n and an inductance with circuit in 60 s is: 19 Jan. 2019 (IM
L= 2 rnH. An ideal battery of I 5Vis connected in the circuit. 2 3
(a) 5.65 X !0 J (b) 2.26 X !0 J
What will be the current through the battery long after the (c) 5.17 x 102 J (d) 3.39 x 10 J
3
switch is closed? ,----.----,112 Jan. 2019 Oll 70. In LC circuit the inductance L =40 rnH and capacitanee C•
(a) 5,5 A
100 µF. If a voltage V(t) = IO sin(3 I 4 I) is applied lo the
L circuit, the current in the circuit is given ~s:
(b) 7.SA 19 Jan. 2019 (11)1
R (a) 0.52 cos 314 t (b) !Ocos314t
(c) 3 A (c) 5.2cos314t (d) 0.52 sin 3141
L R
R
(d) 6A 71.

67. l...__...j I I.
C R, E S
L R, As shown in the figure, a battery of emf Eis connected Ill
I,
an inductor Land resistance R in series. The switch iscloa
at t = 0. The total charge that flows from the ball~ betMII
t = 0 and 1=t, (t, is the time constant ofthe circuit)is:
I8 J 11. 20ll !IIM
 Alternating Current B151

(a) R2e
ER
(b)
I)
EL( I--;
Jif (a) -
1-e
e A / C ~-

El ER (b) I _J_
(c) Ji! (d) el2
(c) -1
-,- !' ~L

72. An emfof20 Vis applied at timet=O to a circuit containing

in series IO rnH inductor and 5 f.l resistor. The ratio oft he l-e
currents at time t = oo and at t = 40 s is close to: (d) e
(fake e'= 7.389) 17 Jan. 2020 (11)1
(a) l.!XJ (b) 1.15 (c) 1.46 (d) 0.84 78. When the rms voltages VL' Vc and V R are measured
73. In an a.c. circuit, the instantaneous e.m.( and current are given respectively across the inductor L, the capacitor C and the
by • resistor Rina series LCR circuit connected to an AC source,
e= 100sin30t it is found that the ratio VL: Ve: VR =I: 2: 3. If therms
voltage of the AC sources is I 00 V, the V R is close to:
i=20sin (301-~) {Onllnt April 9, 2014!
(a) 50V (b) 70V (c) 90V (d) 100 V
In one cycle of a.c., the average power consumed by the
circuit and the watt less current are, respectively: 79. In an LCR circuit as shown below both switches are open
initially. Now switch S is closed, S2 kept open. (q is charge
!2018! 1
on the capacitor and t = RC is Capacitive time constant).
1000
(a) SOW, IOA (b) ✓2 W, IOA Which of the following statement is correct?
(2013!

50 V
(c) Ji. W,O (d) 50W,O

74. A sinusoidal voltage of peak value 283 V and angular

frequency 320rad/s is applied to a series LCR circuit. Given
that R =5 n, L= 25 mH and C = I 000 µF. The total impedance,
l
~s,
and phase difference between the voltage across the source
and the current will respectively be: C I S,
[Online Aprll 9, 2017(

(a) JO n and tan- 1 ( f) L

(a) Work done by the battery is halfofthe energy dissipated
(b) 7 n and 45° in the resistor
(b) At, t = t, q =CV/2
(c) 10 n and tan-I(¾) (c) At, t= 2r, q =CV (t -e-2)
(d) At,t=2t,q=CV(l-e-1)
(d) 7 n and tan-1 ( ¾) 80. A series LR circuit is connected to an ac source of frequency
ro and the inductive reactance is equal to 2R. A capacitance
75. An arc lamp requires a direct CUJTent of IO A at 80 V to function.
ofcapacitive reactance equal to R is added in series with L
Ifit is connected to a 220 V (rms), 50 Hz AC supply, the series
and R. The ratio of the new power fuctor to the old one is :
inductor needed for it to work is close to: (2016!
(Online April 25, 20131
(a) 0.044H (b) 0.065H(c) 80H (d) 0.08H
?6. An inductor (L = 0.03 H) and a resistor (R = 0.1 S kn) are
connected in series to a battery of 15V em fin a circuit shown
below. The key K 1 has been kept closed for a long time.
(a) # (b) J¾

a
~hen at t = 0, K 1 is opened and key K2 is closed
simultaneously. At t = I ms, the current in the circuit will
(c) J¾ (d) J%
be: (e5 :::; I50) O.o3 H O.IS kfl (20151
8 I. When resonance is produced in a series LCR circuit, then
(a)6.7mA
{b) 0.67 mA K, which ofthe following is not correct?
(C) I00 mA i---/ (Onllnt April 25, 20131
(d) 67mA ISV K, (a) Current in the circuit is in phase with the applied voltage.
'7. In the circuit shown here, the point 'C' is kept connected to (b) Inductive and capacitive rcactances are equal.
point 'A' till the current flowing through the circuit becomes (c) IfR is reduced, the voltage across capacitor will increase.
constant. Afterward, suddenly, point 'C' is disconnected
(d) Impedance ofthe circuit is maximum. .
from point 'A' and connected to point 'B'at timct = 0. Ratio
82. In the circuit shown here, the voltage across L and C arc
of the voltage across resistance and the inductor at t = UR
respectively 300 V and 400 V. The voltage E ofthe ac source
will be equal to: (2014)
is: !Online April 9, 2013]
8152
V
L (a) VR1 R2 all = 0 and R att = oo
✓R,2 +Ri 2
C V V(R, +R2) _
(b) - all = 0 and RR all - oo
R2 I 2
E V VR1R2
(a) 400\k>lt (b) 500\k>lt (c) 100\.blt (cl) 700\.blt (c) - atl =0and ~ a t t a a co
8]. In an LCR circuit shown in the following figure. what will be R2 ✓Rf +Ri
the readings ofthe voltmeter across the resistor and ammeter
ifan a.c. source of220V and 100 Hz is connected to it as (d) V(R1 + R2 ) at t = 0 and -V att = oo
shown? (Onllnt May 7, 2012)
R1R2 R2

