Note: Please read the Important Instructions and Disclaimer file before solving the MCQs 9. ELECTROSTATICS
1)
The constant K of an insulator can be A) dielectric 4 B) -4 C) 0 D) 0.4
2)
The dielectric constant K of an insulator cannot be A) 4 B) 6 C) 9 D) infinity
3)
A charge q is placed at the centre of a cube of side a. The electric flux through any one face of the cube is A) q/ 0 B)
q/3 0
C)
q/6 0
D)
6q/ 0
4)
A hollow spherical conductor of radius 2m carries a charge of 500 C. Then the electric field strength at its surface is A) Zero 6 B) 1.125 × 10 N/C 6 C) 2.25 ×10 N/C D) 4.5 × 106 N/C
5)
Two thin concentric hollow conducting spheres of radii R1 and R2 bear charges Q1 and Q2 respectively. If R1 > R2, then the potential at a point at a distance r, such that R1 > r > R2, is A) (1/4 0 ). (Q1 + Q2)/ r B)
(1/4 0 ). [(Q1/ r ) + (Q2 / R2)]
C)
(1/4 0 ) . [(Q1/ R1) + (Q2 / R2)]
D)
(1/4 0 ). [(Q1 / R1 ) + (Q2 / r)]
6)
If the dielectric constant and dielectric strength be denoted by K and X respectively, then a material suitable for use as a dielectric in a capacitor must have A) high K and high X B) high K and low X C) D)
low K and high X low K and low X.
7)
Two identical metallic solid spheres A & B each of radius r kept at a distance d apart (d > 2r). A is given + q charge. B is now earthed and then disconnected from earth. What is now the charge on sphere B? A) – q(d-r)/2r B) –qr/d C) –q D) zero
8)
A hollow spherical conductor of radius 1 m has a charge of 2.5 C. Then the electric potential at a point distant 5 metre from the centre of the spherical conductor is A) zero B) 22.5 × 103 volt C) 4.5 × 103 volt D) 45 × 103 volt .
9)
If one penetrates a uniformly charged metallic sphere, the electric field strength E A) increases B) decreases C) remains the same as at the surface D) is zero at all points
10)
A. hollow spherical conductor of radius 1 meter has a charge of 250 C, the electric intensity at a point distance 0.5 metre from the centre of the spherical conductor is A) Zero B) 2.25 × 106 N/C C) 45 × 104 N/C D) 9 × 104 N/C
11)
An electric field can deflect A) X rays B) Neutrons C) – rays D) rays
12)
Two identical metal plates are given positive charges Q 1 and Q2 (Q2 < Q1) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is A) (Q1 + Q2)/(2C) B) (Q1 + Q2)/C C) (Q1 – Q2)/C D)
13)
(Q1 – Q2)/(2C)
Two spherical conductors A and B of radius a and b (b > a) are placed in air concentrically. B is given charge + Q coulomb and A is grounded. The equivalent capacitance of these is ab A) 4 0 ba B) 4 0 a b C)
4 0 b
D)
4 0
b2 ba
14)
Capacitance (in F) of a spherical conductor with radius 1 m is A) 1.1 × 1 -10 B) 10-6 C) 9 × 10-9 D) 10-3
15)
Capacitance of a parallel plate capacitor becomes
times its srcinal value if a 3 dielectric slab of thickness t = d /2 is inserted between the plates [ d is the separation between the plates]. The dielectric constant of the slab is A) 6 B) 2 C) D)
16)
4
8 4.
A parallel plate air capacitor has a capacitance of 100 F . The plates are at a distance d apart. A slab of thickness t = d and dielectric constant 5 is introduced between the parallel plates. Then the capacitance can be A) 100 F . B) 50 F . C) 200 F . D) 500 F .
17)
3 capacitors 2, 3 and 6 F are joined with each other. What is the minimum effective capacitance? 1 A) F . 2 B) 1 F . C) D)
2 F . 3 F .
18)
A spherical drop of capacitance 1 F is broken into eight droplets of equal radii. Then the capacitance of each droplet will be 1 A) F . 2 1 B) F . 4 1 C) F . 8 D) 8 F .
19)
A parallel plate air capacitor has a capacitance of 100 pF. The plates are at a distance d apart. A slab of thickness t (t < d) and dielectric constant 5 is introduced between the parallel plates. Then the capacitance will be A) 50 pF B) 100 pF C) 200 pF D) 500 pF
20)
The capacity of parallel plate air capacitor is 10 F and it is given a charge of 40 C . The electrical energy stored in this capacitor is A) 80 × 10-6 ergs B) 800 ergs C) 8000 ergs D) 20000 ergs
21)
A parallel plate capacitor has circular plates of 10 cms radius separated by an air gap of 1 mm. It is charged by connecting the plates to a100 volt battery. Then the change in energy stored in the capacitor when the plates are moved to a separation of 1 cm and when the plates are maintained in connection with battery is A) loss of 12.5 ergs B) gain of 12.5 ergs C) gain of 125 ergs D) loss of 125 ergs.
22)
A parallel plate capacitor has a capacitance of 50 F in air and 110 F when immersed in an oil. The dielectric constant of the oil is A) 0.45 B) 0.55 C) 1.10 D) 2.20.
