Electrostatic Potential and Capacitance

Five capacitors of capacitances C1 = C2 = C3 = C4 = 10 μF and C5 = 2.5 μF are connected as shown, along with a battery of 50 V. [figure] The equivalent capacitance and the charges on each capacitor respectively are :

1. 4 μF, 250 μC on C1 to C4 and 125 μC on C5
2. 5 μF, 250 μC on all capacitors
3. 5 μF, 125 μC on C1 to C4 and 25 μC on C5
4. 5 μF, 125 μC on all capacitors

Consider two uncharged capacitors of equal capacitance 200 pF. One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is :

1. 0.5 J
2. 1.0 10-6 J
3. 0.5 10-6 J
4. 1.0 J

Which of the following statements are correct ? Choose the correct answer from the options given below :

1. A, C and D only
2. A, C and E only
3. C, D and E only
4. A, B and D only

Three identical capacitors, P, Q and S, each of the capacitance C, are connected to a battery of voltage V, as shown in the figure. If the energy stored in the capacitor P and total energy stored in the system are UP and UT, respectively, then the ratio UPUT is: [figure]

1. 1/6
2. 2/3
3. 1/3
4. 1/2

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having uniform positive charge density , as shown in the figure. The initial and final positions of the charge are marked by A and B at distance 2R and 3R respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is R2n 0. The value of n is : ( 0 is the permittivity of vacuum) [figure]

1. 18
2. 2
3. 6
4. 9

Consider a fixed uniformly charged insulating sphere with radius R and total charge +Q. A point charge -q (q Q) with mass m is released from rest at a distance of 3R from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is: ( 0 is the permittivity of vacuum, neglect gravitational forces).

1. Qq4 0 mR
2. 3Qq4 0 mR
3. 2Qq3 0 mR
4. Qq3 0 mR

A point charge Q is placed inside a cavity within a solid isolated conducting sphere. Consider points A, B and C as shown in the figure, where the magnitudes of the electric fields are EA, EB, EC, respectively. The points B and C are at the same distance from the center of the solid sphere. The correct option is : [figure]

1. EA 0, EB < EC
2. EA = 0, EB = EC
3. EA 0, EB = EC
4. EA = 0, EB > EC

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness 38d and d2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1 = 1.25K2, the value of K1 is:

1. 1.60
2. 1.33
3. 2.66
4. 2.33

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is: (Take 14 0 = 9 109 SI units) [figure]

1. 3 105
2. 1 105
3. 0.5 105
4. Zero

In the following circuit, the equivalent capacitance between terminal A and terminal B is : [figure]

1. 2
2. 1
3. 0.5
4. 4

In the light of the above statements, choose the correct answer from the options given below:

1. Both A and R are true and R is the correct explanation of A.
2. Both A and R are true and R is NOT the correct explanation of A.
3. A is true but R is false.
4. A is false but R is true.

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then Choose the most appropriate answer from the options given below:

1. A, B and E only
2. A, C and E only
3. B, D and E only
4. A, B and C only

A 12 pF capacitor is connected to a 50 V battery, the electrostatic energy stored in the capacitor in nJ is

1. 15
2. 7.5
3. 0.3
4. 150

The capacitance of a capacitor with charge q and a potential difference V depends on

1. both q and V
2. the geometry of the capacitor
3. q only
4. V only

The value of electric potential at a distance of 9 cm from the point charge 4 10-7 C is [Given 14 0 = 9 109 N m2 C-2]:

1. 4 102 V
2. 44.4 V
3. 4.4 105 V
4. 4 104 V

The equivalent capacitance of the system shown in the following circuit is: [figure]

1. 3
2. 6
3. 9
4. 2

An electric dipole is placed as shown in the figure. [figure] The electric potential (in 102 V) at point P due to the dipole is ( 0 = permittivity of free space and 14 0 = K) :

1. ( 58 ) qK
2. ( 85 ) qK
3. ( 83 ) qK
4. ( 38 ) qK

The angle between the electric lines of force and the equipotential surface is

1. 0
2. 45
3. 90
4. 180

Two hollow conducting spheres of radii R1 and R2 (R1 >> R2) have equal charges. The potential would be

1. More on bigger sphere
2. More on smaller sphere
3. Equal on both the spheres
4. Dependent on the material property of the sphere

A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostatic energy stored by the system (b) is [figure]

1. 4.5 10-6 J
2. 3.25 10-6 J
3. 2.25 10-6 J
4. 1.5 10-6 J

The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to

1. C4
2. 2C
3. C2
4. 4C

The effective capacitances of two capacitors are 3 and 16 , when they are connected in series and parallel respectively. The capacitance of two capacitors are :

1. 1.2 , 1.8
2. 10 , 6
3. 8 , 8
4. 12 , 4

Six charges +q, -q, +q, -q, +q, and -q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q0 to the centre of the hexagon from infinity is ( 0 - permittivity of free space) [figure]

1. -q24 0 d (6 - 1 2 )
2. Zero
3. -q24 0 d
4. -q24 0 d (3 - 1 2 )

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : ( 0 = permittivity of free space)

1. E2Ad 0
2. 12 0E2
3. 0EAd
4. 12 0E2Ad

Polar molecules are the molecules :

1. having a permanent electric dipole moment
2. having zero dipole moment
3. acquire a dipole moment only in the presence of electric field due to displacement of charges
4. acquire a dipole moment only when magnetic field is absent

Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres ( 1 / 2) is :

1. R12R22
2. R1R2
3. R2R1
4. ( R1R2 )

The equivalent capacitance of the combination shown in the figure is : [figure]

1. 3C/2
2. 3C
3. 2C
4. C/2

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

1. 1980 V
2. 660 V
3. 1320 V
4. 1520 V

A short electric dipole has a dipole moment of 16 10-9 C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60 with the dipole axis is : ( 14 0 = 9 109 N m2/C2 )

1. 200 V
2. 400 V
3. zero
4. 50 V

The capacitance of a parallel plate capacitor with air as medium is 6 . With the introduction of a dielectric medium, the capacitance becomes 30 . The permittivity of the medium is : ( 0 = 8.85 10-12 C2 N-1 m-2)

1. 1.77 10-12 C2 N-1 m-2
2. 0.44 10-10 C2 N-1 m-2
3. 5.00 C2 N-1 m-2
4. 0.44 10-13 C2 N-1 m-2