. L 1000 88. E
L
R,

- ...,
300V 300V
V
VR
1 s
R,

~ - - - - - - f.....\ - - - - - - - - '
An inductor of inductance L = 400 mH and resistors of
220V, 100 Hz resistance R = 2n a~d }½ = 20 are ~nnected to a battay
1
(a) 800V,8A (b) 11ov;1.1A ofemf 12 Vas shown m the figure. The mternal resistanccti
(c) 300V,3A (d) 220V,2.2A the battery is negligible. The switch Sis closed at,,. o. The
8-t A fully charged capacitor Cwith initial chargeq0 is connected potential drop across£ as a function of time is 12..,,1
to a coil of self inductance L att =0. The time at which the (a) ge-3'y (b) 6(t-e_,,o.2)v
energy is stored equally between the electric and the I 51
magnetic fields is: 120111 (c) 12e-5'V (d) 6e- V
89. In a series resonant LCR circuit, the voltage across Ris 100
(a) ¾Fc (b) 27!.JLC volts and R = l k!l with C = 2µF. The resonant frcqucncyr,
is 200 rad/s. At resonance the voltage across Lis llOIIJ
(c) ✓ LC (d) 7!✓ LC (a) 2.5 x 10-2 V (b) 40V
85. A resistor 'R' and 2µF capacitor in series is connected (c) 250V (d) 4x 10-3 y
through a switch to 200 V direct supply. Across the capacitor 90. An inductor (L = 100 mH), a resistor (R = 100 Q) and a
is a neon bulb that lights up at 120 V. Calculate the value of battery(£= I00 V) are initially connected in seriesassholn
R to make the bulb light up 5 s after the switch has been in the figure. After a long time the battery is disconncctcd
closed. (log 19 2.5 = 0.4) (20 II) after short circuitin·g the points A and B. The current intbc
(a) J.7xJO>n (b) 2.7xID6f2 circuit I ms after the short circuit is 120061
(c) 3.3 x 101 n (d) 1.3 x urn L
86. Combination oftwo identical capacitors, a resistor Rand a
de voltage source ofvoltage 6V is used in an experiment on
a (C-R) circuit. It is found that for a parallel combination of R
the capacitor the time in which the voltage of the fully
charged combination reduces to half its original voltage is
10 second. For series combination the time needed for A ·-····I ~--··· ~ I

reducing the voltage ofthe fully charged series combination ' I• E •

(a) 1/eA (b) eA (c) 0.IA (d) IA
by half is 12011 RS] 91. The phase difference between_ the alternating current and
(a) IO second (b) 5 second
(c) 2.5 second (d) 20 second emfis ~ . Which ofthe following cannot be the coostitucut
2
87. In the circuit sho\W below, the key K is closed at I= 0. The ofthe circuit? (2005(
current through the battery is 1201 OJ (a) R, L (b) C alone (c) Lalone (d) L, C
92. A circuit has a resistance of 12 ohm and an impedance ofIS
V /K ohm. The power factor ofthe circuit will be
.----ii I I (ltOll
L (a) 0.4 (b) 0.8 (c) 0.125
(d) 1.25
93. A coil of inductance 300 mHand resistance2n iscamectal
to a source of voltage 2V. The current reaches halfof its
R2
steady state value in 12005)
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15s
 Alternating Current e153

9~. Thesclfinductance of the motor ofan electric fan is 10 H. In In the given circuit the sliding contact is pulled outwards
order to impart maximum power at 50 Hz, it should be such that electric current in the circuit changes at the rate of
connected to a capacitance of 12oos1 8 Ns. At an instant when R is 12 n the value of the current
(a) 8µF (b) 4µF (c) 2µF (d) lµF in the circuit will be __A. ' IJ••· 23, 2025 (1)1
I 03. When a coil is connected across a 20 V de supply, it draws
95. In an LCR series a.c. circuit, the voltage across each of the a current of5 A. When it is connected across 20 V, 50 Hz ac
components, L, C and R is 50V. The voltage across the LC supply, it draws a current of4 A. The self inductance of the
combination will be 120041 coil i9 _ _ mH. (Taken=3) fAprll 9, 2024 (l)J

(a) IOOV (b) 50✓ 2V 104. A capacitor ofreactance 4..fjn and a resistor of resistance
(c) 50V (d) OV (zero) 4n are connected in series with an ac source of peak value
96. In a LCR circuit capacitance is changed from C to 2 C. For 8✓ 2V . The power dissipation in the circuit i s _ W.
the resonant frequency to remain unchangcd, the inductance IAprll 9, 2024 (II))
should be changed from L to 105. When a de voltage of JOOV is applied to an inductor, a de
current ofSA flows through it. When an ac voltage of200V
120041
peak value is connected to induct.or, its inductive reactance
(a) U2 (b) 2L (c) 4L (d) IJ4
97. The power factor of an AC circuit having resistance (R) and is found to be 20✓3 n. The power dissipated in the circuit
is _ _ _W. )April 6, 2024 (1)1
inductance (L) connected in series and an angular velocity
106. Fer a given series LCR circuit it is found that maximum current
ro is 120021 is drawn when value of variable capacitance_ is
(a) RI WL (b) RJ(R2 + ffi2£2)112 2.5 nF. Ifresistance of200n and I 00 mH inductor is being
(c) wIJR (d) Rl(R2 - 002£2)112 used in the given circuit. The frequency of ac source is
_ _ x 103 Hz. (given -rc2 = 10) (April 6. 2024 (11)1
98. The inductance between A and Dis 120021
107. An ac source is connected in given series LCR circuit. The

~
rms potential difference across the capacitor of
20 µFis .............. V. JApril 5, 2024 (1)1
L= IH R=300n