23)
The plates of a parallel plate air capacitor are 2 cm apart. A slab of dielectric constant 5 and thickness 1 cm is placed between the plates. The distance between the plates is altered so as to keep the capacitance of the new capacitor unchanged. The new separation between the plates is A) 2.2 cm B) 2.8 cm C) 3.0 cm D) 3.2 cm
24)
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is A) increased proportional to 2 B) decreased proportional to 1/2 C)
increased proportional to
D)
decreased proportional to 1/ 2
2
25)
Three capacitors, with capacitances of 1 F , 2 F and 3 F are connected in series. Each capacitor gets punctured if a potential difference just exceeding 100 volts is applied. If the group is connected across a 300 volt circuit then the capacitor most likely to puncture first is A) of capacitance 1 F B) of capacitance 2 F C) of capacitance 3 F D) of capacitance 6 F
26)
The capacity of a pure capacitor is 1 farad. In DC circuit its effective resistance will be A) zero B) 1 C) infinite 1 D) r 2
27)
A potential difference of 300 volts is applied to a combination of 2 F & 8 F capacitors connected in series. The charge on the 2 F capacitor is A) B) C)
2.4 × 10 4 coulomb 7.2 × 10 4 coulomb 4.8 × 10 4 coulomb
D)
9.6 × 10
4
coulomb
28)
A capacitor of capacitance of 1 F withstands the maximum voltage 6 kV while a capacitor of capacitance 2 F withstands the maximum voltage of 4 kV. If the two capacitors are connected in series , then the two capacitors combined can take up a maximum voltage of A) 2.4 kV B) 5 kV C) 9 kV D) 10 kV
29)
A metal plate of thickness half the separation between the capacitor plates of capacitance C, is inserted between the plates. The new capacitance is A) C C B) 2 C) 0 D) 2C
30)
The capacitance of a parallel plate capacitor is 16 F when a glass slab is placed between the plates. The potential difference reduces to
1 8
th of the srcinal value.
What is the dielectric constant of the glass? A) 4 B) 8 C) D) 31)
16 32
A 10 mF capacitor has been charged to a potential of 100 V. Suddenly, it explodes. The energy given out in this explosion is A) 500 J B) 100 J C) 5 × 10 4 J D) 300 J
32)
The amount of energy a capacitor can store is called its A) resistance B) Capacitance C) Inductance D) reactance
33)
A condenser having capacity of 2 F is charged to 200volt & then the plates of the capacitor are connected to a resistance wire. The heat produced in Joules will be A) 4 × 10 4 J B) 4 × 10 10 J C) 4 × 10- 2 J D) 4 × 10 2 J
34)
A 500 F capacitor is charged at a steady rate of 100 C per second. How long will it take to raise the potential difference between the plates of the capacitor to 10 volt? A) 5s B) C) D)
10 s 50 s 100s
35)
A variable capacitor and an electroscope are connected in parallel to a battery. The reading of the electroscope would be decreased by A) Increasing the area of overlapping of the plates B) Placing a dielectric between the plates C) Decreasing the distance between the plates D) Decreasing the battery potential
36)
The dimensions of 0 are A)
[ A 3T 2 L2 M 3 ]
B) C) D)
[ A0 T 0 L0 M 0 ]
A 2 M 1 L3T 4 2 3 3 1 [A T L M ]
37)
A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is ‘a’ and that of spherical shell is ‘b’ (b>a). The electric field at a distance R (a
3Q 4 0 R 3Q 4 0 R 2
Q 4 0 R
38)
Which one of the following graphs represents the variation of electric field strength E with distance ‘r’ from the centre of a uniformly charged non conducting sphere?
39)
A conducting sphere of radius 5 cm is charged to 15 µ C. Another uncharged sphere of radius 10 cm is allowed to touch it for enough time. After the two are separated, the surface density of charge on the two spheres will be in the ratio A) 1:1 B) 1:2 C) 3:1 D) 2:1
40)
When a negatively charged conductor is connected to earth, A) Protons flow from the conductor to the earth B) Electrons flow from the earth to the conductor C) Electrons flow from the conductor to the earth D) No charge flow occurs.
41)
A Gaussian sphere encloses an electric dipole within it. Total flux across the sphere is A) Zero B) half that due to a single charge C) double that due to single charge D) dependent on position of the charge
42)
In the electric field of a point charge q, a certain charge is carried from point A to B,C,D, & E. Work done is
A) B) C) D) 43)
Zero along any one of the path AB, AC, AD & AE Is least along the path AB Is least along the path AD Is least along the path AE.
A cylinder of cylinder radius R axis. and length L isflux placed uniform fieldisEgiven parallel to the The total for in thean surface of electric the cylinder by A) 1) R 2 E B) 2) R 2 L2 C) 0 D) 2 R 2 E
44)
An uncharged sphere of metal is placed inside a charged parallel plate capacitor. The lines of force look like
45)
A hollow spherical conductor of radius 2m carries a charge of 500 C. Then electric field strength at its surface is A) 1.125 10 6 N/C B) 2.25 10 6 N/C C) Zero D) 4.5 10 6 N/C
46)
A tennis ball which has been covered with charges is suspended by a thread so that it hangs between two metal plates. One plate is earthed, while other is attracted to a high voltage generator. The ball A) hangs without moving B) swings backward & forward hitting each plate in turn C) is attracted to the high voltage plate and stays there D) is repelled by earthed plate and stays there.
