Q.1. In a certain region of space with volume 0.2 m3, 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
D: 0.5 N/C
given v = const. (5 volt)
E = 0
Q.2. 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)
(ε0 = 8.85×10-12 C2 N-1 m-2)
A: 0.44×10-10 C2 N-1 m-2
B: 5.00 C2 N-1 m-2
C: 0.44×10-13 C2 N-1 m-2
D: 1.77×10-12 C2 N-1 m-2
Cmed = KCair
30μF = K6μF
K = 5
∴ ε = ε0k = 8.85 × 10-12 × 5
ε = 44.25 × 10-12
ε = 0.4425 × 10-10
ε = 0.44 × 10-10 C2N-1m-2
Q.3. 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
Q.4. 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.
F = QE
∴ Electrostatic force is independent of distance between plates
Q.5. 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
Charge on capacitor
q = CV
when it is connected with another uncharged capacitor.
Q.6. 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
W = qΔV
as ΔV is same in all conditions, work will be same.
Q.7. 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)
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.8. 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
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 CV2
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.9. 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)
Q.10. 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)
B: Both are zero
Electric field inside, Einside = 0
Potential, Vinside = Vsurface