Capacitance PYQs Set 7 (PDF)

Set 7 of 8 · Questions 181-210 of 239

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 7 (Q181-210)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
181. $In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in the circuit in terms of capacitance ‘C’ and total charge ‘Q’ is:$ (1) $\frac{1}{8} \frac{Q ^{2}}{C}$ (2) $\frac{3}{8} \frac{Q ^{2}}{C}$ (3) $\frac{5}{8} \frac{Q ^{2}}{C}$ (4) $\frac{3}{4} \frac{Q ^{2}}{C}$ 182. $Consider a uniform spherical charge distribution of radius R1 centered at the origin O. In this distribution, a spherical cavity of radius R2, centered at P with distance OP = a = R1 - R2 (see figure) is made. If the electric field inside the cavity at position r is E (r), then the correct statement(s) is(are)$ (1) $E is uniform, its magnitude is independent of R_{2} but its direction depends on r$ (2) $E is uniform, its magnitude depends on R_{2} and its direction depends on r$ (3) $E is uniform, its magnitude is independent of a but its direction depends on a$ (4) $E is uniform, and both its magnitude and direction depends on a$ 183. $A capacitor is made of a flat plate of area A and a second plate of stair-like structure as shown in the figure. The area of each stair is \frac{A}{3} and the height is d. The capacitance of the arrangement is$ (1) $\frac{ϵ _{0} A}{3 d}$ (2) $\frac{6 ϵ _{0} A}{11 d}$ (3) $\frac{3 ϵ _{0} A}{d}$ (4) $\frac{11 ϵ _{0} A}{18 d}$ 184. $Consider a system of three charges \frac{q}{3}, \frac{q}{3} and - \frac{2 q}{3} placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60º.$ (1) $The electric field at point O is \frac{q}{8 π ϵ _{0} R ^{2}} directed along the negative x-axis.$ (2) $The potential energy of the system is zero.$ (3) $The magnitude of the force between the charges at C and B is \frac{q ^{2}}{54 π ϵ _{0} R ^{2}} .$ (4) $The potential at point O is \frac{q}{12 π ϵ _{0} R} .$ 185. $Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF . When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be:$ (1) $1.6 μF$ (2) $16 μF$ (3) $4 μF$ (4) $1 4 μF$ 186. $A capacitor is made of two square plates each of side a making a very small angle α between them, as shown in figure. The capacitance will be close to:$ (1) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{αa}{2 d})$ (2) $ϵ_{0} a^{2} (1 - \frac{αa}{d})$ (3) $\frac{ϵ _{0} a ^{2}}{d} (1 + \frac{αa}{2 d})$ (4) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{αa}{4 d})$ 187. $A parallel plate capacitor is made two square plates of side ‘a’, separated by a distance d (d ≪ a) . The lower triangular portion is filled with dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:$ (1) $\frac{K \in _{0} a ^{2}}{2 d ( K + 1 )}$ (2) $\frac{K \in _{0} a ^{2}}{d ( K - 1 )} ln K$ (3) $\frac{K \in _{0} a ^{2}}{d} ln K$ (4) $\frac{1}{2} \frac{K \in _{0} a ^{2}}{d}$ 188. $A parallel plate capacitor with plate area A and plate separation d=2 m has a capacitance of 4µF. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K=3 (as shown in figure) will be:$ (1) $2µF$ (2) $32µF$ (3) $6µF$ (4) $8µF$ 189. $A system of three charges are placed as showed in the figure: If D >> d, the potential energy of the system is best given by$ (1) $\frac{1}{4 π \in _{0}} (\frac{- q ^{2}}{d} \frac{- qQd}{2 D ^{2}})$ (2) $\frac{1}{4 π \in _{0}} (\frac{- q ^{2}}{d} + \frac{2 qQd}{D ^{2}})$ (3) $\frac{1}{4 π \in _{0}} (+ \frac{q ^{2}}{d} + \frac{qQd}{D ^{2}})$ (4) $\frac{1}{4 π \in _{0}} (- \frac{q ^{2}}{d} - \frac{qQd}{D ^{2}})$ 190. $The capacitance of a parallel plate capacitor is 2.5 μF . When it is half filled with a dielectric as shown in figure, its capacitance becomes 5 μF . The dielectric constant of the dielectric is$ (1) $7.5$ (2) $3$ (3) $4$ (4) $5$ 191. $The charge stored by the capacitor C in the given circuit in the steady state is____μC .