47)
A & B are two metal plates arranged as shown. A small particle having mass ‘m’ and negative charge ‘q’ is held at rest at P. A constant potential difference is applied between A & B (plate A being at higher potential). The particle is then released. Its path as it falls will be best represented by the curve
48)
For a charged conductor of arbitrary shape, inside the conductor A) E and V are zero B) E=0, but V is same as on the surface and non-zero C) V 0 and E 0 D) E is non-uniform but V is zero everywhere.
49)
Six equal capacitors each of capacitance C are connected as shown. The equivalent capacitance between A & B is
B)
2 C 3 3 2 C
C) D)
2C 4C
A)
50)
Three capacitors of 4 F each are to be connected in such a way that the net capacitance is 6 F. Then A) All three should be connected in series B) All three should be connected in parallel C) Two should be connected in parallel and one in series D) Two should be connected in series and one in parallel
51)
An infinite number of capacitors of capacitances C, 2C, 4C, 8C, 16C, 32C ……. are connected in series. The equivalent capacitance is A) O C B) 2 C) 2C D) infinite
52)
Two identical parallel plate capacitors are connected in series to a battery of 100 V. A dielectric slab of dielectric constant 4.0 is inserted between the plates of second capacitor. The potential difference across the capacitor will now be respectively, A) 50 V, 50 V B) 80V, 20 V C) 20V, 80 V D) 75V, 25 V
53)
To make a condenser of 16 F, 1000 volts, how many condensers are needed which have written on them “8 F, 250 volts”? A) 40 B) 32 C) 8 D) 2
54)
Four capacitors each of 25 F are connected in a circuit as shown in figure. The d.c. voltmeter V reads 200 V. The charge on each plate of capacitor is
A) B) C) D) 55)
2 10 3 C 2 10 2 C 5 10 3 C 5 10 2 C
When 2 charged conductors are connected by a wire, A) there is always loss of energy B) there is always gain of energy C) there will not be any change in energy D) there is loss or gain of energy depending upon the potentials of the conductors.
56)
An air filled parallel plate capacitor has a capacity of 2 pF. The separation of the plates is doubled and the space is filled with wax. If capacity is increased to 4 pF, the dielectric constant of wax is A) 2 B) 3 C) D)
4 6
57)
A capacitor is fully charged by a 20 V battery. It is then discharged through a resistance wire of a specific heat 300 J/ Kg/K and of mass 0.2 kg. If the temperature of the wire rises by 0.1 K, then the value of the capacitance is A) 20 F B) 0.03 F C) 33.3 F D) 0.06 F
58)
When a P.D. of 1000 V is applied between A and B, a charge of 0.75 C is stored in the system of capacitors. The value of C is
59)
A) B) C)
0.75 F 0.8 F 1 F
D)
0.2 F
The equivalent capacitance between A and B in the figure shown is
A) B) C)
C/2 C 2C
D)
3 C/2
60)
In series combination of capacitors, potential drops across the individual capacitors are equal to A) direct ratio of capacitors B) inverse ratio of capacitors C) direct ratio of charges stored D)
inverse ratio of charges stored.
61)
An electrolytic capacitor is marked 8 F, 220 V. It can be used in a circuit where the p.d. across the capacitor may be A) 1000 V B) 500 V C) 300 V D) 200 V
62)
Two capacitors of capacitance 2 F and 3 F are connected in series across a potential difference of 5 V. The ratio of charge on the first capacitor to the charge on the second capacitor will be A) 2:1 B) 2:3 C) 1 D) none of these.
63)
What will be the area of pieces of paper in order to make a paper condenser of capacitance 0.04 µF, if the dielectric constant of paper is 2.5 and its thickness is 0.025 mm? A) 1 m2 B) 2 10-3 m2 C) 4.51 10-3 m2 D) 10-3 m2
64)
The of the dielectric to increase the capacitance is due to A) action electric polarization B) movement of charges to the sides of dielectric C) neutralization of charges D) dipole orienting parallel to the plates.
65)
In electrolytic capacitors positive terminal is A) one on which aluminium oxide film is not formed B) either of the two terminals C) one on which aluminium oxide film is formed D) none of the above.
66)
In electrolytic capacitors dielectric is A) thin film of aluminium oxide on cathode B) thin film of aluminium oxide on anode. C) electrolyte used D) not present.
67)
Submarine cables act as A) parallel plate capacitor B) spherical capacitor C) cylindrical capacitor with outer cylinder earthed D) cylindrical capacitor with inner cylinder earthed.
68)
Dielectric polarization is the phenomenon A) in which atomic dipoles are aligned in the direction of electric field and reduce the electric field between the plates. B) In which atomic dipoles are aligned in the direction of electric field and increase the electric field between the plates. C) In which atomic dipoles are aligned opposite to the direction of electric field and reduce the electric field between the plates. D)
In which atomic dipoles are aligned opposite to the direction of the electric field and increase the electric field between the plates.