(a) 3.66 H (b) 9 H (c) 0.66H (d) 1H C= 20 µF

@ ~ i"i1111K'rk \'ahtr Qnrstions

a
99. An inductor ofreactance l 00 n, capacitor ofreactance 50
V = 50✓2 sin IOOt volt
n, and a resistor ofresistance 50 n are connected in series
with an AC source of l OV, 50 Hz. Average power dissipated 1 1o-3
108. A series LCR circuit with L = OO mH, C = - - F and
by the circuit is _ _ _ W. [April 7, 2025 (11)1 It 7t
R = IO n, is connected across an ac source of220 V, 50 Hz
100. For ac circuit shown in figure, R = I 00 kn and C = I00 pF supply. The power factor of the circuit would be _ __
and the phase difference between ~" and ( V8 - J/A) is 90•. (Jan. 27, 2024 (II)]
The input signal frequency is I or rad/sec, where 'x is _ _ 109. In the given figure, an inductor and a resistor are connected

in series with a battery ofemfE volt. £2b J / s represents the

maximum rate at which the energy is stored in the ma&rnetic
C b
V,,, {rv: field (inductor). The numerical value of - will be
a
(April 13, 2023 (1)1
R
L,.4H
!April 6, 2025 (1)1
JOI. In a series LCR circuit, a resistor of 300 n, a capacitor
of25 nF and an inductor of l 00 mH are used. For maximum
current in the circuit, the angular frequency of the ac
E
source is _ _ x 104 radians s- 1. fJan. 23, 202s (llll
110. Acoil has an inductanceof2 Hand resistance of2 n.A
102. 3H IO V is applied across the coil. The energy stored in the
magnetic field after the current has built up to its equilibrium

~ value will be x L0-2 J. fAprll 11, 2023 (11)1

111. A series LCR circuit is connected to an ac source of220V,
50Hz. The circuit contain a resistance R = 1000 and an
12V~ inductorofinductivereactance XL= 79.6n. The capacitance
ofthe capacitor needed to maximize the average rate at which
R energy is supplied will be _ _ µF. fFcb. 1, 2023 Clll
a154
MW1:q
112. An inductor of0.5 mH, a capacitor of20 µF and resistance of
20 n are connected in series with a 220 V ac source. If the E=lOV
current is in phase with the emf, the amplitude ofcurrent of
the circuit is ✓ x A. The value ofx is• (Jan. 31, 2023 (Ill r=lOO
113. Aseries LCR circuit consists ofR = 800. XL= IOOO, and Xe R=lOOO
-= 400. The input voltage is 2500 ca;() 00 irt) V. The amplitude
ofcurrent, in the circuit, is._ _ _ _A.
JJao. 31, 2023 (11)1
114. An inductor of inductance 2 µHis connected in series with
a resistance, a variable capacitor and an AC source of R'=200n
frequency 7 kHz. The value of capacitance for which 122. The effective current I in the given circuit at very higlt
I frequencies will be _ A . 1July26,20ll{lij
maximum current is drawn into the circuit is - Fwherethe
X
value ofx is_ _. 40 50.!"ff

(Taken=-)
22
IJ■ n. 29, 2023 (11)1
T0.5 µF T0.51Lf
7 ~~, t\Vr--J
115. An LCR series circuit ofcapacitance 62.5 nF and resistance 0.5 µF 10 0.8 µF 40 0.8 µF 20

of 50 n. is connected to on A.C. source of frequency 2.0

220V
kHz. For maximum value ofamplitude of current in circuit,
the value of inductance is ___mH. (take n2 = I 0) 123. A series LCR circuit with R =
250
n and X = 7on is
JJan. 25, 2023 (1)1 11 L II
116. Aseries LCR circuit is connected to an AC source of220 V, connected across a 220 V, 50 Hz supply. The value (i
50 Hz. Tile circuit contains a resistance R = Son, an induct.or capacitance needed to maximize the average power oftbe
ofinductive reactanceXL = 700, and a capacitor ofcapacitive
• • w1·11 be _ _ µF. (Take: 7t = 22 )
c1rcutt
7
10. The
X
reactance Xe= 1300. The power factor ofcircuit is
JJunc 30, 2022 (IJI
value of xis: JJan. 2s, 2023 (ll)I
117. A capacitor of capacitance 500 µF is charged completely 124. An inductor of0.5 rnH, a capacitor of200 µF andarcsisa
usingadc supply of IOOV. It is now connected toan inductor of 20 are connected in series with a 220 V ac sowte. lfthe
ofinductance 50 mH to form an LC circuit. The maximum current is in phase with the emf, the frequencyofacsoune
current in LC circuit will be ___ A. (July 29, 2022 (Jill will be_x l <>2 Hz. (June 29, 2022 (IQJ
118. The frequencies at which the current amplitude in an LCR 125. A telegraph line oflength 100 km has a capacityof0.01 f!FI
km and it carries an alternating current at 0.5 kiloq,:lepcr
series circuit becomes }i times its maximum value, are 212 second. Ifminimum impedance is required, then thevalue(i
the inductance that needs to be i_ntroduced in i smcs
rad s-1and 232 rads- 1. The value of resistance in the circuit
is R = 5 n. The self inductance in the circuit is _ _ __ - - - mH. (if 1t = Jw) (June 28,lOll(lM
126. An AC source is connected to an inductance oflOOmH,1
mH • (July 28, 2022 (Ill
capacitance of I00 µ F and a resistance of 1200 as showa
119. For the given circuit the current through battery of 6 Vjust
in figure. The time in which the resistance having athermal
after closing the switch 'S' will be _ _ A.
capacity 2 J0 /C will get heated by 16°C is ___s.
[July 28, 2022 (II)]

2/f . IOOµF
m 4n 2n

6V 2n 20✓2 sin I00 t

120. To light, a 50 W, I00 V lamp is connected, in series with a [June 28, 2022 (1)1
127. In the given circuit, the magnitude of VL and Ve arc twice
5 that of VR. Given that/= 50 Hz, the inductanccofthccoilis
capacitor of capacitance ~ µF with 200 V, 50Hz AC
1t,J X 1
source. The value ofx will be __ [July 27, 2022 (Ill - -mH. ThevalueofKis _ _ __
J21. As show in the figure, in steady state, the charge stored in Kit
the capacitor is ___ x 10--0c. !July 27, 2022 (11)1
 Alternating Current 8155 (~
Ve
133. An inductor of IO mH is connected to a 20 Vbattery through a
resista-of!Oknandaswitch.Aflaalongtime, mien maximwn
current is set up in the circuit, the current is switched off. The
\
X
current in the circuit after J µsis mA. Then xis equal to
VL 100
_ _. (Takee-1=0.37) (NA, July 25, 2021 (1)1
134. Two circuits are shown in the figure(a)& (b).At a frequency
(June 28, 2022 (11)1 o~ ___ rad/s the average power dissipated in one cycle
128, A 110 V, 50 Hz, AC source is connected in the circuit (as wtll be same in both the circuits.
shown in figure). The current through the resistance 55 n, Hl 40µ F

c:J:c~
at resonance in the circuit, will be ............... A.