$ (1) $5$ (2) $12.5$ (3) $10$ (4) $7.5$ 192. $A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is 5 cm^{2} . The capacity of the unit is$ (1) $1.06 pF$ (2) $4 pF$ (3) $6.36 pF$ (4) $12.72 pF$ 193. $A resistor 'R' and 2µF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (l o g_{10} 2.5 = 0.4)$ (1) $1.3 \times 104 Ω$ (2) $1.7 \times 105 Ω$ (3) $2.7 \times 106 Ω$ (4) $3.3 \times 107 Ω$ 194. $The charge on capacitor of capacitance 15µF in the figure given below is:$ (1) $60µc$ (2) $130µc$ (3) $260µc$ (4) $585µc$ 195. $In the given circuit, a charge of + 80 μC is given to upper plate of a 4 μF capacitor. At steady state, the charge on the upper plate of the 3 μF capacitor is$ (1) $60 μC$ (2) $48 μC$ (3) $80 μC$ (4) $0^{’} μC$ 196. $Two capacitors C_{1} and C_{2} are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:$ (1) $5 C_{1} = 3 C_{2}$ (2) $3 C_{1} = 5 C_{2}$ (3) $3 C_{1} + 5 C_{2} = 0$ (4) $9 C_{1} = 4 C_{2}$ 197. $A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (i). Then, it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (ii). The electrostatic energy stored by the system (ii) is [NEET 2021]$ (1) $3.25 \times 10^{- 6} J$ (2) $2.25 \times 10^{- 6} J$ (3) $1.5 \times 10^{- 6} J$ (4) $4.5 \times 10^{- 6} J$ 198. $A 100 V battery is connected across the series combination of the two capacitors of 4 μF and 8 μF . The energy stored in the series combination is$ (1) $0.75 \times 10^{- 2} J$ (2) $1.33 \times 10^{- 2} J$ (3) $0.5 J$ (4) $1 J$ 199. $A 2µF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is$ (1) $0%$ (2) $20%$ (3) $75%$ (4) $80%$ 200. $Two charges, each equal to q, are kept at x = - a and x = a on the x-axis. A particle of mass m and charge q_{0} = \frac{q}{2} is placed at the origin. If charge q_{0} is given a small displacement (y <<a) along the y-axis, the net force acting on the particle is proportional to:$ (1) $y$ (2) $-y$ (3) $\frac{1}{y}$ (4) $- \frac{1}{y}$ 201. $A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E_{1} . The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E_{2} . The ratio \frac{E _{2}}{E _{1}} is$ (1) $2 : 1$ (2) $2 : 3$ (3) $1 : 2$ (4) $1 : 4$ 202. $For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \frac{3}{4} d where 'd' is the separationbetween the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance is (C_{0}) given by the following relation:$ (1) $C^{’} = \frac{3 + K}{4 K} C_{0}$ (2) $C^{’} = \frac{4 + K}{3} C_{0}$ (3) $C^{’} = \frac{4 K}{K + 3} C_{0}$ (4) $C^{’} = \frac{4}{3 + K} C_{0}$ 203. $A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is$ (1) $0$ (2) $54 µC$ (3) $27 µC$ (4) $81 µC$ 204. $A parallel plate capacitor with square plates is filled with four dielectrics of dielectrics constant K_{1}, K_{2}, K_{3}, K_{4} arranged as shown in figure. The effective dielectric constant K will be:$ (1) $K = \frac{k _{1} k _{2} ( k _{3} + k _{4} ) + k _{3} k _{4} ( k _{1} + k _{2} )}{( k _{1} + k _{2} ) ( k _{3} + k _{4} )}$ (2) $K = \frac{( K _{1} + K _{2} ) ( K _{3} + K _{4} )}{2 ( K _{1} + K _{2} + K _{3} + K _{4} )}$ (3) $K = \frac{( K _{1} + K _{2} ) ( K _{3} + K _{4} )}{K _{1} + K _{2} + K _{3} + K _{4}}$ (4) $K = \frac{( K _{1} + K _{4} ) ( K _{2} + K _{3} )}{2 ( K _{1} + K _{2} + K _{3} + K _{4} )}$ 205. $Two capacitors having capacitance C_{1} and C_{2} respectively are connected as shown in figure. Initially, capacitor C_{1} is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C_{1} is now connected to uncharged capacitor C_{2} by closing the switch S. The amount of charge on the capacitor C_{2}, after equilibrium is :$ (1) $\frac{C _{1} C _{2}}{( C _{1} + C _{2} )} V$ (2) $\frac{( C _{1} + C _{2} )}{C _{1} C _{2}} V$ (3) $(C_{1} + C_{2}) V$ (4) $(C_{1} - C_{2}) V$ 206. $Seven capacitors, each of capacitance 2 μF, are to be connected in a configuration to obtain an effective capacitance of (\frac{6}{13}) μF . Which of the combinations, shown in figure below, will achieve the desired value?$ (1) (2) (3) (4) 207. $Two capacitors, each having capacitance 40µF are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant K such that the equivalence capacitance of the system became 24µF. The value of K will be:$ (1) $1.5$ (2) $2.5$ (3) $1.2$ (4) $3$ 208. $A galvanometer (G) of 2Ω resistance is connected in the given circuit. The ratio of charge stored in C_{1} and C_{2} is:$ (1) $\frac{2}{3}$ (2) $\frac{3}{2}$ (3) $1$ (4) $\frac{1}{2}$ 209. $Let ρ(r) = \frac{Q}{π R ^{4}} r be the charge density distribution for a solid sphere of radius R and total charge Q. For a point ‘P’ inside the sphere at distance r_{1} from the center of sphere, the magnitude of electric field is:$ (1) $\frac{Q}{4 π ϵ _{0} r _{1}^{2}}$ (2) $\frac{Q r _{1}^{2}}{4 π ϵ _{0} R ^{4}}$ (3) $\frac{Q r _{1}^{2}}{3 π ϵ _{0} R ^{4}}$ (4) $0$ 210. $In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF . All values in the circuit are μF .$ (1) $\frac{7}{11} μF$ (2) $\frac{6}{5} μF$ (3) $4 μF$ (4) $\frac{7}{10} μF$