69)
A 4 F capacitor is charged to 400 V and then its plates are joined through a resistance of 2 . The heat energy produced in the resistance is A) 0.16 J B) 0.32 J C) 0.64 J D) 1.28 J
70)
The energy acquired by a charged particle of 4 µ C when it is accelerated through a potential difference of 8 volt will be A) 3.2 10 7 J B) 3.2 10 5 J C) 2 10 6 J D) 2 10 5 J
71)
An air-filled parallel plate capacitor has a capacitance of 10 12 F. The separation of the plates is doubled and wax is inserted between them, which increases the capacitance to 2 10 12 F. The dielectric constant of wax is A) 2.0 B) 3.0 C) 4.0 D) 8.0
72)
When a capacitor is connected to a battery A) no current flows in the circuit at all B) a current flows in the circuit for sometime and then decreases to zero C) the current keeps on increasing, reaching a maximum value when the capacitor is charged to the voltage of the battery D) an alternating current flows in the circuit.
73)
Seven capacitors each of capacitance 2 F are to be connected in a configuration to obtain an effective capacitance of (10/11) F. Which of the combinations shown in the figure will achieve the desired result?
74)
A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles A) the charge on the capacitor increases B) the voltage across the plates decreases C) the capacitance increases D)
the electrostatic energy stored in the capacitor increases.
75)
The electric field between the plates of a fully charged capacitor is E. If a material of dielectric constant k is introduced between the plates, the electric field at a point between the plates A) remains unchanged B) decreases C) D)
increases becomes E/k
76)
The plates of a parallel plate capacitor are 10 cm apart and have area equal to 2m2. If the charge on each plate is 8.85 10 10 C , the electric field at a point A) between the plates will be zero B) outside the plates will be zero C) between the plates will change from point to point D) between the plates will be 25NC-1
77)
The force with which the plates of a parallel plate capacitor, having charge Q and area of each plate as A, attract each other is A) directly proportional to Q B) directly proportional to A C) inversely proportional to A D) inversely proportional to A2
78)
A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric slab is now introduced to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q, V, E and U are related to the previous quantities as A) Q Q0 B)
V V0
C)
E E0
D)
Q0 Q
79)
Two parallel plate capacitors of capacitances C and 2 C are connected in parallel and charged to a potential difference V by a battery. The battery is then disconnected and the space between the plates of capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes V A) B) C) D)
80)
A parallel plate capacitor of capacitance 100 pF is to be constructed by using paper sheets of 1.0 mm thickness as dielectric. If the dielectric constant of paper is 4.0, the number of circular metal foils of diameter 2.0 cm each required for this purpose is A) B) C) D)
81)
K 1 2V K 2 3V K 2 3V K 3
10 20 30 40
Three capacitors of capacitances C1=2 F, C2=2 F and C3=1 F are connected to a 100 V supply as shown in the figure. What is the charge on capacitor C 2?
A) B) C) D)
4 10-5C 6 10-5C 8 10-5C 1.2 10-4C
82)
What is the equivalent capacitance between A and D of the network shown in the figure?
A) B) C) D) 83)
200 pF 100 pF 200 pF 3 50 pF
Figure showsWhat a network of the capacitors the numbers indicate capacitances in microfarad. must be value ofwhere capacitance C if the equivalent capacitance between points A and B is to be 1 F?
31 A) B) C) D)
23 F 32 F 23 33 F 23 34 F 23
84)
A 2 F capacitor C1 is charged to a voltage 100 V and a 4 F capacitor C2 is charged to a voltage 50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel connection? A) 1.7 J B) 1.7 10-1 J C) 1.7 10-2 J D) 1.7 10-3 J
85)
What are the dimensions of electrical permittivity? A) ML-2 T -2 Q-2 B) M-1 L2 T -3 Q-1 C) M-1 L-3 T2 Q2 D) M-1 L3 T -2 Q-2
86)
If n drops, each of capacitance C and charged to a potential V, coalesce to from a big drop, the ratio of the energy stored in the big drop to that in each small drop will be A) n:1 B) n 4 / 3 :1 C) n 5 / 3 :1 D) n 2 :1
87)
A parallel plate capacitor is made by stacking 10 identical metallic plates equally spaced from one another and having the same dielectric between plates. The alternate plates are then connected. If the capacitor formed by two neighbouring plates has a capacitance C, the total capacitance of the combination will be C A) 10 C B) 9 C) 9C D) 10 C
88)
Figure shows four capacitors connected to an 8 V power supply. What is the potential difference across each 1 F capacitor?
A) B) C) D) 89)
1V 2V 3V 4V
Figure shows three capacitors connected to a 6 V power supply. What is the charge on the 2 F capacitor?
A) B) C) D)
1 C 2 C 3 C 4 C
90)
Figure shows five capacitors connected across a 12 V power supply. What is the potential drop across the 2 F capacitor?
A) B) C) D) 91)
The force with which the plates of parallel plate capacitor, having charge Q and area of each plate A, attract each other is A) zero B) C) D)
92)
6 C 8 C 10 C 12 C
Q2 0A Q2 2 0 A
Q2 2 0 A
Three capacitors of equal capacitances have a net capacitance C1 when they are connected in series and a net capacitance C2 when they are connected in parallel. The ratio C1/C2 is 1 A) 3 1 B) 6 1 C) 9 1 D) 12
93)
The magnitude of the electric field in the annular region of a charged cylindrical capacitor A) is the same throughout B) is higher near the outer cylinder than near the inner cylinder C) varies as 1/r where r is the distance from the axis D) varies as 1/r2 where r is the distance from the axis.