C 220V 220V
figure (a) figure (b)
INA, July 25, 2021 (11)(
135. In an LCR series circuit, an inductor 30 mH and a resistor I
AC Source Qare connected to an AC source of angular frequency 300
(June 26, 2022 (1)1 rad/s. The value ofcapacitance for which, the current leads
129. In a series LCR circuit, the inductance, capacitance and re- the voltage by 45° is ..!.. x I0-3 F. Then the value of x is
sistance are L = I00 mH, C = I00 µF and R = Ion respec- X
tively. They are connected to an AC source of voltage 22OV __ (NA, July 20, 2021 (1)1
•and frequency of50 Hz. The approximate value ofcurrent in 136. A sinusoidal voltage of peak value 250 V is applied to a
thecircuitwillbe ____ A. . (June 25, 2022 (II)[ series LCR circuit, in miich R= sn, L= 24 mH and C = (,() µF.
The value of power dissipated at resonant conditions is x
IOOmH IOOµF 100 kW.
The value ofx to the nearest integer is ___.
(March 16, 2021 (1)1
220 V, 50 Hz 137. A series LCR circuit is designed to resonate at an angular
130.For the given circuit the curr~nt i through the battery when frequency%= IQ5rad/s. The circuit draws 16 W power from
the key in closed and the steady state has been reached 12O,V source at resonance. Thevalueofresistance 'R' in the
is _A. [Sep. I, 2021 (II)( circuit IS !1. (Feb. 24, 2021 (JI))
Hl 138. The angular frequency of alternating current in a L-C-R
circuit is I00 rad/s. The components connected are shown
in the figure. Find the value ofinductance of the coil_ _
:0.5ml IigO.2 H Hand capacity of condenser is _ _.

L
30 R = 60!1
30V
15V
;:rn ;:rn R'=4OQ
C IOV L!ii 20V

131.At very high frequencies, the effective impedance of the

given circuit will be_._ _ 0.
[NA, Aug. 3 I, 2021 (II)) [ Feb. 2S, 2021 (1)1
10 0.5F 2Q O.SF 139. A part ofa complete circuit is shown in the figure. At some
instant, the value ofcurrent I is I A and it is decreasing at a
rate of 102A s- 1. The value of the potential difference Vr-
VQ• (in volts) at that instant, is _ _.
INA Sep. 06, 2020 (1)1
L=5O mH I R=2 n
~~
p 30V Q
220V 14O.In a series LR circuit, power of 400 Wis dissipated from a
132.An ac circuit has an inductor and a resistor ofresistance R in
series, such that XL= 3R Now, a capacitor is added in series source of25O V, 50 Hz. The power factor ofthe circuit is 0.8. In
such that Xe= 2R The ratio of new power factor with the old order to bring the power factor to unity, a capacitor of value
C is added in series to the Land R. Taking the value C as
power factor of the circuit is ✓5: x . The value of x is
(A, Aug. 27, 2021 (II))
( :) µF, then value ofn is _ _. (NA Sep. 06, 2020 (11))
3

l
1156 wµ,nww
147. For the given circuit, comment on the t)pe oftransfonncr
used. !Morch 16,?Ul(IIJI
'Topic 3-Transformers and LC Oscillatlo1
ii jL O.IIA

$ \lultiJ'I•• <'hoi,-r <jm--tion,

141. A transformer has an efficiency of 80% and works al I OV

and 4 kW. If the secondary voltage is24OV, then the current
in the secondary coil is:
(a) 1.33A (b) 13. 33A
IFeb. I. 2024 (11)1
22ovA
ml!$ I~
D
60W 1l
(c) 1.59A (d) IS. I A
142. A capacitor of capacitance IOOµF is charged to a potential (a) Step-up transformer
of 12 V and connected to a 6.4 mH inductor to produce (b} Auto transformer
oscillations. The maximum current in the circuit would be: (c) Step down transformer
IJ••· 29. 2024 (1)1 (d) Aux.illiarytransfonncr
(a) 1.2A I.SA
(b)
148. For the given input voltage waveform Vin(I), the OUlpll
(c) 3.2A (d) 2.0A
voltage waveform V0 (1). across the capacitor is comaJy
143. Primary side ofa transformer is connected to 230 V, 50
depicted by : !Sep. 06, 2021 UJ
Hz supply. Turns ratio of primary to secondary winding
islO: I. Load resistance connected to secondary side is
46il. The power consumed in it is :
(a) 12.5 W
(c) 11.5 W
(b) 10.0 W
(d) 12.0 W
(Jan. 27, 2024 (11)1
+5VrL,

---ov-f':~--~~1,~~
n~
Ii vr
144. In an LC oscillator, if values of inductance and capacitance
become twice and eight times, respectively, then the 0
resonant frequency of oscillator becomes x times its initial
resonant frequeru:y Wo· The value of x is: Jan. 2S, 2023 (I)] v (tJ
0

(a) 1/4 (b) 16

(c) 1/16 (d) 4 (a)
145. A transfom1er operating at primary voltage 8 kV and sec-
ondary voltage 160 V serves a load of8O kW. Assuming the 5),s I Oµs I 5µ, 1'

transformer to be ideal with purely resistive load and work-

ing on unity power factor, the loads in the primary and sec-
ondary circuit would be (Jul~· 28, 2022 (IIJI
(a) 800 n and 1.06 n (b),v0v]
(b) 10nand soon ! i +
(c) 800·UandO.3Hl 5µs IOµs I5µs I

