Capacitance PYQs Set 9 (PDF)

Set 9 of 11 · Questions 241-270 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 9 (Q241-270)
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241. $A resistor 'R' and 2µF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (l o g_{10} 2.5 = 0.4)$ (1) $1.3 \times 104 Ω$ (2) $1.7 \times 105 Ω$ (3) $2.7 \times 106 Ω$ (4) $3.3 \times 107 Ω$ 242. $The charge on capacitor of capacitance 15µF in the figure given below is:$ (1) $60µc$ (2) $130µc$ (3) $260µc$ (4) $585µc$ 243. $In the given circuit, a charge of + 80 μC is given to upper plate of a 4 μF capacitor. At steady state, the charge on the upper plate of the 3 μF capacitor is$ (1) $60 μC$ (2) $48 μC$ (3) $80 μC$ (4) $0^{’} μC$ 244. $Two capacitors C_{1} and C_{2} are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:$ (1) $5 C_{1} = 3 C_{2}$ (2) $3 C_{1} = 5 C_{2}$ (3) $3 C_{1} + 5 C_{2} = 0$ (4) $9 C_{1} = 4 C_{2}$ 245. $A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (i). Then, it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (ii). The electrostatic energy stored by the system (ii) is [NEET 2021]$ (1) $3.25 \times 10^{- 6} J$ (2) $2.25 \times 10^{- 6} J$ (3) $1.5 \times 10^{- 6} J$ (4) $4.5 \times 10^{- 6} J$ 246. $A uniformly charged solid sphere of radius R has potential V_{0} (measured with respect to ¥) on its surface. For this sphere the equipotential surfaces with potentials \frac{3 V _{0}}{2}, \frac{5 V _{0}}{4}, \frac{3 V _{0}}{4} and \frac{V _{0}}{4} have radius R_{1}, R_{2}, R_{3} and R_{4} respectively. Then$ (1) $R_{1} = 0 and R_{2} > (R_{4} - R_{3})$ (2) $R_{1} \neq 0 and (R_{2} - R_{1}) > (R_{4} - R_{3})$ (3) $R_{1} = 0 and R_{2} < (R_{4} - R_{3})$ (4) $2R < R_{4}$ 247. $A 100 V battery is connected across the series combination of the two capacitors of 4 μF and 8 μF . The energy stored in the series combination is$ (1) $0.75 \times 10^{- 2} J$ (2) $1.33 \times 10^{- 2} J$ (3) $0.5 J$ (4) $1 J$ 248. $A 2µF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is$ (1) $0%$ (2) $20%$ (3) $75%$ (4) $80%$ 249. $Two charges, each equal to q, are kept at x = - a and x = a on the x-axis. A particle of mass m and charge q_{0} = \frac{q}{2} is placed at the origin. If charge q_{0} is given a small displacement (y <<a) along the y-axis, the net force acting on the particle is proportional to:$ (1) $y$ (2) $-y$ (3) $\frac{1}{y}$ (4) $- \frac{1}{y}$ 250. $A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E_{1} . The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E_{2} . The ratio \frac{E _{2}}{E _{1}} is$ (1) $2 : 1$ (2) $2 : 3$ (3) $1 : 2$ (4) $1 : 4$ 251. $For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \frac{3}{4} d where 'd' is the separationbetween the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance is (C_{0}) given by the following relation:$ (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) $C^{’} = \frac{4}{3 + K} C_{0}$ 252. $A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is$ (1) $0$ (2) $54 µC$ (3) $27 µC$ (4) $81 µC$ 253. $A parallel plate capacitor with square plates is filled with four dielectrics of dielectrics constant K_{1}, K_{2}, K_{3}, K_{4} arranged as shown in figure. The effective dielectric constant K will be:$ (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) $K = \frac{( K _{1} + K _{4} ) ( K _{2} + K _{3} )}{2 ( K _{1} + K _{2} + K _{3} + K _{4} )}$ 254. $Two capacitors having capacitance C_{1} and C_{2} respectively are connected as shown in figure. Initially, capacitor C_{1} is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C_{1} is now connected to uncharged capacitor C_{2} by closing the switch S. The amount of charge on the capacitor C_{2}, after equilibrium is :$ (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) $(C_{1} - C_{2}) V$ 255. $Seven capacitors, each of capacitance 2 μF, are to be connected in a configuration to obtain an effective capacitance of (\frac{6}{13}) μF . Which of the combinations, shown in figure below, will achieve the desired value?