Capacitance PYQs Set 2 (PDF)

Set 2 of 11 · Questions 31-60 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 2 (Q31-60)
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31. $Two points charges are kept in air with a separation between them. The force between them is F_{1}, if half of the space between the charges is filled with a dielectric constant 4 and the force between them is F_{2}, if \frac{1}{3} rd of the space between the charges is filled with dielectric of dielectric constant 9 . Then \frac{F _{1}}{F _{2}} is$ (1) $\frac{27}{64}$ (2) $\frac{16}{81}$ (3) $\frac{81}{64}$ (4) $\frac{100}{81}$ 32. $A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is$ (1) $\frac{1}{2} (K-1) C V^{2}$ (2) $C V^{2} (K - 1)/K$ (3) $(K - 1) C V^{2}$ (4) $zero$ 33. $When an additional charge of 2 C in given to a capacitor, energy stored in it is increased by 21 % . The original charge of the capacitor is$ (1) $30 C$ (2) $40 C$ (3) $10 C$ (4) $20 C$ 34. $If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C):$ (1) $10$ (2) $20$ (3) $30$ (4) $40$ 35. $Positive and negative point charges of equal magnitude are kept at (0, 0, \frac{a}{2}) and (0, 0, \frac{- a}{2}), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is$ (1) $positive$ (2) $negative$ (3) $zero$ (4) $depends on the path connecting the initial and final positions.$ 36. $A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plate. The work done by the capacitor on the slab is$ (1) $692 pJ$ (2) $600 pJ$ (3) $508 pJ$ (4) $560 pJ$ 37. $Statement -I: For practical purposes, the earth is used as a reference at zero potential in electrical circuits. And Statement -II: The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by \frac{Q}{4 π ϵ _{0} R} .$ (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) $Statement -I is False, Statement -II is True.$ 38. $A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength \frac{81 π}{7} \times 1 0^{5} V m^{-1} . When the field is switched off, the drop is observed to fall with terminal velocity 2 \times 10-3 m s^{-1} . Given g = 9.8 m s^{-2}, viscosity of the air = 1.8 \times 10-5 Ns m^{-2} and the density of oil = 900 kg m^{-3}, the magnitude of q is:$ (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) $8.0 \times 1 0^{-1} 9 C$ 39. $A capacitance of 2µF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1µF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:$ (1) $32$ (2) $2$ (3) $16$ (4) $24$ 40. $Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t_{1} is the time taken for the energy stored in the capacitor to reduce to half its initial value and t_{2} is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t_{1} / t_{2} will be$ (1) $1$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $2$ 41. $A parallel plate capacitor has a capacity 80 \times 10^{- 6} F, when air is present between its plates. The space between the plates is filled with a dielectric slab of dielectric constant 20. The capacitor is now connected to a battery of 30 V by wires. The dielectric slab is then removed. Then, the charge passing through the wire is$ (1) $12 \times 10^{- 3} C$ (2) $25.3 \times 10^{- 3} C$ (3) $120 \times 10^{- 3} C$ (4) $45.6 \times 10^{- 3} C$ 42. $Capacitance of an isolated conducting sphere of radius R_{1} becomes n times when it is enclosed by a concentric conducting sphere of radius R_{2} connected to earth. The ratio of (\frac{R _{2}}{R _{1}}) their radii (\frac{R _{2}}{R _{1}}) is:$ (1) $\frac{n}{n - 1}$ (2) $\frac{2 n}{2 n + 1}$ (3) $\frac{n + 1}{n}$ (4) $\frac{2 n + 1}{n}$ 43. $A series combination of n_{1} capacitors, each of value C_{1} is charged by a source of potential difference 4V. When another parallel combination of n_{2} capacitors, each of value C_{2}, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C_{2}, in terms of C_{1}, is then$ (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) $\frac{16 C _{1}}{n _{1} n _{2}}$ 44. $The potential at a point x (measured in µm) due to some charges situated on the x-axis is given by V(x) = 20/(x^{2} - 4) volts. The electric field E at x = 4 µm is given by:$ (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) $10/9 volt/µm and in the +ve x direction$ 45. $A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 \times 1 0^{4} V/m, the charge density of the positive plate will be close to:$ (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) $6 \times 1 0^{4} C/ m^{2}$ 46. $A capacitor of capacitance 100 μF is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be:$ (1) $3.2 A$ (2) $1.5 A$ (3) $2.0 A$ (4) $1.2 A$ 47. $Two identical capacitors each of capacitance 5 μ F are charged to potentials 2 k V and 1 k V respectively. The -ve ends are connected together. When the +ve ends are also connected together, the loss of energy of the system is$ (1) $160 J$ (2) $0 J$ (3) $5 J$ (4) $1.25 J$ 48. $A capacitor with capacitance 5 μF is charged to 5 μC . If the plates are pulled apart to reduce the capacitance to 2 μF, how much work is done?$ (1) $6.25 \times 10^{- 6} J$ (2) $3.75 \times 10^{- 6} J$ (3) $2.16 \times 10^{- 6} J$ (4) $2.55 \times 10^{- 6} J$ 49. $A parallel plate capacitor is charged by connecting a 2 V battery across it. It is then disconnected from the battery and a glass slab is introduced between plates. Which of the following pairs of quantities decrease?$ (1) $Energy stored and capacitance.$ (2) $Charge and potential difference.$ (3) $Capacitance and charge,$ (4) $Potential difference and energy stored.$ 50. $A parallel plate capacitor having capacity C_{0} is charged to V_{0} . With battery disconnected, if the separation between the plates is doubled then the energy stored in it is E_{1} . Instead if the separation between the plates is doubled, with battery in connection, the energy stored in it is E_{2} . Then the value of \frac{E _{2}}{E _{1}} is$ (1) $0.5$ (2) $1.5$ (3) $2$ (4) $0.25$ 51. $The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When te capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is:$ (1) $\frac{nV}{K + n}$ (2) $V$ (3) $\frac{V}{K + n}$ (4) $\frac{( n + 1 ) V}{( K + n )}$ 52. $A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are$ (1) $\frac{Q}{3}, \frac{2 Q}{3}$ (2) $\frac{Q}{2}, \frac{Q}{2}$ (3) $\frac{Q}{5}, \frac{4 Q}{5}$ (4) $\frac{Q}{4}, \frac{3 Q}{4}$ 53. $A condenser of 2µF capacitance is charged steadily from 0 to 5C. Which of the following graph represents correctly the variation of potential difference (V) across it's plates with respect to the charge (Q) on the condenser ?$ (1) (2) (3) (4) 54. $A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be$ (1) $1$ (2) $2$ (3) $1/4$ (4) $1/2$ 55. $A parallel plate capacitor has charge 5 \times 10^{- 6} C . A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is 4 \times 10^{- 6} C then the dielectric constant of the slab is .$ 56. $A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25 % more charge from the battery than before. The dielectric constant of the sheet is_____$ 57. $A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric x constant 3.5. Then the capacitance becomes \frac{x}{4} pF. The value of x is$ 58. $The displacement current of 4.425 µA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 1 0^{6} V s^{- 1} . The area of each plate of the capacitor is 40 cm. The distance between each plate of the capacitor is x \times 1 0^{- 3} m. The value of x is, (Permittivity of free space, E_{0} = 8.85 x 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$ 59. $A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is_______nJ.$ 60. $A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is_____µJ.$