Q.1. A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is A(m^{2}), the energy (joule) stored in the condenser is (2021)
A:
B:
C:
D:
Ans: C
Capacitance of a parallel plate capacitor is
Potential difference between the plates is
V = Ed ........ (ii)
The energy stored in the capacitor is
Q.2. The equivalent capacitance of the combination shown in the figure is: (2021)
A: C/2
B: 3C/2
C: 3C
D: 2C
Ans: D
(one capacitor gets short)
⇒ Ceq = C1 + C2
= C + C
= 2C
Q.3 Two charged spherical conductors of radius R_{1} and R_{2} are connected by a wire. Then the ratio of surface charge densities of the spheres (σ_{1}/σ_{2}) is : (2021)
A:
B:
C:
D:
Ans: D
For a conducting sphere,
As both spheres have same potential after connecting with wire,
V_{1} = V_{2}
Q.4. 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. (2021)
A: 1520 V
B: 1980 V
C: 660 V
D: 1320 V
Ans: B
⇒ V_{2} = 220 × 9
= 1980 Volt
Q.5. In a certain region of space with volume 0.2 m^{3}, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is: (2020)
A: 1 N/C
B: 5 N/C
C: Zero
D: 0.5 N/C
Ans: C
given v = const. (5 volt)
E = 0
Q.6. The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is : (2020)
(ε_{0} = 8.85×10^{12} C^{2} N^{}^{1} m^{2})
A: 0.44×10^{10} C^{2} N^{1} m^{2}
B: 5.00 C^{2} N^{1} m^{2}
C: 0.44×10^{13} C^{2} N^{1} m^{2}
D: 1.77×10^{12} C^{2} N^{1} m^{2}
Ans: A
C_{med} = KC_{air}
30μF = K6μF
K = 5
∴ ε = ε_{0}k = 8.85 × 10^{12} × 5
ε = 44.25 × 10^{12}
ε = 0.4425 × 10^{10}
ε = 0.44 × 10^{10} C^{2}N^{1}m^{2}
Q.7. A 40 μF capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly: (2020)
A: 2.5 A
B: 25.1 A
C: 1.7 A
D: 2.05 A
Ans: A
Q.8. The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is : (2018)
A: independent of the distance between the plates.
B: linearly proportional to the distance between the plates
C: proportional to the square root of the distance between the plates.
D: inversely proportional to the distance between the plates.
Ans: A
Solution:
F = QE
∴ Electrostatic force is independent of distance between plates
Q.9. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system : (2017)
A: Decreases by a factor of 2
B: Remains the same
C: Increases by a factor of 2
D: Increases by a factor of 4
Ans: A
Solution:
Charge on capacitor
q = CV
when it is connected with another uncharged capacitor.
Q.10. The diagrams below show regions of equipotentials: (2017)
A positive charge is moved from A to B in each diagram.
A: Maximum work is required to move q in figure (c)
B: Minimum work is required to move q in figure (a)
C: Maximum work is required to move q in figure (b)
D: In all the four cases the work done is the same
Ans: D
Solution:
W = qΔV
as ΔV is same in all conditions, work will be same.
Q.11. A capacitor of 21F is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is : (2016)
A: 80%
B: 0%
C: 20%
D: 75%
Ans: A
Solution:
Consider the figure given above.
When switch S is connected to point 1, then initial energy stored in the capacitor is given as,
When the switch S is connected to point 2, energy dissipated on connection across 8μF will be,
Therefore, per centage loss of energy
Q.12. A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect ? (2015)
A: The charge on the capacitor is not conserved.
B: The potential difference between the plates decreases K times
C: The energy stored in the capacitor decreases K times
D: the change in energy stored is
Ans: A
Solution:
A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it.
The charge on the capacitor is given by
Q = CV
The energy stored in the capacitor is
E = 1/2 CV^{2}
When a dielectric slab of dielectric constant K is inserted in it, the charge Q is conserved.
The capacitance becomes K times the original capacitance. (C' = KC)
The voltage becomes 1/K time the original voltage
V' = V/K
The change in energy stored is
Q.13. In a region, the potential is represented by V(x, y, z) = 6x − 8xy − 8y + 6yz, where V is in volts and x, y, z are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is: (2014)
A: 24N
B:
C:
D: 30N
Ans: B
Solution:
Q.14. A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are : (2014)
A:
B: Both are zero
C:
D:
Ans: D
Solution:
Electric field inside, E_{inside} = 0
Potential, V_{inside} = V_{surface}
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