(d) 1.06 n and 500 n

146. Match List-I with List-II • (June 2S, 2022 (1)1 V0 (t)

List-I Llst-U
(c) 2V
(A) AC generator (I) Detects the presence of current in
the circuit Sµs IOµs ISµs t'
(B) Galvanometer (II) Converts mccbanicalenergy into
electrical energy V0 (t)
(Q Transformer (l]n Works on the principle of reso-
nance in AC circuit
(DJ Metal detector (IV) Changes an alternating voltage for
(d) +K--7]
smaller or greater value Sµs IOµs ISµs
Choose the correct answer from the options given below:-
(ai (A)-(11), B-(n, (C)-(IV), (D)-(Jln 149. A transformer consisting of300tums in theprimmyandlll
turns in the secondary gives output power of2.2kW. lf6c
(b) (A)-(II),8-(1), (C)-(III),(D)-(IV)
C cJrrent in the secondary coil is IO A, then the inpld~
(c) (A)-(III), 8-(IV), (C)-{Il), (D)-(1)
aqd current in the primary coil are : (I0AprlltltllX
(d) (A)-(TIO, 8-(0, (C)-(II),(D)-(IV)
 Alternating current 8157

(a) 220 V and 20 A (a) 4A (b) 2A

(b) 440 V and 20 A (c) 6A (d) IOA
(c) 440Vand5A
(d) 220Vaod IOA ~ ~ ~11m,•ri1· \'aim• Q1"'°'tiou..

150. A power transmission line feeds input power at 2300 V to 154. A power transmission line feeds input power at 2.3kVto a
a step down transformer with its primary windings having step down transformer with its primary winding having 3000
4000 turns. The output power is delivered at 230 V by the turns. The output power is delivered at 230 V by the
transformer. If the current in the primary transformer is SA transformer. The current in the primary ofthe transformer is
and its efficiency is 90%, the output current would be: SA and its efficiency is 90%. The winding of transformer is
(Online April 16, 2018 S, 9 Jan. 2019 (11)1 made of copper. The output current of transformer is
(a) 50 A (b) 45 A - - - - A. IJ-■. 30, 2024 (t Ill
(c) 35 A (d) 25 A 155. An oscillating LC circuit consists of a 75 mH inductor and a
151. In an oscillating LC circuit the maximum charge on the 1.2µF capacitor. If the maximum charge to the capacitor is
capacitor is Q. The charge on the capacitor when the energy 2.7µC. The maximum current in the circuit will be _ _mA.
is stored equally between the electric and magnetic field is !April 8, 2023 ( 1)1
12003( 156. An ideal transformer with purely resistive load operates at
12 kV on the primary side. It supplies electrical energy to a
Q Q
number ofnearby houses at 120 V. The average rate ofenergy
(a) 2 (b) ✓3
consumption in the houses served by the transfonner is 60
kW. The value of resistive load (Rs) required in the
Q
secondary circuit will be _ _mil. l,\pril 6, 2023 (Ill
(c) Ji (d) Q
157. A radio set requires 12 V (D.C.) for its operation. The D.C.
152. The core of any transformer is laminated so as to 120031 source is constructed by using a transformer and a rectifier
(a) reduce the energy loss due to eddy currents circuit, which are operated at 220 V (A.C.) on standard
(b) make it light weight domestic A.C. supply. The number of turns of secondary
(c) make it robust and strong coil are 24, then the number ofturns ofprimary are_•_ _
(d) increase the secondary voltage !F~b. 24, 2021 (Ill
153. In a transformer, number ofturns in the primary coil arc 140
and that in the secondary coil are 280. Ifcurrent in primary
coil is 4 A, then that in the secondary coil is 120021

Part-I (JEE Advanced)

R,
Topic 1 • AC Circuit. LCR circuit. Quality
and Power Factor R, c, R,

® 1 )l( Q-," ith 01w ( 'orn'<·t .\tll!Wrr R,

I. An AC voltage source of variable angular frequency oo and c,
fixed amplitude V0 is connected in series with a capacitance
C and an electric bulb of resistance R (inductance zero).
R,
When ro is increased 1201 OJ
(a) the bulb glows dimmer
(b) the bulb glows brighter R,
(c) total impedance of the circuit is unchanged C,
(d) total impedance of the circuit increases R1 =I.Cl. R2 =2n, C1 =4µF, C2 =2µF
2. Find the time constant (in µs) for the given RC circuits in the 8 8 8 8
given order respectively 12006 • 3"· -11 (a) 18,4,
9 (b) 18,
9 ,4 (c} 4, 18,
9 (d) 4,
9 , 18
 -....
1158
circuit. Oo1h the batleries hnvc the s a m e ~
.l. When nn /IC source of emf e = £0 sin( 1001) is connc'Clcd
ncro~~ n circuit, the pha~e d1tTcrcnce between the emf e ond elcctromo1ivc force (emf) and the polarities snu~de Of~
!n the figure. Ignore m~tunl inductanc:rtasind~
the current i in the rncuil is observe-cl 10 he n/4 , ns sho1111 1
1nduc1ors. The current / in the middle w· "''"' ,~
in lhc diilb'Tnm. lf1hecircui1 consisti possiblyonlyofR-Cor maximum magnitude I.,., al time 1 = t. Which;1:achci 11
R-L or l-C in series, find 1hc relationship between the two sta1cmen1s is (arc) true'/ fOI~~
elcmcnls • llOIIJ\I Ud,, lite
(al R•lkn,C• I011F
{b)R=IH l,C=l11F
, ,'['\
,
,7,
I'/'.\ ,'/\
~ L I

