Capacitance PYQs Set 2 (PDF)

Set 2 of 8 · Questions 31-60 of 239

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Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 2 (Q31-60)
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31. $When an additional charge of 2 C in given to a capacitor, energy stored in it is increased by 21 % . The original charge of the capacitor is$ (1) $30 C$ (2) $40 C$ (3) $10 C$ (4) $20 C$ 32. $If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C):$ (1) $10$ (2) $20$ (3) $30$ (4) $40$ 33. $Positive and negative point charges of equal magnitude are kept at (0, 0, \frac{a}{2}) and (0, 0, \frac{- a}{2}), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is$ (1) $positive$ (2) $negative$ (3) $zero$ (4) $depends on the path connecting the initial and final positions.$ 34. $A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plate. The work done by the capacitor on the slab is$ (1) $692 pJ$ (2) $600 pJ$ (3) $508 pJ$ (4) $560 pJ$ 35. $Statement -I: For practical purposes, the earth is used as a reference at zero potential in electrical circuits. And Statement -II: The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by \frac{Q}{4 π ϵ _{0} R} .$ (1) $Statement -I is True, Statement -II is True; Statement -II is a correct explanation for Statement -1$ (2) $Statement -I is True, Statement -II is True; Statement -II is NOT a correct explanation for Statement -I$ (3) $Statement -I is True, Statement -II is False$ (4) $Statement -I is False, Statement -II is True.$ 36. $A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength \frac{81 π}{7} \times 1 0^{5} V m^{-1} . When the field is switched off, the drop is observed to fall with terminal velocity 2 \times 10-3 m s^{-1} . Given g = 9.8 m s^{-2}, viscosity of the air = 1.8 \times 10-5 Ns m^{-2} and the density of oil = 900 kg m^{-3}, the magnitude of q is:$ (1) $1.6 \times 1 0^{-19} C$ (2) $3.2 \times 1 0^{-19} C$ (3) $4.8 \times 1 0^{-19} C$ (4) $8.0 \times 1 0^{-1} 9 C$ 37. $A capacitance of 2µF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1µF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:$ (1) $32$ (2) $2$ (3) $16$ (4) $24$ 38. $Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t_{1} is the time taken for the energy stored in the capacitor to reduce to half its initial value and t_{2} is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t_{1} / t_{2} will be$ (1) $1$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $2$ 39. $A parallel plate capacitor has a capacity 80 \times 10^{- 6} F, when air is present between its plates. The space between the plates is filled with a dielectric slab of dielectric constant 20. The capacitor is now connected to a battery of 30 V by wires. The dielectric slab is then removed. Then, the charge passing through the wire is$ (1) $12 \times 10^{- 3} C$ (2) $25.3 \times 10^{- 3} C$ (3) $120 \times 10^{- 3} C$ (4) $45.6 \times 10^{- 3} C$ 40. $Capacitance of an isolated conducting sphere of radius R_{1} becomes n times when it is enclosed by a concentric conducting sphere of radius R_{2} connected to earth. The ratio of (\frac{R _{2}}{R _{1}}) their radii (\frac{R _{2}}{R _{1}}) is:$ (1) $\frac{n}{n - 1}$ (2) $\frac{2 n}{2 n + 1}$ (3) $\frac{n + 1}{n}$ (4) $\frac{2 n + 1}{n}$ 41. $A series combination of n_{1} capacitors, each of value C_{1} is charged by a source of potential difference 4V. When another parallel combination of n_{2} capacitors, each of value C_{2}, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C_{2}, in terms of C_{1}, is then$ (1) $\frac{2 C _{1}}{n _{1} n _{2}}$ (2) $16 \frac{n _{2}}{n _{1}} C_{1}$ (3) $2 \frac{n _{2}}{n _{1}} C_{1}$ (4) $\frac{16 C _{1}}{n _{1} n _{2}}$ 42. $The potential at a point x (measured in µm) due to some charges situated on the x-axis is given by V(x) = 20/(x^{2} - 4) volts. The electric field E at x = 4 µm is given by:$ (1) $5/3 volt/µm and in the -ve x direction$ (2) $5/3 volt/µm and in the +ve x direction$ (3) $10/9 volt/µm and in the -ve x direction$ (4) $10/9 volt/µm and in the +ve x direction$ 43. $A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 \times 1 0^{4} V/m, the charge density of the positive plate will be close to:$ (1) $6 \times 10-^{7} C/ m^{2}$ (2) $3 \times 10-^{7} C/ m^{2}$ (3) $3 \times 1 0^{4} C/ m^{2}$ (4) $6 \times 1 0^{4} C/ m^{2}$ 44. $A capacitor of capacitance 100 μF is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be:$ (1) $3.2 A$ (2) $1.5 A$ (3) $2.0 A$ (4) $1.2 A$ 45. $Two identical capacitors each of capacitance 5 μ F are charged to potentials 2 k V and 1 k V respectively. The -ve ends are connected together. When the +ve ends are also connected together, the loss of energy of the system is$ (1) $160 J$ (2) $0 J$ (3) $5 J$ (4) $1.25 J$ 46. $A capacitor with capacitance 5 μF is charged to 5 μC . If the plates are pulled apart to reduce the capacitance to 2 μF, how much work is done?