Capacitance PYQs Set 3 (PDF)

Set 3 of 11 · Questions 61-90 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 3 (Q61-90)
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61. $A parallel plate air filled capacitor of capacitance ' C ' has plate area ' A ' and the distance between the plates ' d '. When a metal sheet of thickness (\frac{d}{2}) and of the same area ' A ' is introduced between the plates, its capacitance becomes ' C_{2}'. The ratio C_{2} : C_{1} is$ (1) $2 : 1$ (2) $3 : 2$ (3) $4 : 1$ (4) $3 : 1$ 62. $Statement I: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Statement II: The net work done by a conservative force on an object moving along a closed loop is zero.$ (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) $Statement-I is true, Statement-II is false.$ 63. $The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is 6 μF . The value of capacitance of each capacitor is$ (1) $4 μF$ (2) $6 μF$ (3) $2 μF$ (4) $3 μF$ 64. $The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances 1 pF, 2 pF and 4 pF is$ (1) $\frac{7}{4} pF$ (2) $\frac{4}{7} pF$ (3) $1 pF$ (4) $2 pF$ 65. $Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ϵ_{0} is the permittivity of free space between the plates, then potential energy stored in the capacitor is$ (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) $\frac{3}{4} ϵ_{0} E^{2} Ad$ 66. $The electric field in an electromagnetic wave is given as E = 20 sin ω (t - \frac{x}{c}) j N C^{- 1}, where ω and c are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of 5 x 10-4 m^{3} will be (Given ϵ_{0} = 8. 85 x 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$ (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) $8.85 x 1 0^{- 13} J$ 67. $A parallel-plate capacitor of capacitance 40 μ F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2 . Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are$ (1) $4 mC and 0.2 J$ (2) $8 mC and 2.0 J$ (3) $2 mC and 0.4 J$ (4) $2 mC and 0.2 J$ 68. $A long hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.$ (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) $No potential difference appears between the two cylinders when same charge density is given to both the cylinders.$ 69. $A parallel plate capacitor with air between the plates has capacitance 12 μF . If the distance between the plates is doubled and the space between the plates filled with a substance of dielectric constant 4, the capacitance of the capacitor will be is$ (1) $24 μF$ (2) $72 μF$ (3) $6 μF$ (4) $12 μF$ 70. $Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s).$ (1) $The angular momentum of the charge -q is constant.$ (2) $The linear momentum of the charge -q is constant.$ (3) $The angular velocity of the charge - q is constant.$ (4) $The linear speed of the charge -q is constant.$ 71. $A parallel plate capacitor with plates of area 1 m^{2} each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is: (Take \in_{0} = 8.85 \times 10^{- 12} (\frac{C ^{2}}{N - M ^{2}})$ (1) $7.85 \times 10^{- 10} C$ (2) $6.85 \times 10^{- 10} C$ (3) $8.85 \times 10^{- 10} C$ (4) $9.85 \times 10^{- 10} C$ 72. $A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness (\frac{1}{3})^{rd} of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :$ (1) $\frac{4 KC}{3 K - 1}$ (2) $\frac{3 C K ^{2}}{( 2 K + 1 ) ^{2}}$ (3) $\frac{3 KC}{2 K + 1}$ (4) $\frac{CK}{2 + K}$ 73. $A 10 μF capacitor is fully charge to a potential difference of 50V. After removing the source voltage is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20V. The capacitance of the second capacitor is$ (1) $20 μF$ (2) $10 μF$ (3) $15 μF$ (4) $30 μF$ 74. $If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then [NEET 2024](A) the charge stored in it, increases.(B) the energy stored in it, decreases.(C) its capacitance increases.(D) the ratio of charge to its potential remains the same.