$ (1) (2) (3) (4) 256. $Two capacitors, each having capacitance 40µF are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant K such that the equivalence capacitance of the system became 24µF. The value of K will be:$ (1) $1.5$ (2) $2.5$ (3) $1.2$ (4) $3$ 257. $A galvanometer (G) of 2Ω resistance is connected in the given circuit. The ratio of charge stored in C_{1} and C_{2} is:$ (1) $\frac{2}{3}$ (2) $\frac{3}{2}$ (3) $1$ (4) $\frac{1}{2}$ 258. $Let ρ(r) = \frac{Q}{π R ^{4}} r be the charge density distribution for a solid sphere of radius R and total charge Q. For a point ‘P’ inside the sphere at distance r_{1} from the center of sphere, the magnitude of electric field is:$ (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) $0$ 259. $In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF . All values in the circuit are μF .$ (1) $\frac{7}{11} μF$ (2) $\frac{6}{5} μF$ (3) $4 μF$ (4) $\frac{7}{10} μF$ 260. $A parallel plate capacitor is formed by two plates each of area 30 π c m^{2} separated by 1 mm. A material of dielectric strength 3.6 \times 1 0^{7} V m^{- 1} is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 \times 1 0^{- 6} C, the value of dielectric constant of the material is: (Use : \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2})$ (1) $1.66$ (2) $1.75$ (3) $2.25$ (4) $2.33$ 261. $A capacitor of capacitance 10 μ F is charged to 10 V . The energy stored in it is$ (1) $100 μJ$ (2) $500 μJ$ (3) $1000 μJ$ (4) $1 μ J$ 262. $Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R, Assertion A: Two metallic spheres are charged to the same potential One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R: Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.$ (1) $A is false but R is true$ (2) $Both A and R are true and R is the correct explanation of A$ (3) $A is true but R is false$ (4) $Both A and R are true but R is not the correct explanation of A$ 263. $Identify the correct statements :(A) Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.(B) When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.(C) Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.(D) For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below:$ (1) $B and D Only$ (2) $A, B and C Only$ (3) $C and D Only$ (4) $A, C and D Only$ 264. $At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V? [Take: ln 5 = 1.6, ln 3 = 1.1]$ 265. $Space between the plates of a parallel plate capacitor of plate area 4 cm^{2} and separation of 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is _ pF. (Given ϵ_{0} = 8.85 \times 10^{- 12} F / m)$ 266. $A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be......... \in_{0} J. (Where \in_{0} is the permittivity of free space)$ 267. $Four identical rectangular plates with length, l = 2 cm and breadth, b = \frac{3}{2} cm are arranged as shown infigure. The equivalent capacitance between A and C is \frac{x ϵ _{0}}{d} . The value of x is (Round off to the Nearest Integer)$ 268. $A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C1 and C2 be the capacitance of the system for x = \frac{1}{3} d and x = \frac{2 d}{3}, respectively. If C1 = 2 μ F, the value of C2 is _____μ F.$ 269. $A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected between its plates to potential difference of 12.0 V . The battery is now disconnected and a dielectric slab (ϵ_{r} = 6) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ____ pJ.$ 270. $A capacitor P with capacitance 10 \times 10^{- 6} F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance 20 \times 10^{- 6} F . The charge on capacitor Q when equilibrium is established will be α \times 10^{- 5} C (assume capacitor Q does not have any charge initially), the value of α is___.$