CBSE Class 12 Physics Electrostatic Potential and Capacitance Worksheet Set B

CBSE Class 12 Physics Electrostatic Potential and Capacitance Worksheet Set B

 

Question. The four capacitors, each of 25 m F are connected as shown in fig. The dc voltmeter reads 200 V. The charge on each plate of capacitor is
(a) ± 2 x 10^-3C
(b) ± 5 x 10^-3C
(c) ± 2 x 10^-2C
(d) ± 5 x 10^-2C

Answer: B

Question. An air capacitor of capacity C = 10 mF is connected to a constant voltage battery of 12 volt. Now the space between the plates is filled with a liquid of dielectric constant 5. The (additional) charge that flows now from battery to the capacitor is
(a) 120 μ C
(b) 600 μ C
(c) 480 μ C
(d) 24 μ C

Answer: C

Question. A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitors is
(a) 3 U/2
(b) U
(c) U/4
(d) U/2

Answer: C

Question. Two capacitors when connected in series have a capacitance of 3 μF, and when connected in parallel have a capacitance of 16 μF. Their individual capacities are
(a) 1 μF, 2 μF
(b) 6 μF, 2 μF
(c) 12 μF, 4 μF
(d) 3 μF, 16 μF

Answer: C

Question. If a charge – 150 nC is given to a concentric spherical shell and a charge +50 nC is placed at its centre then the charge on inner and outer surface of the shell is
(a) –50 nC, –100 nC
(b) +50 nC, –200 nC
(c) –50 nC, –200 nC
(d) 50 nC, 100 nC

Answer: A

Question. A ball of mass 1 g carrying a charge 10–8 C moves from a point A at potential 600 V to a point B at zero potential. The change in its K.E. is
(a) – 6 × 10^–6 erg
(b) – 6 × 10^–6 J
(c) 6 × 10^–6 J
(d) 6 × 10^–6 erg

Answer: C

Question. Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is
(a) 16 times
(b) 8 times
(c) 4 times
(d) 2 times

Answer: D

Question. From a supply of identical capacitors rated 8 μF, 250V, the minimum number of capacitors required to form a composite 16 μF, 1000V is
(a) 2
(b) 4
(c) 16
(d) 32

Answer: D

Question. Calculate the area of the plates of a one farad parallel plate capacitor if separation between plates is 1 mm and plates are in vacuum
(a) 18 × 10⁸ m²
(b) 0.3 × 10⁸ m²
(c) 1.3 × 10⁸ m²
(d) 1.13 × 10⁸ m²

Answer: D

Question. A sphere of radius R has uniform volume charge density.
The electric potential at a points (r <R) is
(a) due to the charge inside a sphere of radius r only
(b) due to the entire charge of the sphere
(c) due to the charge in the spherical sheel of inner and outer radii r and R, only
(d) independent of r

Answer: A

Question. An air capacitor C connected to a battery of e.m.f. V acquires a charge q and energy E. The capacitor is disconnected from the battery and a dielectric slab is placed between the plates. Which of the following statements is correct ?
(a) V and q decrease but C and E increase
(b) V remains unchange, but q, E and C increase
(c) q remains unchanged, C increases, V and E decrease
(d) q and C increase but V and E decrease.

Answer: C

Question. The potential at a point x (measured in μ m) due to some charges situated on the x-axis is given by V(x) = 20/(x² – 4) volt The electric field E at x = 4 μ m is given by
(a) (10/9) volt/ μ m and in the +ve x direction
(b) (5/3) volt/ μ m and in the –ve x direction
(c) (5/3) volt/ μ m and in the +ve x direction
(d) (10/9) volt/ μ m and in the –ve x direction

Answer: A

Question. A large insulated sphere of radius r charged with Q units of electricity is placed in contact with a small insulated uncharged sphere of radius r´ and is then separated. The charge on smaller sphere will now be
(a) Q (r' + r)
(b) Q (r + r')
(c) Q/r '+ r
(d) Qr '/r '+ r

Answer: D

Question. Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass 1.96 × 10^–15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is
(a) 8
(b) 6
(c) 0.1
(d) 3

Answer: D

Question. Identical charges – q each are placed at 8 corners of a cube of each side b. Electrostatic potential energy of a charge + q which is placed at the centre of cube will be
(a) -4√2q²/πε₀b
(b) -8√2q²/πε₀b
(c) -4q²/√3πε₀b
(d) -8√2q²/πε0b

Answer: C

Question. A charge +q is fixed at each of the points x = x₀, x = 3x₀, x = 5x₀, .... upto ∞ on X-axis and charge –q is fixed on each of the points x = 2x₀, x = 4x₀, x = 6x₀, .... upto ∞ . Here x₀ is a positive constant. Take the potential at a point due to a charge Q at a distance r from it to be Q/4πε₀r . Then the potential at the origin due to above system of charges will be
(a) zero
(b) q/8πε₀x₀ log_e²
(c) infinity
(d) q log_e²/4πε₀x0