(c) R•IHl,L =IO/f

(d) R=lkO, l•l/f I' I
;, ~ Int, ,., \ 11111 \11,11,·r ,"
4. Consider on LC c1rcui1, 111i1h inductance l = 0.1 II and
capncunncc C = Io·3F, kepi on n plane. The area of 1he
~
circuit is I,,,:_ II is placed in n cons1on1 magnetic field of
V • V
s1rcng1h B11 which is perpendicular 10 1he plane of the (o) I..._,= 2R (b) /max= 4R
circuit. Al time r = 0, lhc magnetic field strength starts
increasing linearly ns B = B0 + pr wilh P= 0.0-l T ,rt. The
maximum magnitude of1he currcnl in the circuit is l 2L
(c) t= Rln2 (d) t=Rln2
nL4. I• \d,•, 20lll
5. Two inductors Lt (inductance I mH, in1cmal resistance 3 n) IO. lnthecircuilshown,L= I µH,C= I µFandR=Jkn.Tit CJ I
nnd L, (inductance 2 mil, internal resistance 4 Q), and o • • •h
areconnected m scncs wu an a.c. source V = v0sinc,x 111
resistor R(resistance 12 Q) arc all connected in parallel across
shown. Which of1he following options is/arc correct?
a 5 V bat1cry. The circuit is switched on at time t = 0. The
ratio of the moximum 10 the minimum current IAd1.111:1
(l,N, / I min) dra\111 from the baucry is IAd,. ?0161 L=lµHC= lµF R=lkfl

E7
~: :t ,11111t·rir \i•\\ "km 11.,,...,1 <2111,tion,·
Siem for Qs. 6-7
In a circuit. a metal filoment lamp is connected in series with a
capacitor ofcapacitance C µF across a 200 V, 50 Hz supply. The
power consumed by the lamp is 500 W while the voltage drop (a) The current will be in phase wi1h lhe volLlge ii
ucross it is 100 V. Assume that there is no inductive load in 1he w= 104 rad.s•t
circuit. Take mis values of the vohages. The magnitude of the (b) The frequency al which the current will be in pill!! 1
phase-angle (in degrees) between the current and the supplyvolt- with the voltage is independent ofR
nge is 4). (c) At w ~ 0 the current flowing through lhe cimiit
Assume. 11✓3" 5. becomes nearly zero
6. The value ofC is__ I \d•·. zozt J (d) At w» ID6 rad. s•t, the circuit behaves likeacipaciu
7. The value of<j) is __. IAd'-2021) I J. In 1he given circuit, 1he AC source has w = 100 rad'l
8. The inductors of two LR circuits are placed next to each Considering the inductor and capacitor to be ideal, theama
other. as shown in the figure. The values of the self- choicc(s) is (are) JllllJ
induclnnce ofthe inductors. resistances, mutual-inductance IOOµf 1000
and applied voltages arc specified in the given circuit. After
both the s11itchcs are closed simultaneously, the total work
done by the baueries against the induced EMF in 1he
inductors by the time the currents reach their steady state
values is_ _ _ mJ. !Adv. 20201
lf1 •SO lf:•10O
20V

1□•
D
(a) The current through 1he circuit,/ is OJ A.

~T ~ ~,,
Ji (b) The current through lhc circuit,/ is 0.3./iA
(c) The vohage across I00 fl resistor= Io./iY
/ (d) The voltage across 50 0 resistor= 10 V

® ti 'I( <l-- "ith One• or ,ton• than 01lt' ('orn·d \11..,,H'l

® 7 \luld11111° J•'ollo11i1;;i'
1
I 2. The circuit shown in the figure contains an inductor: L,
9. In the figure below, the switches St and S2 are closed capacitor C0, a resistor Ro and an ideal battery The al(IIII
simultaneously at I = 0 and a current starts to flow in the also contains two keys K1 and K2. Jnilially, both the kl)S
 nd there is no charge on the capacit
arc ope~ 3 K is closed and immediately
instan'., ,cYnJ be 1 . After a long time
or. At an
after this the current A B R
a15 9 q
c? . '
. o_ is ,ou 10 1 , the current attains
in ''O d state value 1 . The ft .
2 rea er, ~ 1s closed and
a stca Y usly Kt is ope ned and the voltage across c
51•111_ultaneo
with amplitude V and angular frequen 0
osc1tlatcs 0 cy Wo·
K, C,• IOµ F
·'- -1
sr-----~
15. In a series L-R circuit (l c
35 mH and R = I I 0), a variable
l•2 5m H emf source (V c V sin (1)1) of
0
R.• 50 V,,,,, • 220 V and frequency
_ _ _j'K , )('· ,.. .
50Hzisapplied.Findthecurrcnt
I or
'\. I J •
20V amplitude in the circuit and 2T
Match the quantities mentioned in_ List phase of current with
-I with their values in
List-II and choose the correct opuon. respect to voltage. Draw current-time grap
!Adv. 202◄ 1 h on given graph
List-I List-II (11='2211).
(P) The value of11 in 1200
◄ • ◄ \hr bl
(I) 0 16. An inductor of
Ampcre1s inductance l =400
(Q) The valu_c of/2 in (2) 2
An,pcre1s mH and resistors of
resistances R = 2fl £
(R) The val~c of~ • in
kilo-rad1ans/s 1s
(S) The value of V, in
(3) 4

(4) 20
and R2 = 2 n arc
1

connected to a s •
J R,

Volt is battery of R1
(5) 200
(a) P ➔ l;Q ➔ 3;R ➔ 2;S ➔ 5 em f£= 12 Vas shown in the figure. The
internal resistance
(b) P ➔ l;Q ➔ 2;R ➔ 3;S ➔ 5 of the battery is negligible. The switch
Sis closed at time I=
(c) P ➔ l;Q ➔ 3;R ➔ 2;S ➔ 4 0. What is the potential drop across las
(d) P ➔ 2;Q ➔ 5;R ➔ 3;S ➔ 4 a function oftime?
After the steady state is reached, the swit
13. Aseries LCRcircuit is connected ch is opened. What
to a 45 sin((l)l) Volt source. is the direction and the magnitude ofcurr
The resonant angular frequency of the ent through RI as
circuit is I0 5 rad s•t a functioo of time?
and current amplitude at resonance is 1 12001-s MorS..I
. When the angular
frequency of the source is w = 8 x Io◄0 17. A solenoid has an inductance of
rad s·1, the current IO henry and a resistance
amplitude in the circuit is 0.051 • IfL = of2 ohm. It is connected to a IO volt batt
0 50 mH, match each ery. How long will
entry in List-I with an appropriat e value from List-II and it take for the magnetic energy to reach
choose the correct option. 1/4 ofits maximum
IAdv. 20231 value?
List-I 119 9'-J ~tar t.sl
List-II 18. A circuit containing a two position

