Capacitance PYQs Set 8 (PDF)

Set 8 of 11 · Questions 211-240 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 8 (Q211-240)
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211. $The equivalent capacitance between A and B in the given circuit is$ (1) $3 μF$ (2) $1 μF$ (3) $2 μ$ (4) $1.5 μF$ 212. $A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to$ (1) $\frac{1}{ϵ _{0}} σ^{2} R^{2}$ (2) $\frac{1}{ϵ _{0}} σ^{2} R$ (3) $\frac{1}{ϵ _{0}} \frac{σ ^{2}}{R}$ (4) $\frac{1}{ϵ _{0}} \frac{σ ^{2}}{R ^{2}}$ 213. $Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)$ (1) $600$ (2) $100$ (3) $400$ (4) $200$ 214. $A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4µF and 9µF capacitors), at a point distance 30 m from it, would equal:$ (1) $360 N/C$ (2) $420 N/C$ (3) $480 N/C$ (4) $240 N/C$ 215. $A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k_{1} = 3 and thickness d/3 while the other one has dielectric constant k_{2} = 6 and thickness 2d/3. Capacitance of the capacitor is now:$ (1) $45 pF$ (2) $40.5 pF$ (3) $20.25 pF$ (4) $1.8 pF$ 216. $Four metal plates, each with surface area A on one side, are placed with separation ' d ' as shown in the figure. The capacitance between a and b is (ϵ_{0} -) permittivity of free space)$ (1) $\frac{3 ϵ _{0} A}{d}$ (2) $\frac{2 ϵ _{0} A}{d}$ (3) $\frac{2 ϵ _{0} A}{3 d}$ (4) $\frac{3 ϵ _{0} A}{2 d}$ 217. $The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = \frac{A}{r}, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:$ (1) $\frac{Q}{2 π ( b ^{2} - a ^{2} )}$ (2) $\frac{2 Q}{π ( a ^{2} - b ^{2} )}$ (3) $\frac{2 Q}{π a ^{2}}$ (4) $\frac{Q}{2 π a ^{2}}$ 218. $In the following circuit, the equivalent capacitance between terminal A and terminal B is [NEET 2024]$ (1) $2 μF$ (2) $1 μF$ (3) $0.5 μF$ (4) $4 μF$ 219. $The following figure shows a 9 V battery and 3 uncharged capacitors of capacitances C_{1} = C_{2} = C_{3} = 1 μF . The switch is thrown to the right side until capacitor C_{1} is fully charged, then the switch is thrown fo the left. The final charge on capacitor C_{2} is$ (1) $1 μC$ (2) $2 μC$ (3) $3 μC$ (4) $4 μC$ 220. $A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is E_{1} . Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E_{2} . The ratio E_{1} / E_{2} will be:$ (1) $\frac{1}{10}$ (2) $\frac{2}{5}$ (3) $\frac{5}{13}$ (4) $\frac{5}{26}$ 221. $A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?$ (1) $The energy stored in the capacitor decreases K times.$ (2) $The chance in energy stored is \frac{1}{2} C V^{2} (\frac{1}{K} - 1)$ (3) $The charge on the capacitor is not conserved.$ (4) $The potential difference between the plates decreases K times.$ 222. $In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in the circuit in terms of capacitance ‘C’ and total charge ‘Q’ is:$ (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) $\frac{3}{4} \frac{Q ^{2}}{C}$ 223. $Consider a uniform spherical charge distribution of radius R1 centered at the origin O. In this distribution, a spherical cavity of radius R2, centered at P with distance OP = a = R1 - R2 (see figure) is made. If the electric field inside the cavity at position r is E (r), then the correct statement(s) is(are)$ (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) $E is uniform, and both its magnitude and direction depends on a$ 224. $A capacitor is made of a flat plate of area A and a second plate of stair-like structure as shown in the figure. The area of each stair is \frac{A}{3} and the height is d. The capacitance of the arrangement is$ (1) $\frac{ϵ _{0} A}{3 d}$ (2) $\frac{6 ϵ _{0} A}{11 d}$ (3) $\frac{3 ϵ _{0} A}{d}$ (4) $\frac{11 ϵ _{0} A}{18 d}$ 225. $Consider a system of three charges \frac{q}{3}, \frac{q}{3} and - \frac{2 q}{3} placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60º.