94)
n identical capacitors are joined is parallel and the combination is charged to a voltage V. The total energy stored is U. The capacitors are now disconnected and joined in series. The total energy stored in the series combination will be U A) n B) U C) nU D) n 2U
95)
A parallel plate capacitor is made by stacking n equally spaced identical plates connected alternately. If the capacitance between any two plates is C, the total capacitance of the capacitor is A) nC C B) n C) C D) (n-1)C
96)
If the potential difference between the plates of a capacitor is increased by 0.1%, the energy stored in the capacitor increases by very nearly A) 0.1% B) 0.11% C) 0.144% D) 0.2%
97)
Three capacitors connected in series have an effective capacitance of 2 F. If one of the capacitors is removed, the effective capacitance becomes 3 F. The capacitance of the capacitor that is removed is A) 1 F B) C) D)
3 2 2
F
F 3 6 F
98)
The effective capacitance of two capacitors of capacitances C1 and C2 (with 25 C2>C1) connected in parallel is times the effective capacitance when they are 6 connected in series. The ratio C2/C1 is 3 A) 2 4
B)
3 5
C)
3 25
D) 99)
6
A parallel plate capacitor of value 1.77 F is to be designed using a dielectric material (dielectric constant 200, breakdown strength of 3 106 Vm-1). In order to make such a capacitor, which can withstand a potential difference of 20 V across the plates, the separation d between the plates and the area A of the plates can be
(0 A) B) C) D) 100)
-12
8.85 -610 d=10 m, d=10-5m, d=10-4m, d=10-4m,
2
-1
-2
CN m ) A=10-3m2 A=10-2m2 A=10-4m2 A=10-5m2
A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to a potential difference 2V. The charging battery is then disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is A) zero B) C) D)
3 CV 2 2 25 CV 2 6 9 CV 2 2
101)
A parallel combination of 0.1 M resistor and a 10 F capacitor is connected across a 1.5 V source of negligible resistance. The time (in seconds) required for the capacitor to get charged up to 0.75 V is approximately A) B) log e 2 C) D)
102)
Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is
A) B) C) D) 103)
log10 2 zero
zero q/2 q 2q
Two identical capacitors, have the same capacitance C. One of them is charged to potential V1 and the other to V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is 1 A) C (V12 V22 ) 4 B) C) D)
1 C (V12 V22 ) 4 1 C (V1 V2 ) 2 4 1 C (V1 V2 ) 2 4
104)
A metallic shell has a point charge q kept inside its circular cavity. The charge is not exactly at the centre of the cavity. Which of the following diagrams correctly represents the electric lines of force?
105)
If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21%. The srcinal charge on the capacitor (in coulomb) is A) 10 B) 20 C) 30 D) 40
106)
A parallel plate capacitor of capacity 100 F is charged by a battery of 50 volts. The battery remains connected and if the plates of the capacitor are brought closer so that the distance between them becomes half the srcinal distance, the additional A) 125energy 10-3 given by the battery to the capacitor in joules is: B) 12.5 10-3 C) 1.25 10-3 D) 0.125 10-3
107)
Between the plates of a parallel plate capacitor of capacitance C, two parallel plates, of the same material and area same as the plate of the srcinal capacitor, 1 are placed. If the thickness of these plates is equal to th of the distance between 5 the plates of the srcinal capacitor, then the capacitance of the new capacitor is 5 A) 3C B) C) D)
108)
A cube of side b has a charge q at each of its vertices, the electric field at the centre of the cube is 4q A) 2 B) C) D)
109)
3 C 5 3 C 10 10 C 3
3 b 3q b 2 2q b 2 zero
A long thin flat sheet has a uniform surface charge density . The magnitude of the electric field at a distance r from it is given by A) B) C) D)
2 r 2 r
110)
Two parallel plane sheets 1 and 2 carry uniform charge densities ( 1 > 2) (see Fig.). The electric field in the region marked I is
111)
1
2
1
A)
-
B)
- 2 2
C)
-
D)
-
2
1 2 2
1 2 2
In Q.110 what is the electric field in the region marked II? 1 A) 2 B) C) D)
2 2 1 2 2 1 2 2
1
and
2
112)
In Q. 110 the electric field in the region marked III is ( 1 2 ) A) 2 -
C)
( 1 2) 2
D)
113)
2
( 1 2 ) 2
The magnitude of the electric field on the surface of a sphere of radius r having a uniform surface charge density is A) B) C) D)
114)
( 1 2 )
B)
2 r 2 r
Six charges, each equal to + q, are placed at the corners of a regular hexagon of side a. The electric field at the point of intersection of diagonals is A) zero 1 q B) 4 a 2 C) D)
1 4 1
6q 2
a 3q
4 2a 2
115)
A pendulum bob of mass m carrying a charge q is at rest with its string making an angle with the vertical in a uniform horizontal electric field E. The tension in the string is mg A) sin B) mg C) D)
116)
A point charge + q is placed at the mid point of a cube of side L. The electric flux emerging from the cube is q A) B) zero C) D)
117)
qE sin qE cos
6qL2
q 6 L2
A metallic solid sphere is placed in a uniform electric field. In the figure, which path will the lines of force follow?