Answer: D

Question. Two equally charged spheres of radii a and b are connected together. What will be the ratio of electric field intensity on their surfaces?
(a) a/b
(b) a²/b²
(c) b/a
(d) b²/a2

Answer: C

Question. 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 similary charged to a potential difference 2V. The charging battery is now 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) 3/2 CV²
(c) 25/6 CV²
(d) 9/2 CV²

Answer: B

Question. A solid conducting sphere having a charge Q is surrounding by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of – 3Q, the new potential difference between the same two surfaces is
(a) V
(b) 2 V
(c) 4 V
(d) – 2 V

Answer: A

Question. In the electric field of an point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done is 

(a) least along the path AB
(b) least along the path AD
(c) zero along any one of the path AB, AC, AD andAE
(d) least along AE

Answer: C

Question. A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is 

(a) 0
(b) 54 μC
(c) 27μC
(d) 81 μC

Answer: C

Question. If a slab of insulating material 4 × 10^–5 m thick is introduced between the plates of a parallel plate capacitor, the distance between the plates has to be increased by 3.5 × 10^–5 m to restore the capacity to original value. Then the dielectric constant of the material of slab is
(a) 8
(b) 6
(c) 12
(d) 10

Answer: A

Question. Three capacitors each of capacity 4mF are to be connected in such a way that the effective capacitance is 6 mF. This can be done by
(a) connecting two in parallel and one in series
(b) connecting all of them in series
(c) connecting them in parallel
(d) connecting two in series and one in parallel

Answer: D

Question. If a capacitor 900 μF is charged to 100 V and its total energy is transferred to a capacitor of capacitance 100 μF then its potential is
(a) 200 V
(b) 30 V
(c) 300 V
(d) 400 V

Answer: C

Question. The capacitance of a metallic sphere is 1μF , then it’s radius is nearly
(a) 1.11 m
(b) 10 m
(c) 9 km
(d) 1.11 cm

Answer: C

Question. The capacitor, whose capacitance is 6, 6 and 3μF respectively are connected in series with 20 volt line. Find the charge on 3μF.
(a) 30 μc
(b) 60 μF
(c) 15 μF
(d) 90 μF

Answer: A

Question. The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?
(a) 2.55 × 10^–6 J
(b) 1.55 × 10^–6 J
(c) 8.15 × 10^–6 J
(d) 5.5 × 10^–6 J

Answer: A

Question. Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material fo dielectric constant K. The potential difference across the capacitors now becomes
(a) 3V/K+2
(b) KV
(c) V/K
(d) 3/KV 

Answer: A

Question. In the circuit given below, the charge in μC, on the capacitor having 5 μF is
(a) 4.5
(b) 9
(c) 7
(d) 15

Answer: B

Question. Two capacitors, C₁ = 2μF and C₂ = 8 μF are connected in series across a 300 V source. Then
(a) the charge on each capacitor is 4.8×10^–4 C
(b) the potential difference across C₁ is 60 V
(c) the potential difference across C₂ is 240 V
(d) the energy stroed in the system is 5.2 × 10^–2 J

Answer: A

Question. van de graaff generator is based on the phenomenon of corona discharge, which is used for developing
a) electric current of order of 10×10⁶ A
b) electric potential of order of 10×10⁶ 6 V
c) electric power of order of 10×10⁶ W
d) electric charge of order of 10×10⁶ C

Answer : B

Question. A charge 2Q is placed at each corner of a cube of side a. The potential at the centre of the cube is
a) 8Q/ε₀a
b) 4Q/4πε₀a
c) 8Q/√3πε₀a
d) 8Q/πε₀a

Answer : C

Question. To find the value of potential at a point, the external force at every point of the path is to be equal and opposite to the
a) work done
b) electrostatic force on the test charge at that point
c) potential energy
d) None of the above

Answer : B

Question. Three capacitors each of capacitance 9 pF are connected in series. What is the potential difference across each
capacitor, if the combination is connected to a 120 V supply?
a) 40 V
b) 60 V
c) 80 V
d) 50 V

Answer : A

Question. The extent of polarisation depends on
a) the dipole potential energy in the external field tending to align the dipoles with the field
b) thermal energy tending to disrupt the alignment
c) Both (a) and (b)
d) Neither (a) nor (b)

Answer : C

Question. Two charges 3×10^-8 C and - 2×10^-8 C located 15 cm apart. At what point on the line joining the two charges is the electric potential zero?
a) 9 cm
b) 42 cm
c) 18 cm
d) 20 cm

Answer : A

Question. For a uniform electric field E, along the X-axis, the equipotential surfaces are plane
a) perpendicular to Z-axis
b) parallel to the yz-plane
c) perpendicular to yz-plane
d) perpendicular toY-axis

Answer : B

Question. The variation of electric potential of an electric dipole with distance r is
a) E ∝ 1/r³ 
b) E ∝ 1/r²
c) E ∝ 1/r
d)  E ∝ 1

Answer : B

Question. Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge - 2q is placed at mid-point. The potential energy of the system is (ε₀ = permittivity of free space)
a) - q/8πε₀a
b) - 3q²/8πε₀a
c) - 5q²/8πε₀a
d) - 7²/8πε₀a