-
(P) 10 in mA switch Sis shown in fig.
(1) 44.4
(Q} The quality factor of the 11991. 4 + ◄ M1 rbl
circuit
(R) The bandwidth of the circuit
(2) 18
R3
,~
-..--.~ I
(3) 400 2µF
in rad s· 1 R, 2ll IOI R,
(S) The peak power dissipated
(4) 2250 2ll 12V
al resonance in Watt
R,
(5) 500
A
i {2 'WMWII.--!
(a) P ➔ 2,Q ➔ 3, R ➔ 5, S ➔ 1 3\" m 30J R,
(b) P ➔ 3,Q ➔ 1,R ➔ 4,S ➔ 2 _l,_
(c) P ➔ 4, Q ➔ 5, R ➔ 3, S ➔ I IOmH
.(d) P ➔ 4, Q ➔ 2, R ➔ I, S ➔ 5 (a) The switch S is in position 'I'.
Find the potential
~ 10 l-luhjMi\l• l'mhll•n" difference VA - V and the rate ofproll
8 uction ofjoule
heat inR 1•
l4. In the figure both cells A and Bare (b) If now the switch Sis put in position
ofequal emf. Find R for 2 atr • Ofind
which potential difference across batt
ery
long time after the switch is closed. Inte A will be zero, (i) • steady current in R, and
rnal resistance of (ii) the time when current in R is half the
baucries A and Bare , and , respecti 4 steadyvalue.
1 2 vely (r1> r 2). Also calculate the energy stored in the indu
12004 - ◄ Maries! ctor lat that
time
 ~ ~~
1160

-~----~--~--~---~
Toplc•2: Miscellaneous (Mixed eoncepts)
problem•
(D) /

to/
0, V2is proportional(~)
[::!]
6mlt
lµF

I(
""' V •

®, a I:-.i11111,:;:;;:-,,.11 sh•m 11.!::.,1Q111-.ti1111-._ (t)~

Sttm for Qs. No. 19-20

In the circuit sho\\11 below, the switch S is connected to position ~f :;
P for a long time so thnt the charge on the capacitor becomes q1
µC. Then S is switched to position Q. After a long time, the charge
® ~
ll ( 01111in•l1t•11,io11 llw,i1I Qt"'°'1iotL~•
on the capacitor is qi µC.
~ Jfl, 2ll Passage 1

i~ I 1 In the given circuit the capacitor (C) may be charged th1

19.
'11
The magnitudeofq 1 is _ _ .
T'µF r (Adv, 20211
resistance R by a battery Vby closing switch S . Also Wh ~

inductor(L).
2
REJ'.7., •~
opened and S is closed the capacitor is conncbcd in serien Sl is

The magnitude ofq, is_. IAdv. 20211

20.

@ 6 ~I('(~" ith Onr or ~Ion• thrm 0111• l'orn~·t .\n"wr I

21. A series R- C circuit is connected to AC voltage source. :7s,
Consider two cases; (A) when C is without a dielectric L
medium and (B) when C is filled with dielectric ofconstant 4. 23. At the start, the capacitor w.is uncharged. When~ .
The current I~ through the resistor and voltage V, across closed and S2 is kept open, the time constant ofthiscirQlit~•
the capacitor arc compared in the two cases. Which of the Which ofthe following is correct ll*-i,t~
following is/arc true? 12011I
(a) after time interval t, charge on the capacitor is £!
(a) 1: > 1: (b) 1: <If 2
(b) after time interval 2t, charge on the capacitor DfO'
(c) V/>Vl (d) vt <Vl (l -c2)

® j
l.
\111td1 l111· FollowinA -- (c) the work done by the voltage source will be balfci6r
heat dissipated when the capacitor is fullyclwpd
22. You are given many resistances, capacitors and inductors. (d) after time interval 2t, charge on the capacitor is
These are connected to a variable DC voltage source (the CV(l-e-1)
first two circuits) or an AC voltage source of50 Hz frequency 24. When the capacitor gets charged completely, S1 is ClpCIIII
(the next three circuits) in different ways as shown in and S1 is closed. Then, (2006-l\l,-~
Column U. When a current I (steady state for DC or rms for (a) at I= 0, energy stored in the circuit is purely in tbein
AC) Dows through the circuit, the corresponding voltage of magnetic energy
V1and V2 , (indicated in circuits) are related as shown in (b) arany time 1 > 0, current in the circuit is in the_
Column I. Match the two 120101 direction
Column 1 Column II (c) at 1 > 0, there is no exchange of energy bclwcal lie
v, v, inductor and capacitor
0 Ii: is proportional (p) ~· -
to , J * • 1
(A) H lµF (d) at any time 1 > 0, instantaneous current in thecili,
6m .
maybe V 1£
V"'i ,
V
V1 V2 25. Given that the total charge stored in theLCcirtUitisQ,fr
(B) I ,. 0, V2 > V1 (q) I ~ 0, the charge on the capacitor is 12•-lll.~

(C) V1 =0,V2 = V (r)--

~YI yl
(a) Q=Q0 cos(~➔ ic)
(c) Q=-LCd 2Q
(b) Q=G,c os(i-i)