$ (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) $The potential at point O is \frac{q}{12 π ϵ _{0} R} .$ 226. $Six point charges are kept at the vertices of a regular hexagon of side L and center O, as shown in the figure. Given that K = \frac{1}{4 π ϵ _{0}} \frac{q}{L ^{2}}, which of the following statement (s) is (are) correct?$ (1) $the electric field at O is 6K along OD$ (2) $The potential at O is zero$ (3) $The potential at all points on the line PR is same$ (4) $The potential at all points on the line ST is same.$ 227. $Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF . When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be:$ (1) $1.6 μF$ (2) $16 μF$ (3) $4 μF$ (4) $1 4 μF$ 228. $A capacitor is made of two square plates each of side a making a very small angle α between them, as shown in figure. The capacitance will be close to:$ (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) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{αa}{4 d})$ 229. $A parallel plate capacitor is made two square plates of side ‘a’, separated by a distance d (d ≪ a) . The lower triangular portion is filled with dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:$ (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) $\frac{1}{2} \frac{K \in _{0} a ^{2}}{d}$ 230. $A few electric field lines for a system of two charges Q_{1} and Q_{2} fixed at two different points on the x-axis are shown in the figure. These lines suggest that:$ (1) $\| Q_{1} \| > \| Q_{2} \|$ (2) $\| Q_{1} \| < \| Q_{2} \|$ (3) $at a finite distance to the left of Q_{1} the electric field is zero$ (4) $at a finite distance to the right of Q_{2} the electric field is zero$ 231. $A parallel plate capacitor with plate area A and plate separation d=2 m has a capacitance of 4µF. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K=3 (as shown in figure) will be:$ (1) $2µF$ (2) $32µF$ (3) $6µF$ (4) $8µF$ 232. $A system of three charges are placed as showed in the figure: If D >> d, the potential energy of the system is best given by$ (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) $\frac{1}{4 π \in _{0}} (- \frac{q ^{2}}{d} - \frac{qQd}{D ^{2}})$ 233. $The capacitance of a parallel plate capacitor is 2.5 μF . When it is half filled with a dielectric as shown in figure, its capacitance becomes 5 μF . The dielectric constant of the dielectric is$ (1) $7.5$ (2) $3$ (3) $4$ (4) $5$ 234. $The charge stored by the capacitor C in the given circuit in the steady state is____μC .$ (1) $5$ (2) $12.5$ (3) $10$ (4) $7.5$ 235. $In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?$ (1) $The voltmeter displays -5 V as soon as the key is pressed, and displays +5 V after a long time$ (2) $The voltmeter will display 0 V at time t = ln 2 seconds$ (3) $The current in the ammeter becomes 1/e of the initial value after 1 second$ (4) $The current in the ammeter becomes zero after a long time$ 236. $A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is 5 cm^{2} . The capacity of the unit is$ (1) $1.06 pF$ (2) $4 pF$ (3) $6.36 pF$ (4) $12.72 pF$ 237. $The charge accumulated on the capacitor connected in the following circuit is μC (Given C = 150 μF)$ 238. $A charge particle of 2µC accelerated by a potential difference of 100V enters a region of uniform magnetic field of magnitude 4 mT at right angle to the direction of field. The charge particle completes semicircle of radius 3 cm inside magnetic field. The mass of the charge particle is_____\times 1 0^{- 18} kg.$ 239. $A capacitor of 50 μF is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ..... μC .$ 240. $At steady state the charge on the capacitor, as shown in the circuit below, is μC .$