Capacitance PYQs Set 4 (PDF)

Set 4 of 11 · Questions 91-120 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 4 (Q91-120)
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91. $Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 10^{6} V/m. The plate area is 10^{- 4} m^{2} . What is the dielectric constant if the capacitance is 15 pF ? (given \in_{0} = 8.86 \times 10^{- 12} C^{2} m^{2})$ (1) $3.8$ (2) $8.5$ (3) $4.5$ (4) $6.2$ 92. $The energy of a parallel plate capacitor when connected to a battery is E. With the battery still in connection, if the plates of the capacitor are separated, so that the distance between them is twice the original distance, then the electrostatic energy becomes$ (1) $2E$ (2) $\frac{E}{4}$ (3) $\frac{E}{2}$ (4) $4E$ 93. $A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:$ (1) $692 pJ$ (2) $508 pJ$ (3) $560 pJ$ (4) $600 pJ$ 94. $Two points P and Q are maintained at the potentials of 10 V and -4 V respectively. The work done in moving 100 electrons from P to Q is$ (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) $-9.60 \times 1 0^{-17} J$ 95. $Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be$ (1) $3 C, \frac{V}{3}$ (2) $\frac{C}{3}, 3 V$ (3) $3 C, 3 V$ (4) $\frac{C}{3}, \frac{V}{3}$ 96. $Two capacitors C_{1} = 2 μF and C_{2} = 8 μF are connected in series across a 300 V source, then$ (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) $the energy stored in the system is 52 \times 10^{- 2} J$ 97. $The ratio of potential difference that must be applied across parallel and series combination of two capacitors C_{1} and C_{2} with their capacitance in the ratio 1 : 2 so that energy stored in these two cases becomes same is$ (1) $3 : 2$ (2) $2 : 3$ (3) $2 : 9$ (4) $9 : 2$ 98. $Assume each oil drop consists of a capacitance of C. If combine n drops to form a bigger drop, then the capacitance of bigger drop C' would be$ (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) $C^{’} = C . n^{1/3}$ 99. $In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2. If the initial capacity of the capacitor is 4 μF, then its new capacity is$ (1) $32 μF$ (2) $18 μF$ (3) $8 μF$ (4) $44 μF$ 100. $A series combination of N_{1} capacitors (each of capacity C_{1}) is charged to potential difference ' 3V '. Another parallel combination of N_{2} capacitors (each of capacity C_{2}) is charged to potential difference ' V '. The total energy stored in both combinations is same. The value of C_{1} in terms of C_{2} is$ (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) $\frac{C _{2} N _{2}}{9 N _{1}}$ 101. $The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is$ (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) $Inversely proportional to the distance between the plates$ 102. $A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be$ (1) $400 %$ (2) $66.6 %$ (3) $33.3 %$ (4) $200 %$ 103. $The equivalent capacitance between A and B is,$ (1) $150 pF$ (2) $50 pF$ (3) $300 pF$ (4) $\frac{100}{3} pF$ 104. $Which of the following combination of 7 identical capacitors each of 2 μF gives a capacitance of \frac{10}{11} μF ?$ (1) $5 in parallel and 2 in series$ (2) $4 in parallel and 3 in series$ (3) $3 in parallel and 4 in series$ (4) $2 in parallel and 5 in series$ 105. $A simple pendulum has a length l and the mass of the bob is m . The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by$ (1) $2 π \frac{l}{g}$ (2) $2 π \frac{l}{g + \frac{qE}{m}}$ (3) $2 π \frac{l}{g - \frac{qE}{m}}$ (4) $2 π \frac{1}{g ^{2} + ( \frac{qE}{m} ) ^{2}}$ 106. $A parallel plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants K_{1}, K_{2}, K_{3} and K_{4} as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by [NEET 2021]$ (1) $K = K_{1} + K_{2} + K_{3} + 3 K_{4}$ (2) $K = \frac{2}{3} (K_{1} + K_{2} + K_{3}) + 2 K_{4}$ (3) $\frac{2}{K} = \frac{3}{K _{1} + K _{2} + K _{3}} + \frac{1}{K _{4}}$ (4) $\frac{1}{K} = \frac{1}{K _{1}} + \frac{1}{K _{2}} + \frac{1}{K _{3}} + \frac{3}{2 K _{4}}$ 107. $Effective capacitance of parallel combination of two capacitors C_{1} and C_{2} is 10µF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C_{2} is 4 times that of C_{1} . If these capacitors are connected in series, their effective capacitance will be$ (1) $4.2 µF$ (2) $8.4 µF$ (3) $3.2 µF$ (4) $1.6 µF$ 108. $In the network shown below, the charge accumulated in the capacitor in steady state will be:$ (1) $10.3µC$ (2) $4.8µC$ (3) $12µC$ (4) $7.2µC$ 109. $A parallel plate capacitor is of area 6 c m^{2} and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K_{1} = 10, K_{2} = 12 and K_{3} = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:$ (1) $4$ (2) $14$ (3) $36$ (4) $12$ 110. $Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q_{1}, Q_{2}, Q_{3}, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q_{1} : Q_{2} : Q_{3}, is$ (1) $1 : 2 : 3$ (2) $1 : 3 : 5$ (3) $1 : 4 : 9$ (4) $1 : 8 : 18$ 111. $A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is \frac{d}{3} initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is$ (1) $\frac{6 ϵ _{0} R}{5 d + 3 V t}$ (2) $\frac{( 15 d + 9 V t ) ϵ _{0} R}{2 d ^{2} - 3 d V t - 9 V ^{2} t ^{2}}$ (3) $\frac{6 ϵ _{0} R}{5 d - 3 V t}$ (4) $\frac{( 15 d - 9 V t ) ϵ _{0} R}{2 d ^{2} + 3 d V t - 9 V ^{2} t ^{2}}$ 112. $A capacitor is fully charged with a battery and then disconnected. A dielectric is then inserted into the capacitor. How do charges on surface of the dielectric and outer surface of the plates of the capacitor would change respectively?$ (1) $Increases, decreases$ (2) $Decreases, increases$ (3) $Increases, remain unchanged$ (4) $Remains unchanged, increases$ 113. $Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, - σ and + σ respectively. The potential of shell B is:$ (1) $\frac{σ}{ϵ _{0}} (\frac{b ^{2} - c ^{2}}{b} + a)$ (2) $\frac{σ}{ϵ _{0}} (\frac{b ^{2} - c ^{2}}{c} + a)$ (3) $\frac{σ}{ϵ _{0}} (\frac{a ^{2} - b ^{2}}{a} + c)$ (4) $\frac{σ}{ϵ _{0}} (\frac{a ^{2} - b ^{2}}{b} + c)$ 114. $The electric field between the two parallel plates of a capacitor of 1.5 μF capacitance drops to one third of its initial value in 6.6 μs when the plates are connected by a thin wire. The resistance of this wire is______Ω . (Given, log 3 = 1.1)$ 115. $A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5 μ F . The dielectric constant of the medium between the capacitor plates is 1. It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be Vs^{- 1} .$ 116. $A particle, of mass 10-3kg and charge 1.0 C, is initially at rest. At time t = 0, the particle comes under the influence of an electric field E (t) = E_{0} sin ω t i where E_{0} = 1.0 N C^{-1} and ω = 103 rad s^{- 1} . Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s^{-1}, attained by the particle at subsequent times is ____________.$ 117. $A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is 7 \times \frac{10 ^{8} V}{s} then the integer value of the distance between the parallel plates is (Take, ϵ_{0} = 9 \times 10^{- 12} \frac{F}{m}, π = \frac{22}{7}) μm .$ 118. $In a parallel plate capacitor set up, the plate area of capacitor is 2m² and the plates are separated by 1m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2m² (see fig.) the capacitance of the set-up will be ___ϵ_{0} . (Dielectric constant of the material =3.2) (Round off to the Nearest Integer)$ 119. $A 16Ω wire is bend to form a square loop. A 9 V battery with internal resistance 1Ω is connected across one of its sides. If a 4 μF capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \frac{x}{2} μJ . where x =_____$ 120. $Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be_______V$