A) B) C) D)
1 2 3 4
118)
Eight dipoles of charges of magnitude e are placed inside a cube. The total electric flux coming out of the cube will be 8e A) 16e
B)
e
C)
zero
D) 119)
A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy attained by the particle after moving a distance x is A) q Ex2 B) qE2x C) qEx D) q2Ex
120)
There is a uniform field of strength 10 3 Vm-1 along the y-axis. A body of mass 1 g and charge 10 -6 C is projected into the field from the srcin along the positive xaxis with a velocity of 10 ms-1. Its speed (in ms -1) after 10 second will be (neglect gravitation) A) 10
121)
B)
5 2
C) D)
10 2 20
64 water drops having equal charges combine to form one bigger drop. The capacitance of the bigger drop, as compared to that of smaller drop will be A) 4 times B) 8 times C) D)
16 times 64 times
122)
Four capacitors, each of capacitance 50 F are connected as shown in the figure. If the voltmeter reads 100 V, the charge on each capacitor is
A) B) C) D)
2 10-3 C 5 10-3 C 0.2 C 0.5 C
123)
Three condensers of capacity 2 µ F, 4 µ F and 8 µ F respectively, are first connected in series and then connected in parallel. The ratio of the equivalent capacitance in the two cases will be A) 7:3 B) 49 : 4 C) 3:7 D) 4 : 49
124)
Which material sheet should be placed between the plates of a parallel plate capacitor in order to increased its capacitance? A) mica B) copper C) D)
tin iron
125)
A capacitor of capacitance C = 2 F is connected as shown in the figure. If the internal resistance of the cell is 0.5 , the charge on the capacitor plates is
A) B) C) D) 126)
zero 2 C 4 C 6 C
The electric field between the plates of a fully charged capacitor is E. If a material of dielectric constant 2K is introduced between the plates electric field at a point between the plates will be A) E B) 2KE C) 4K2E E D) 2K
127)
Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V by a battery. The battery is then disconnected and the space between the plates of capacitor C is completely filled with a material of dielectric constant K = 3. The potential difference across the capacitors now becomes V A) B) C) D)
4 2V 5 3V 5 3V 6
128)
In the network shown in the figure, C 1 = 6 F and C = 9 F. The equivalent capacitance between points P and Q is
A) B) C) D) 129)
3 F 6 F 9 F 12 F
Three capacitors, each of capacitance C = 3 mF, are connected as shown in the figure. The equivalent capacitance between points P and S is
A) B) C) D)
1 F 3 F 6 F 9 F
130)
A parallel plate air filled capacitor shown in the Fig. (a) has a capacitance of 2 F. When it is half filled with a dielectric of dielectric constant k = 3 as shown in Fig. (b), its capacitance becomes
A) B) C) D) 131)
1
F 3 1 F 3 F 9 F
A parallel plate air filled capacitor shown in Fig. (a) has a capacitance of 2 F. When it is half filled with a dielectric of dielectric constant k= 3 as shown in Fig. (b), its capacitance becomes
A)
4 F
B) C) D)
3 F 1.5 F 0.5 F
132)
In the arrangement show in the figure, each capacitor has a capacitance C = 1F. What is the equivalent capacitance across PQ?
A) B) C) D)
0.5 F 1F 2F infinity
133)
A 2 F capacitor C1 is charged to a voltage 100 V and a 4 F capacitor C2 is charged to a voltage 50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel connection? A) 1.7 J B) 1.7 10-1 J C) 1.7 10-2 J D) 1.7 10-3 J
134)
A parallel plate capacitor of plate area A has a charge Q. The force on each plate of the capacitor is A) B) C) D)
135)
2Q 2
Q2 Q2 2 zero
A capacitor of capacitance C is fully charged by a 200 V supply. It is then discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat 2.5 102 J kg-1 K -1 and of mass 0.1 kg. If the temperature of the block rises by 0.4 K, what is the value of C? A) 500 F B) 400 F C) 300 F D) 200 F
136)
The capacitance of a parallel plate capacitor in air is 2 µ F. If a dielectric medium is placed between the plates, the potential difference reduces to 1/6 of the srcinal value. The dielectric constant of the medium is A) 6 B) 3 C) 2.2 D)
4.4
137)
The capacitance of a parallel plate capacitor is 5 F. When a glass slab of thickness equal to the separation between the plates is introduced between the plates, the potential difference reduces to 1/8 of the srcinal value. The dielectric constant of glass is A) 1.6 B) 5 C) 8 D) 40
138)
Four capacitors are connected as shown in the figure. The effective capacitance between points A and B will be
A) B) C) D) 139)
28
F 9 4 F 5 F 18 F
A parallel plate capacitor of value 1.77 F is to be designed using a dielectric material (dielectric constant 200, breakdown strength of 3 106 Vm-1). In order to make such a capacitor, which can withstand a potential difference of 20 V across the plates, the separation d between the plates and the area A of the plates should be( = 8.85 10-12 C2 N-1 m-2) A) B) C) D)
D = 10-6 m, A=10-3 m2 d = 10-5 m, A=10-2 m2 d = 10-4 m, A=10-4 m2 d = 10-4 m, A=10-5 m2
140)
If the diameter of earth is 128 102 km, then its capacitance will be A) 711 µ F B) 331 µ F C) 211 µ F D) 111 µ F
141)
A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. The capacitor is given some charge. As x goes from 0 to 3d, A) the magnitude of the electric field remains the same. B) the direction of the electric field changes continuously C) the electric potential increases continuously D) the electric potential increases at first time, then decreases and again increases.
