Capacitance PYQs Set 3 (PDF)

Set 3 of 8 · Questions 61-90 of 239

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Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 3 (Q61-90)
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61. $A parallel plate capacitor with air between the plates has capacitance 12 μF . If the distance between the plates is doubled and the space between the plates filled with a substance of dielectric constant 4, the capacitance of the capacitor will be is$ (1) $24 μF$ (2) $72 μF$ (3) $6 μF$ (4) $12 μF$ 62. $Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s).$ (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) $The linear speed of the charge -q is constant.$ 63. $A parallel plate capacitor with plates of area 1 m^{2} each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is: (Take \in_{0} = 8.85 \times 10^{- 12} (\frac{C ^{2}}{N - M ^{2}})$ (1) $7.85 \times 10^{- 10} C$ (2) $6.85 \times 10^{- 10} C$ (3) $8.85 \times 10^{- 10} C$ (4) $9.85 \times 10^{- 10} C$ 64. $A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness (\frac{1}{3})^{rd} of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :$ (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) $\frac{CK}{2 + K}$ 65. $A 10 μF capacitor is fully charge to a potential difference of 50V. After removing the source voltage is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20V. The capacitance of the second capacitor is$ (1) $20 μF$ (2) $10 μF$ (3) $15 μF$ (4) $30 μF$ 66. $If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then [NEET 2024](A) the charge stored in it, increases.(B) the energy stored in it, decreases.(C) its capacitance increases.(D) the ratio of charge to its potential remains the same.(E) the product of charge and voltage increases. Choose the most appropriate answer from the options given below$ (1) $A, B and E only$ (2) $A, C and E only$ (3) $B, D and E only$ (4) $A, B and C only$ 67. $The amount of work done in increasing the voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 15 V will be$ (1) $W$ (2) $0.6 W$ (3) $1.25 W$ (4) $1.67 W$ 68. $Two identical thin metal plates has charge q_{1} and q_{2} respectively such that q_{1} > q_{2} . The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is:$ (1) $\frac{( q _{1} + q _{2} )}{C}$ (2) $\frac{( q _{1} - q _{2} )}{C}$ (3) $\frac{( q _{1} - q _{2} )}{2 C}$ (4) $\frac{2 ( q _{1} - q _{2} )}{C}$ 69. $The force of repulsion between two identical positive charges when kept with a separation r in air is F . Half the gap between the two charges is filled by a dielectric slab of dielectric constant 4. Then the new force of repulsion between those two charges becomes$ (1) $\frac{F}{3}$ (2) $\frac{F}{2}$ (3) $\frac{F}{4}$ (4) $\frac{4 F}{9}$ 70. $A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. Asa result the potential difference between the plates$ (1) $increases$ (2) $decreases$ (3) $does not change$ (4) $becomes zero$ 71. $A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is 2R and the inner radius is R.$ (1) $4 π ϵ_{0} R$ (2) $8 π ϵ_{0} R$ (3) $\frac{8 π ϵ _{0}}{R}$ (4) $\frac{4 π ϵ _{0}}{R}$ 72. $Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is$ (1) $2 times$ (2) $8 times$ (3) $4 times$ (4) $16 times$ 73. $A capacitor is fully charged with voltage V_{0} . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \frac{C}{2} . The energy loss in the process after the charge is distributed between the two capacitors is$ (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) $\frac{1}{2} C V_{0}^{2}$ 74. $The capacitance of a parallel plate capacitor with air as medium is 6 μF . With the introduction of a dielectric medium, the capacitance becomes 30 μF . The permittivity of the medium is (ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}) [NEET 2020]$ (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) $0.44 \times 10^{- 13} C^{2} N^{- 1} m^{- 2}$ 75. $Two parallel plate air capacitors of same capacity C are connected in series to a battery of emf E. Then one of the capacitors is completely filled with dielectric material of constant K. The change in the effective capacity of the series combination is$ (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) $\frac{C}{2} (\frac{K - 1}{K + 1})^{2}$ 76. $A parallel plate capacitor has plate of length is connected to a battery of emf V. A dielectric slab of same thickness ‘d’ and dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?