I d2Q
(d) Q=-rc t/J2
d,2

0 Passage 2
Athc:rmal power plant produces electric power of600 kW•d '
V.

which is to be transported to a place 20 km away from die,,,-

~:•,mu•
plant forcab
..,w . ~
:c rs '
conle of lar usage. It can be• transponcd either directly
ge current carrying capa •
city or by using a
.
m the step-up transformer
is
11 61 ~
consumers has to be supplied I : IO. If the power to the
of step-up and step-dow t
b au on n transformers at the two at
~ oftums in the primary to tha 200 V, the ratio ofthe number
10
e drawback ofthe d'1r~t tra • • • th 1ar
cndS- ~ In the metho nsm1ss 1on IS e- . ~e ~ergy t in the secondary in the ste
d us mg tra nsform down transfcrnter is p-
. ·,.,
d1SS1,,.- uo n- ers, the d1ss1pat1on is
11 In this me thod , a step-up , me • (a) 200: I (b) 150: I
(c) 100: I
tra
··"
rn~• 511 . 1a soer.that the current 1s
plaOI side , nd a step-d
• reduced
ns ,or r 1s used at lhe
to a smaller value. At the ®' -~ ~ln kh 111<' Fol11111inl,\
(d) 50: I

_.,..,,,r own transformer is used to 28. Acircuit with an electr

cOI""'". s erncrs , . . supply pov,-er ical
at the specifie d lower voltage. It 1s reasonable to nected with an AC sourceload having impedance .. is con-
1olhc~SUthepowct' cable as
is purely resistive and thetra sourtcvoltagevarics in tim shown in the diagram. Toe
JSS1110C at __,. power factor nsfonncrs e as V(r)• 300 sin(400r) V,
'deal wtu• unity. All the currents an r is time in J. List-I shows va where
1
aJC . cd arc rms values. d voltages possible currents i(r) in the rious options for the load. Toe
rnco h d' reel transmission me
00 0 given in List-II. circuit as a function oftim
(Adv. lll e uc
16. If ~~ ~- 1 is used, thod with a cable of resistanl) !Adv. 2025]
the power dissipation! (in ce
0.

~
. . ¾) during
smiss
iran 'l) 1on 1s(b) 30
(c) «> (d) 50
(a) h method using the tra
11, ~:i,: ns
number ofturns in the prima
formers, assume that the rat
ry to that in the secondary
io Choose the option that descr
ibe
the entries in List-I to those s the correct match bctWccn
in List-ll. IA<h.10251
List-I
Ust-O

5□
30 0
2.5
(Pl -- -/ lf \M , (\) i(1) O
-2.5
- 50 Jt/2 3"'2 21t
4001

30 0 1oomH
{Q) ~ (2) i(1):
~

-05xflL V J
It 31112 2K
4001

(R)
SOµf
.1 ~
30 0 25 mH
(3) i(I)
10□
~
-5
-10
0 xfl 4001" 31112 2K

50 µF 60 n 125 mH 10
{S) 1~ (4) i(1) 2
o 0[w

~o ~
-20 11/2 400r"

(5) i(l):f?
\'7

- 5 ~
0 1112 1t 31112 21t
400t
{a) (P)-+(3),(Q) ➔ (5),(R)
➔ (2),(S) ➔ (l)
(b) (P) ➔ (l),{Q) ➔ (5),(R) ➔
(2),(S) ➔ (3)
(c) (P) ➔ (3),(Q) ➔ (4),(
R)-+(2), (S) ➔ (l)
(d) (P) ➔ (l).(Q) ➔ (4),(R) ➔
(2),(S) ➔ (5)
1162 e@maf
' Answer Key
-. ----- ----- ----- ----- ----- ---- .~

Part-A(JEE Main) __.

1 (c) 17 (a) 33 (c) 49 (c) 65 (d) 81 (d) 97 (b) 113 (25) 129 (22) 145 <cL
2 le 18 (22) 34 (a) so (b) 66 (d) 82 (c) 98 (d) 114 (3872' 130 (\0) I~ ~
(2) (a)
147 ~
J (a) 19 (8) JS (d) SI (a) 67 (None) 83 (d) 99 (I) 115 (100) 131
4 (c' 20 (242) 36 (c) 52 (c) 100 (5) 116 (8) 132 (I) 141 lJ!1.
68 (b) 84 fa)
5 (b) 21 (11) 37 (c) SJ (b) 101 (2) 117 (10) 133 (74) 14' (c)
(c) 69 (c) 85 ~

6 lbl 22 (c) 38 (n) 54 (a) (a) (c) 101 (3) 118 (250) 134 (SO(}) 151 l!l
70 86
7 (c) 23 (b) 39 (a) (10) 119 (1) 135 (3) 151 (c)
~
55 (None) 71 (a) 87 (b) 103
8 (d' 24 (n) 40 lb) (c) 104 (4) 120 136 (3.q()(j\
(3) 152 (al
56 (c) 72 (a) 88
9 (b) 25 (b) 41 (a) 57 (c) 73 (b) 89 (c) 105 (250) 121 (10) 137 (900) 15! ~
Cd) 26 (10) 122 (44) 138 (0.8, 250'
154 (4?.l
10 (a) 42 (a) 58 (c) 74 lb) 90 (al 106
11 (a) 27 (50) 123 (500) 139 (33) 155 ~
(c) 43 (c) 59 (a) 75 (b) 91 (a) 107
(5) J,fO (400) 15' ~
12 (a) 28 (c) 44 (d) 60 (d) 76 lb) 92 lb) 108 (I) 114
(b} 157 (4«7)
(25) 125 (100) 141

-
~
13 (d) 29 (d) 45 (c) 61 (a) 77 (c) 93 (a) 109
{b)
14 lbl JO (d) 46 lb) 62 (b) 78 (c) 94 (d) 110 (625) 126 (15) J.C2
15 (c) JI (c) 47 (c) 63 (d) 79 (c) 95 (d) 111 (40) 117 (0) 143
(c) -
(a)
(242) 118 (0) 144
~

16 (b) 31 Cd) 48
--
(b) 64 (c) 80 /d) 96 (a) Ill
Part-B (JEE Advanced)
(c) 27 (b) -
1 (b) 4 (4) 7 (60.00) 10 (b, c) (b) 20 (0.67) 23 (b) 2S
2 (b) s (8) 8 (55.00) 11 la, c)
13
19 11.33) 21 (a,c) 24 (d) 26 (a)
28 {a)
-
I~
3 (a) 6 (100.00) 9 (b. d) 12 (a) 22 A-r,s,t; B-q,r,s,t; C-p,q; D-q,r,s,t

"