$ (1) $6.25 \times 10^{- 6} J$ (2) $3.75 \times 10^{- 6} J$ (3) $2.16 \times 10^{- 6} J$ (4) $2.55 \times 10^{- 6} J$ 47. $A parallel plate capacitor is charged by connecting a 2 V battery across it. It is then disconnected from the battery and a glass slab is introduced between plates. Which of the following pairs of quantities decrease?$ (1) $Energy stored and capacitance.$ (2) $Charge and potential difference.$ (3) $Capacitance and charge,$ (4) $Potential difference and energy stored.$ 48. $A parallel plate capacitor having capacity C_{0} is charged to V_{0} . With battery disconnected, if the separation between the plates is doubled then the energy stored in it is E_{1} . Instead if the separation between the plates is doubled, with battery in connection, the energy stored in it is E_{2} . Then the value of \frac{E _{2}}{E _{1}} is$ (1) $0.5$ (2) $1.5$ (3) $2$ (4) $0.25$ 49. $The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When te capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is:$ (1) $\frac{nV}{K + n}$ (2) $V$ (3) $\frac{V}{K + n}$ (4) $\frac{( n + 1 ) V}{( K + n )}$ 50. $A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are$ (1) $\frac{Q}{3}, \frac{2 Q}{3}$ (2) $\frac{Q}{2}, \frac{Q}{2}$ (3) $\frac{Q}{5}, \frac{4 Q}{5}$ (4) $\frac{Q}{4}, \frac{3 Q}{4}$ 51. $A condenser of 2µF capacitance is charged steadily from 0 to 5C. Which of the following graph represents correctly the variation of potential difference (V) across it's plates with respect to the charge (Q) on the condenser ?$ (1) (2) (3) (4) 52. $A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be$ (1) $1$ (2) $2$ (3) $1/4$ (4) $1/2$ 53. $A parallel plate air filled capacitor of capacitance ' C ' has plate area ' A ' and the distance between the plates ' d '. When a metal sheet of thickness (\frac{d}{2}) and of the same area ' A ' is introduced between the plates, its capacitance becomes ' C_{2}'. The ratio C_{2} : C_{1} is$ (1) $2 : 1$ (2) $3 : 2$ (3) $4 : 1$ (4) $3 : 1$ 54. $Statement I: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Statement II: The net work done by a conservative force on an object moving along a closed loop is zero.$ (1) $Statement-I is true, Statement-II is true; Statement-II is the correct explanation of Statement-I.$ (2) $Statement-I is true, Statement-II is true; Statement-II is not the correct explanation of Statement-I.$ (3) $Statement-I is false, Statement-II is true.$ (4) $Statement-I is true, Statement-II is false.$ 55. $The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is 6 μF . The value of capacitance of each capacitor is$ (1) $4 μF$ (2) $6 μF$ (3) $2 μF$ (4) $3 μF$ 56. $The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances 1 pF, 2 pF and 4 pF is$ (1) $\frac{7}{4} pF$ (2) $\frac{4}{7} pF$ (3) $1 pF$ (4) $2 pF$ 57. $Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ϵ_{0} is the permittivity of free space between the plates, then potential energy stored in the capacitor is$ (1) $ϵ_{0} E^{2} Ad$ (2) $\frac{1}{2} ϵ_{0} E^{2} Ad$ (3) $\frac{1}{4} ϵ_{0} E^{2} Ad$ (4) $\frac{3}{4} ϵ_{0} E^{2} Ad$ 58. $The electric field in an electromagnetic wave is given as E = 20 sin ω (t - \frac{x}{c}) j N C^{- 1}, where ω and c are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of 5 x 10-4 m^{3} will be (Given ϵ_{0} = 8. 85 x 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$ (1) $88.5 x 1 0^{- 13} J$ (2) $17. 7 x 1 0^{- 13} J$ (3) $28.5 x 1 0^{- 13} J$ (4) $8.85 x 1 0^{- 13} J$ 59. $A parallel-plate capacitor of capacitance 40 μ F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2 . Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are$ (1) $4 mC and 0.2 J$ (2) $8 mC and 2.0 J$ (3) $2 mC and 0.4 J$ (4) $2 mC and 0.2 J$ 60. $A long hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.$ (1) $A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.$ (2) $A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.$ (3) $No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.$ (4) $No potential difference appears between the two cylinders when same charge density is given to both the cylinders.$