$ (1) $\frac{l}{4}$ (2) $\frac{l}{2}$ (3) $\frac{2 l}{3}$ (4) $\frac{l}{3}$ 77. $A capacitor is discharging through a resistor R. Consider in time t_{1}, the energy stored in the capacitor reduces to half of its initial value and in time t_{2}, the charge stored reduces to one eighth of its initial value. The ratio t_{1} / t_{2} will be :$ (1) $1/2$ (2) $1/3$ (3) $1/4$ (4) $1/6$ 78. $Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 10^{6} V/m. The plate area is 10^{- 4} m^{2} . What is the dielectric constant if the capacitance is 15 pF ? (given \in_{0} = 8.86 \times 10^{- 12} C^{2} m^{2})$ (1) $3.8$ (2) $8.5$ (3) $4.5$ (4) $6.2$ 79. $The energy of a parallel plate capacitor when connected to a battery is E. With the battery still in connection, if the plates of the capacitor are separated, so that the distance between them is twice the original distance, then the electrostatic energy becomes$ (1) $2E$ (2) $\frac{E}{4}$ (3) $\frac{E}{2}$ (4) $4E$ 80. $A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:$ (1) $692 pJ$ (2) $508 pJ$ (3) $560 pJ$ (4) $600 pJ$ 81. $Two points P and Q are maintained at the potentials of 10 V and -4 V respectively. The work done in moving 100 electrons from P to Q is$ (1) $9.60 \times 1 0^{-17} J$ (2) $-2.24 \times 1 0^{-16} J$ (3) $2.24 \times 1 0^{-16} J$ (4) $-9.60 \times 1 0^{-17} J$ 82. $Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be$ (1) $3 C, \frac{V}{3}$ (2) $\frac{C}{3}, 3 V$ (3) $3 C, 3 V$ (4) $\frac{C}{3}, \frac{V}{3}$ 83. $Two capacitors C_{1} = 2 μF and C_{2} = 8 μF are connected in series across a 300 V source, then$ (1) $the charge on each capacitor is 4.8 \times 10^{- 4} C$ (2) $the potential difference across C_{1} is 60 V$ (3) $the potential difference across C_{2} is 240 V$ (4) $the energy stored in the system is 52 \times 10^{- 2} J$ 84. $The ratio of potential difference that must be applied across parallel and series combination of two capacitors C_{1} and C_{2} with their capacitance in the ratio 1 : 2 so that energy stored in these two cases becomes same is$ (1) $3 : 2$ (2) $2 : 3$ (3) $2 : 9$ (4) $9 : 2$ 85. $Assume each oil drop consists of a capacitance of C. If combine n drops to form a bigger drop, then the capacitance of bigger drop C' would be$ (1) $C^{’} = \frac{2 n ^{1/3}}{3} C$ (2) $C^{’} = \frac{5 n ^{1/3}}{4} C$ (3) $C^{’} = \frac{n ^{1/3}}{5} C$ (4) $C^{’} = C . n^{1/3}$ 86. $In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2. If the initial capacity of the capacitor is 4 μF, then its new capacity is$ (1) $32 μF$ (2) $18 μF$ (3) $8 μF$ (4) $44 μF$ 87. $A series combination of N_{1} capacitors (each of capacity C_{1}) is charged to potential difference ' 3V '. Another parallel combination of N_{2} capacitors (each of capacity C_{2}) is charged to potential difference ' V '. The total energy stored in both combinations is same. The value of C_{1} in terms of C_{2} is$ (1) $\frac{C _{2} N _{1} N _{2}}{9}$ (2) $\frac{C _{2} N _{1}^{2} N _{2}^{2}}{9}$ (3) $\frac{C _{2} N _{1}}{9 N _{2}}$ (4) $\frac{C _{2} N _{2}}{9 N _{1}}$ 88. $The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is$ (1) $Independent of the distance between the plates$ (2) $Linearly proportional to the distance between the plates$ (3) $Proportional to the square root of the distance between the plates$ (4) $Inversely proportional to the distance between the plates$ 89. $A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be$ (1) $400 %$ (2) $66.6 %$ (3) $33.3 %$ (4) $200 %$ 90. $The equivalent capacitance between A and B is,$ (1) $150 pF$ (2) $50 pF$ (3) $300 pF$ (4) $\frac{100}{3} pF$