(E) the product of charge and voltage increases. Choose the most appropriate answer from the options given below$ (1) $A, B and E only$ (2) $A, C and E only$ (3) $B, D and E only$ (4) $A, B and C only$ 75. $The amount of work done in increasing the voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 15 V will be$ (1) $W$ (2) $0.6 W$ (3) $1.25 W$ (4) $1.67 W$ 76. $Two identical thin metal plates has charge q_{1} and q_{2} respectively such that q_{1} > q_{2} . The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is:$ (1) $\frac{( q _{1} + q _{2} )}{C}$ (2) $\frac{( q _{1} - q _{2} )}{C}$ (3) $\frac{( q _{1} - q _{2} )}{2 C}$ (4) $\frac{2 ( q _{1} - q _{2} )}{C}$ 77. $The force of repulsion between two identical positive charges when kept with a separation r in air is F . Half the gap between the two charges is filled by a dielectric slab of dielectric constant 4. Then the new force of repulsion between those two charges becomes$ (1) $\frac{F}{3}$ (2) $\frac{F}{2}$ (3) $\frac{F}{4}$ (4) $\frac{4 F}{9}$ 78. $A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. Asa result the potential difference between the plates$ (1) $increases$ (2) $decreases$ (3) $does not change$ (4) $becomes zero$ 79. $A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is 2R and the inner radius is R.$ (1) $4 π ϵ_{0} R$ (2) $8 π ϵ_{0} R$ (3) $\frac{8 π ϵ _{0}}{R}$ (4) $\frac{4 π ϵ _{0}}{R}$ 80. $Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is$ (1) $2 times$ (2) $8 times$ (3) $4 times$ (4) $16 times$ 81. $A capacitor is fully charged with voltage V_{0} . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \frac{C}{2} . The energy loss in the process after the charge is distributed between the two capacitors is$ (1) $\frac{1}{4} C V_{0}^{2}$ (2) $\frac{1}{3} C V_{0}^{2}$ (3) $\frac{1}{6} C V_{0}^{2}$ (4) $\frac{1}{2} C V_{0}^{2}$ 82. $The capacitance of a parallel plate capacitor with air as medium is 6 μF . With the introduction of a dielectric medium, the capacitance becomes 30 μF . The permittivity of the medium is (ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}) [NEET 2020]$ (1) $1.77 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ (2) $0.44 \times 10^{- 10} C^{2} N^{- 1} m^{- 2}$ (3) $5.00 C^{2} N^{- 1} m^{- 2}$ (4) $0.44 \times 10^{- 13} C^{2} N^{- 1} m^{- 2}$ 83. $A spherical metal shell A of radius R_{A} and a solid metal sphere B of radius R_{B} (< R_{A}) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then$ (1) $E_{A inside} = 0$ (2) $Q_{A} > Q_{B}$ (3) $\frac{σ _{A}}{σ _{B}} = \frac{R _{B}}{R _{A}}$ (4) $E_{Aon surface} < E_{Bon surface}$ 84. $Two parallel plate air capacitors of same capacity C are connected in series to a battery of emf E. Then one of the capacitors is completely filled with dielectric material of constant K. The change in the effective capacity of the series combination is$ (1) $\frac{C}{2} (\frac{K - 1}{K + 1})$ (2) $\frac{2}{C} (\frac{K - 1}{K + 1})$ (3) $\frac{C}{2} (\frac{K + 1}{K - 1})$ (4) $\frac{C}{2} (\frac{K - 1}{K + 1})^{2}$ 85. $A parallel plate capacitor has plate of length is connected to a battery of emf V. A dielectric slab of same thickness ‘d’ and dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?$ (1) $\frac{l}{4}$ (2) $\frac{l}{2}$ (3) $\frac{2 l}{3}$ (4) $\frac{l}{3}$ 86. $A capacitor is discharging through a resistor R. Consider in time t_{1}, the energy stored in the capacitor reduces to half of its initial value and in time t_{2}, the charge stored reduces to one eighth of its initial value. The ratio t_{1} / t_{2} will be :$ (1) $1/2$ (2) $1/3$ (3) $1/4$ (4) $1/6$ 87. $A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = k r^{a}, where k and a are constants and r is the distance from its center. If the electric field at r = \frac{R}{2} is \frac{1}{8} times that at r = R, find the value of a.$ 88. $A parallel plate capacitor whose capacitance C is 14pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelain plate with k=7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ______ pJ (Assume no friction)$ 89. $27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is___ times that of a smaller drop.$ 90. $A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2C and potential 2V. Then the loss of energy is \frac{x}{3} E, where x is____$