142)
Two identical metal plates are given positive charges Q 1 and Q 2 (
Q1 Q2 C Q1 Q2 C Q1 Q2 2C
143)
A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants K 1, K2 and K 3 as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by
A)
B)
C)
D)
144)
1
K
K
1
K1 K 2 K1 K 2 K1 K 2
1 2K 3
2K 3
K = K1 + K2 + K3
A parallel plate capacitor of capacitance 5 F and plate separation 6 cm is connected to a 1 V battery and charged. A dielectric of dielectric constant 4 and thickness 4 cm is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is A) 2 C B) 3 C C) 5 C D)
145)
1 1 1 1 K K 1 K 2 2K 3
10 C
A condenser is charged to a potential difference of 200 volts, as a result of which it gains a charge of 0.1 C. When it is discharged, the energy released will be A) 1J B) 2J C) 10 J D) 20 J
146)
Two dielectric stabs, each of thickness d, area of one face
and dielectric 2 constant K1 and K2 are inserted between the plates of a parallel plate capacitor as shown in the diagram. Then the equivalent capacitance is
A) B) C) D)
147)
K1 K 2 0 A 2d K1 K 2 0 A 2 d 2 K1 K 2 0 A
K1 K 2 d ( K1 K 2 )
d
0 A
d , area of one face A and dielectric 2 constants K1 and K2, are inserted between the plates of a parallel plate capacitor with separation d and face area of one side of one plate. A as shown in the figure. Then the equivalent capacitance is. Two dielectric stabs each of thickness
A) B) C) D)
K1 K 2 0 A 2 d K1 K 2 0 A 2 d 2 K1 K 2 0 A
K1 K 2 d ( K1 K 2 )
0 A
d
148)
In an isolated parallel plate capacitor of capacitance C, the four surfaces have charges Q1, Q2, Q3 and Q4 as shown in the figure. The potential difference between the plates is.
A) B) C) D)
Q1 Q2 Q3 Q4 2C Q2 Q3 2C Q2 Q3 2C
Q1 Q4 2C
149)
A capacitor is connected to a cell of emf E and of some internal resistance. The potential difference of. A) cell is E B) cell is < E C) capacitor is < E D) capacitor > E
150)
In a parallel plate capacitor of capacity C, a metal sheet is inserted between the plate, parallel to them. The thickness of sheet is half of separation between plates. The new capacity is. A) 4C B) 2C C C) 2 C D) 4
151)
In the given circuit, a potential difference of 60 V is applied across AB. The potential difference between points M & N is.
A) B) C) D) 152)
In a parallel plate capacitor, the region between plates is filled by dielectric slab. The capacitor is connected to cell and slab is removed. Then A) some more charge is drawn from cell B) some charge is returned to cell C) D)
153)
10 V 15 V 20 V 30 V
the potential difference across cell is reduced work is done by external agent in taking the slab out.
The numerical value of the charge on either side of the capacitor C shown in the figure is
A) B) C) D)
CE CER
R2 r CER2 R2 r CER1 R1 r
154)
Given E = 5 volt, r = 1 ohm, R1 = R3 = 1 ohm, R2 = 4 ohm and each C = 3 F. Find numerical value of the charge on each plate.
A) B) C) D)
24 C 12 C 6 C 3 C
155)
A charged sphere of radius a is put in contact with another uncharged sphere of radius b. Show that ratio of srcinal surface density to that of final surface density of charge on first sphere is a A) b b B) a ab C) a b D) ab
156)
A parallel plate capacitor is made of 15 plates, each of 6 cm × 4 cm separated by a sheet of mica of dielectric constant r and constant thickness of 0.15 mm. Find its capacitance. A) 0.03 F B) 0.02 F C) 0.0119 F D) 0.198 F
157)
A parallel plate capacitor has a plate area A and plate separation d . It is charged to potential v and then battery is disconnected. Now a dielectric slab of dielectric constant r and of thickness d is inserted between plates. Find the energy change after insertion of the slab. 2 1 AV 1
A) B) C)
D)
r
r 2 1 0 AV r 1 2 d r 2 1 0V r 1 2 Ad r 2 1 V r 2 Ad r 1 0
2
d
158)
A parallel plate capacitor contains a mice sheet (thickness 10 -3m) and a sheet of fibre (thickness 0.5 × 10 -3m). The dielectric constant of mica & fibre are 8 and 2.5 respectively. Now fibre breaks down at an electric field of 6.4 ×106 Vm-1. What is the max. safe voltage that can be applied to fibre capacitor ? A) 1800 V B) 3600 V C) 4400 V D) 5200 V
159)
What is equivalent capacity in given system ?
A) B) C) D)
0A
d 2 0 A d 3 0 A d 4 0 A d
160)
Find the resultant capacitance.
A) B) C) D)
161)
4
0 A
d 3 0 A d 30A 2 d 20A 3 d
Three identical capacitors are first connected in series and then first and last conductors are connected to earth. A charge Q is given to second conductor of the first capacitor. Then potential of this conductor is.
A) B) C) D)
2Q 3C Q 3C 3C
Q 3C 2Q
162)
Find the equivalent capacity in system given below:
A) B) C) D) 163)
Find the charges in capacitors in given system.
A) B) C) D) 164)
C 2 C ( 2 - 1) 2 ( 3 1) C 2 3C 2 ( 5- 1)
5 C each 6 C each 8 C each 10 C each
What is the output voltage across 2C ?