Answer : D

Question. Three point charges + q₁, - 2q and - 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be
a) 1/4πε₀  2q²/a
b) 1/4πε₀  q²/2a
c) 1/4πε₀  q/a²
d) zero

Answer : D

Question. The potential difference between a cloud and the earth is 107 V. Calculate the amount of energy dissipated when the charge of 100 C is transferred from the cloud to the ground due to lightning bolt.
a) zero
b) 10⁹ J
c) 60 J
d) 10⁷ J

Answer : B

Question. What happens when a conductor is placed in an external electric field?
a) The electric field due to induced charge opposes the external field within the conductor
b) In the static situation, the two fields cancel each other and the electrostatic field in the conductor is zero
c) Both (a) and (b)
d) Neither (a) nor (b)

Answer : C

Question. If a conductor is given an excess of charge, then it
a) resides on its surface
b) move to its centre
c) escape from its surface
d) distributes equally inside it

Answer : A

Question. The total dipole moment of dielectric with polar molecules in absence of an external electric field is
a) zero
b) negative
c) infinite
d) None of these

Answer : A

Question. The potential in the equatorial plane of a dipole of a dipole moment p is
a) infinite
b) zero
c) maximum
d) equal to p

Answer : B

Question. A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1 pF = 10^-12 F). What will be the capacitance, if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 6?
a) 24 pF
b) 96 pF
c) 8 pF
d) 12 pF

Answer : B

Question. If dielectric constant and dielectric strength be denoted by K and X respectively, then a material suitable for using it as a dielectric in a capacitor must have
a) high K and high X
b) high K and low X
c) low K and high X
d) low K and low X

Answer : A

Question. The maximum electric field that a dielectric medium of a capacitor can withstand without breakdown
(of its insulating property) is called its
a) polarisation
b) capacitance
c) dielectric strength
d) None of these

Answer : C

Question. A parallel plate capacitor is connected to a 5V battery and charged. The battery is then disconnected and a glass slab
is introduced between the plates, then the quantities that decrease are
a) charge and potential difference
b) charge and capacitance
c) capacitance and potential difference
d) energy stored and potential difference

Answer : D

Question. A 600 pF capacitor is charged by a 200 V supply, then it is disconnected from the supply and is connected to another
uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
a) 12×10^-6 J
b) 8×10^-6 J
c) 6×10^-6 J
d) 4×10^-6 J

Answer : C

Question. In van de graaff generator, charge is moved from one place to other, which creates a potential difference between two points. The potential produces
a) accelerated charged particles
b) heating in generator
c) decelerated charged particles
d) None of the above

Answer : A

Question. Two charges 5 × 10^-8 C and –3 × 10^-8 C are located 16 cm apart. At what point from positive charge on the line joining the two charges is the electric potential zero? (Take, the potential at infinity to be zero).
a) 6 cm
b) 8 cm
c) 10 cm
d) 30 cm

Answer : C

Question. Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density s.
They are brought in contact and separated. What will be the new surface charge densities on them?
a) σ_P 5/6 σ, σ_Q 5/6 σ
b) σ_P 5/2 σ, σ_Q 5/6 σ
c) σ_P 5/2 σ, σ_Q 5/3 σ
d) σ_P 5/3 σ, σ_Q 5/6 σ

Answer : D

Question. A regular hexagon of side 10 cm has a charge 5 μC at each of its vertices. Calculate the potential at the centre of the hexagon.
a) 3.7×10^-6 V
b) 2.7×10⁶ V
c) 2.7×10^-4 V
d) 3.7×10⁴ V

Answer : B

Question. In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10^-3 m² and the distance between the plates is 3 mm. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the
capacitor?
a) 1.77×10^-9 C
b) 2.77×10^-9 C
c) 1×10^-8 C
d) 4.7×10^-6 C

Answer : A

Question. A charge of 8mC is located at the origin. Calculate thework done in taking a small charge of – 2 × 10⁹ C from a point P(0, 0, 3) (in cm) to a point Q (0, 4, 0) (in cm), via a point R (0, 6, 9) (in cm).
a) 2.4 J
b) 1.2 J
c) 2 J
d) 3.6 J

Answer : B

 

              Very Short Answer

Q1)       What is the unit of energy?

Q2)       What is capacitance of the capacitor?

Q3)       What is polarisation?

Q4)       How positive ions are made?

Q5)       What are linear isotropic dielectrics?

             

              Short Answer

Q6)       Why potential energy is negative?

Q7)       How capacitors are different from capacitance?

Q8)       What do you mean by the parallel plate capacitor?

Q9)       How energy stored in a capacitor?

Q10)     What are fringing of the field?

             

              Long Answer

Q11)     Write short note on combination of capacitors?

Q12)     Explain Van De Graaff Generator?

Q13)     State the difference between dielectric and capacitors?

Q14)     Write shot note on electric displacement?

Q15)     State the difference between conservative forces and non-conservative forces?