Capacitance PYQs Set 4 (PDF)

Set 4 of 8 · Questions 91-120 of 239

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Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 4 (Q91-120)
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91. $Which of the following combination of 7 identical capacitors each of 2 μF gives a capacitance of \frac{10}{11} μF ?$ (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) $2 in parallel and 5 in series$ 92. $A simple pendulum has a length l and the mass of the bob is m . The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by$ (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) $2 π \frac{1}{g ^{2} + ( \frac{qE}{m} ) ^{2}}$ 93. $A parallel plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants K_{1}, K_{2}, K_{3} and K_{4} as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by [NEET 2021]$ (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) $\frac{1}{K} = \frac{1}{K _{1}} + \frac{1}{K _{2}} + \frac{1}{K _{3}} + \frac{3}{2 K _{4}}$ 94. $Effective capacitance of parallel combination of two capacitors C_{1} and C_{2} is 10µF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C_{2} is 4 times that of C_{1} . If these capacitors are connected in series, their effective capacitance will be$ (1) $4.2 µF$ (2) $8.4 µF$ (3) $3.2 µF$ (4) $1.6 µF$ 95. $In the network shown below, the charge accumulated in the capacitor in steady state will be:$ (1) $10.3µC$ (2) $4.8µC$ (3) $12µC$ (4) $7.2µC$ 96. $A parallel plate capacitor is of area 6 c m^{2} and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K_{1} = 10, K_{2} = 12 and K_{3} = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:$ (1) $4$ (2) $14$ (3) $36$ (4) $12$ 97. $Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q_{1}, Q_{2}, Q_{3}, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q_{1} : Q_{2} : Q_{3}, is$ (1) $1 : 2 : 3$ (2) $1 : 3 : 5$ (3) $1 : 4 : 9$ (4) $1 : 8 : 18$ 98. $A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is \frac{d}{3} initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is$ (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) $\frac{( 15 d - 9 V t ) ϵ _{0} R}{2 d ^{2} + 3 d V t - 9 V ^{2} t ^{2}}$ 99. $A capacitor is fully charged with a battery and then disconnected. A dielectric is then inserted into the capacitor. How do charges on surface of the dielectric and outer surface of the plates of the capacitor would change respectively?$ (1) $Increases, decreases$ (2) $Decreases, increases$ (3) $Increases, remain unchanged$ (4) $Remains unchanged, increases$ 100. $Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, - σ and + σ respectively. The potential of shell B is:$ (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) $\frac{σ}{ϵ _{0}} (\frac{a ^{2} - b ^{2}}{b} + c)$ 101. $Four identical metal plates are located in air at equal distance d from each other. The area of each plate is S. If the outer most plates are connected by a conducting wire as shown in the figure the capacitance between points A and B will be$ (1) $\frac{ϵ _{0} S}{d}$ (2) $\frac{3}{2} \frac{ϵ _{0} S}{d}$ (3) $\frac{1}{2} \frac{ϵ _{0} S}{d}$ (4) $\frac{2}{3} \frac{ϵ _{0} S}{d}$ 102. $A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: ϵ (x) = ϵ_{0} + kx, for (0 < x \leq \frac{d}{2}) ϵ (x) = ϵ_{0} + k (d - x), for (\frac{d}{2} \leq x \leq d)$ (1) $(ϵ_{0} + \frac{kd}{2})^{2/ kA}$ (2) $\frac{kA}{2 ln ( \frac{2 ϵ _{0} + kd}{2 ϵ _{0}} )}$ (3) $0$ (4) $\frac{kA}{2} ln (\frac{2 ϵ _{0}}{2 ϵ _{0} - kd})$ 103. $A capacitor C_{1} = 4 μF is connected in series with another capacitor C_{2} = 1 μF . The combination is connected across d.c. source of 200 V . The ratio of potential across C_{2} to C_{1} is$ (1) $2 : 1$ (2) $4 : 1$ (3) $8 : 1$ (4) $16 : 1$ 104. $A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be$ (1) $(K + 3) \frac{C}{4}$ (2) $(K + 2) \frac{C}{4}$ (3) $(K + 1) \frac{C}{4}$ (4) $\frac{KC}{4}$ 105. $A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system [NEET 2017]$ (1) $increases by a factor of 4$ (2) $decreases by a factor of 2$ (3) $remains the same$ (4) $increases by a factor of 2$ 106. $A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is:$ (1) $\frac{Q}{8 π \in _{0} L}$ (2) $\frac{3 Q}{4 π \in _{0} L}$ (3) $\frac{Q}{4 π \in _{0} L ln 2}$ (4) $\frac{Q ln 2}{4 π \in _{0} L}$ 107. $Two identical capacitors C_{1} and C_{2} of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C_{1} using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy?$ (1) $75%$ (2) $0%$ (3) $50%$ (4) $25%$ 108. $When three capacitors of equal capacities are connected in parallel and one of the same capacity is connected in series with its combination. The resultant capacity is 3.75 μF . The capacity of each capacitor is$ (1) $5 μF$ (2) $6 μF$ (3) $7 μF$ (4) $8 μF$ 109. $In the given circuit, the charge on 4 μF capacitor will be:$ (1) $5.4 μC$ (2) $9.6 μC$ (3) $13.4 μC$ (4) $24 μC$ 110. $Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be:$ (1) $\frac{V}{K + 2}$ (2) $\frac{V}{K}$ (3) $\frac{3 V}{K + 2}$ (4) $\frac{3 V}{K}$ 111. $All capacitors used in the diagram are identical and each is of capacitance X. Then the effective capacitance between the points A and B is$ (1) $1.5 C$ (2) $6C$ (3) $C$ (4) $3C$ 112. $Calculate the amount of charge on capacitor of 4 μF . The internal resistance of battery is 1Ω :$ (1) $8 μC$ (2) $zero$ (3) $16 μC$ (4) $4 μC$ 113. $A parallel - plate capacitor with plate area A has separation between the plates. Two dielectric slabs of dielectric constant K_{1} and K_{2} of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:$ (1) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{K _{1} + K _{2}})$ (2) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{2 ( K _{1} + K _{2} )})$ (3) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} + K _{2}}{K _{1} K _{2}})$ (4) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{2 ( K _{1} + K _{2} )}{K _{1} K _{2}})$ 114. $A capacitor of capacitance C = 1 μF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω . The time taken for the capacitor to be charged to get is 50V: [Take ln 2 = 0.69]$ (1) $1.44 \times 1 0^{- 4} s$ (2) $3.33 \times 1 0^{- 4} s$ (3) $0.69 \times 1 0^{- 4} s$ (4) $0.30 \times 1 0^{- 4} s$ 115. $Find the equivalent capacitance between point A and B.$ (1) $4C$ (2) $3C$ (3) $2C$ (4) $1C$ 116. $In the circuit shown, charge on the 5 μF capacitor is$ (1) $16.36 μC$ (2) $18.00 μC$ (3) $5.45 μC$ (4) $10.90 μC$ 117. $The total charge on the system of capacitance C_{1} = 1µ F_{,} C_{2} =2µF, C_{3} =4µF and C_{4} =3µF connected in parallel is (Assume a battery of 20V is connected to the combination)$ (1) $200µC$ (2) $200C$ (3) $10µC$ (4) $10C$ 118. $A capacitor is charged by a battery. The battery is removed, and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system$ (1) $decreases by a factor of 2$ (2) $remains the same$ (3) $increases by a factor of 2$ (4) $increases by a factor of 4$ 119. $The figure shows an experimental plot discharging of a capacitor in an RC circuit. The time constant τ of this circuit lies between:$ (1) $150 sec and 200 sec$ (2) $0 and 50 sec$ (3) $50 sec and 100 sec$ (4) $100 sec and 150 sec$ 120. $A parallel plate capacitor with air medium between the plates has a capacitance of 10 μF . The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant K_{1} = 2 and K_{2} = 4 . The capacitance of the system will be$ (1) $10 μF$ (2) $20 μF$ (3) $30 μF$ (4) $40 μF$