A) B) C) D)
60V 20 V 30 V 40 V
165)
166)
An infinite number of identical capacitors, each of capacitance 1 F are connected as shown in the given figure. Then the equivalent capacitance between A and B is
A) B)
1 F 2 F
C)
1 F 2
D)
A capacitors of capacitance C is charged to a potential V. The total flux of the electric field over a closed surface enclosing the capacitor is. CV A) 2 0
B)
167)
CV
0
C)
zero
D)
2CV
0
If the electric flux entering and leaving an enclosed surface respectively is 1 and 2 , the electric charge inside the surface is A) ( 1 + 2) / 0 B) ( 2 - 1)/ 0 C) ( 1 + 2) 0 D) ( 2 - 1) 0
168)
A sheet of aluminium1 foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of capacitor is A) unchanged B) infinite C) increased D) decreased
169)
All charge on a conductor must reside only on its outer surface. This statement is true A) in all cases B) for solid spherical conductors only C) for hollow spherical conductors only D) for conductors which do not have any sharp points or corners
170)
A point charge Q is placed outside a hollow spherical conductor of radius R, at a distance r (r > R) from its centre C. The field at C due to the induced charges on the conductor is A) zero Q B) b. k r R 2
Q , directed towards Q r2 Q d. k 2 , directed way from Q r
C)
c. k
D) 171)
A positive point charge, which is free to move, is placed inside a hollow conducting sphere with negative charge, away from its centre. It will A) move towards the centre B) move towards the nearer wall of the conductor C) remain stationary D) oscillate between the centre and the nearer wall
172)
In a region of space, the electric field is in the x-direction and proportional to x,
i.e., E = E0x iˆ . Consider an imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates. The charge inside this volume is A) zero 3 B) Є 0 E 0a C) D)
1
0 1 6
E 0a 3 Є 0 E 0a
2
173)
A conducting sphere of radius R, and carrying a charge Q, is joined to an uncharged conducting sphere of radius 2R. The charge flowing between them will be A) Q/4 B) Q/3 C) Q/2 D)
174)
2Q/3
In an isolated parallel plate capacitor of capacitance C, the four surfaces have charges Q 1, Q 2 , Q 3, and Q 4 as shown. The potential difference between the plates is
Q Q Q Q A) B) C) D) 175)
1
2
2C
3
Q2 Q3 2C Q2 Q3 2C Q 1 Q4 2C
A capacitor of capacitance C is charged to potential difference V from a cell and then disconnected from it. A charge +Q is now given to its positive plate. The potential difference across the capacitor is now A) B)
176)
4
V Q V+ C Q C) V+ 2C Q D) Vif V < CV C, A capacitor is connected to a cell of emf and some internal resistance. The potential difference across the A) cell is B) cell is < C) capacitor is < D)
capacitor is >
177)
The capacitance of a conducting metallic sphere will be 1 µF if its radius is nearly A) 1.11 cm B) 10 cm C) 1.11 m D) 9 km
178)
Two large, identical and parallel conducting plates have surfaces X and Y, facing each other. The charge per unit area on X is 1, and on Y it is 2. 1 = + 2 in all cases A) B) 1 = - 2 only if a charge is given to one plate only. C) 1 = 2 = 0 if equal charge are given to both the plates. D) 1 > 2 if X is given more charge than Y.
9. ELECTROSTATICS Ques. No.
Answer
Ques. No.
Answer
Ques. No.
Answer
1
A
45
A
89
2
D
46
B
90
B B
3
C
47
B
91
D
4 5
B D
48 49
B B
92 93
C C
6
A
50
D
94
B
7
A
51
B
95
D
8
C
52
B
96
D
9
D
53
B
97
D
10
A
54
C
98
A
11
C
55
A
99
B
12
D
56
C
100
B
13
A
57
B
101
D
14
C
58
B
102
A
15
B
59
C
103
C
16
C
60
B
104
C
17
B
61
D
105
B
18
A
62
C
106
A
19
C
63
C
107
A
20
B
64
A
108
D
21
A
65
C
109
B
22
D
66
B
110
C
23
B
67
C
111
C
24
A
68
A
112
C
25
A
69
B
113
A
26
C
70
B
114
A
27
C
71
C
115
C
28
C
72
B
116
A
29
D
73
A
117
D
30
B
74
D
118
D
31 32
A B
75 76
D B
119 120
C C
33
C
77
C
121
A
34
C
78
A
122
B
35
D
79
C
123
D
36
C
80
A
124
A
37
C
81
C
125
C
38
C
82
C
126
D
39
D
83
B
127
C
40
C
84
B
128
A
41
A
85
C
129
D
42
A
86
C
130
C
43
C
87
C
131
A
44
C
88
C
132
C
Ques. No.
Answer
Ques. No.
Answer
Ques. No.
Answer
133
B
148
C
164
D
134
C
149
A
165
B
135
A
150
B
166
B
136
A
151
D
167
D
137
C
152
B
168
A
138 139
C B
153 154
C C
169 170
A C
140
A
155
C
171
C
141
C
156
C
172
C
142
D
157
A
173
D
143
B
158
D
174
C
144
C
159
C
175
C
145
C
160
D
176
A
146
B
161
A
177
D
147
C
162
A
178
C
148
C
163
D
