Capacitance PYQs Set 8 (PDF)

Set 8 of 8 · Questions 211-239 of 239

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Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 8 (Q211-239)
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211. $A parallel plate capacitor is formed by two plates each of area 30 π c m^{2} separated by 1 mm. A material of dielectric strength 3.6 \times 1 0^{7} V m^{- 1} is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 \times 1 0^{- 6} C, the value of dielectric constant of the material is: (Use : \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2})$ (1) $1.66$ (2) $1.75$ (3) $2.25$ (4) $2.33$ 212. $A capacitor of capacitance 10 μ F is charged to 10 V . The energy stored in it is$ (1) $100 μJ$ (2) $500 μJ$ (3) $1000 μJ$ (4) $1 μ J$ 213. $Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R, Assertion A: Two metallic spheres are charged to the same potential One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R: Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.$ (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) $Both A and R are true but R is not the correct explanation of A$ 214. $Identify the correct statements :(A) Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.(B) When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.(C) Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.(D) For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below:$ (1) $B and D Only$ (2) $A, B and C Only$ (3) $C and D Only$ (4) $A, C and D Only$ 215. $A capacitor has air as dielectric medium and two conducting plates of area 12 cm^{2} and they are 0.6 cm apart. When a slab of dielectric having area 12 cm^{2} and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given ϵ_{0} = 8.834 \times 10^{- 12} F / m)$ (1) $1$ (2) $1.33$ (3) $0.66$ (4) $1.50$ 216. $sectional area as the plates of a parallel plate \frac{3}{4} d capacitor and thickness d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be: (Given C_{0} = capacitance of capacitor with air as medium between plates.)$ (1) $\frac{4 K C _{0}}{3 + K}$ (2) $\frac{3 K C _{0}}{3 + K}$ (3) $\frac{3 + K}{4 K C _{0}}$ (4) $\frac{K}{4 + K}$ 217. $A parallel plate capacitor is of area 6 c m^{2} and a separation 3 mm . The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K_{1} = 10, K_{2} = 12 and K_{3} = 14 . The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:$ (1) $4$ (2) $14$ (3) $12$ (4) $26$ 218. $The equivalent capacitance of the combination shown is$ (1) $2C$ (2) $f C$ (3) $\frac{C}{2}$ (4) $4C$ 219. $Seven capacitors, each of capacitance 2µF. are to be connected in a configuration to obtain an effective capacitance of . Which of the combinations, shown in figures below, will achieve the desired value?$ (1) (2) (3) (4) 220. $A force of 10N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be:$ (1) $5N$ (2) $10N$ (3) $20 N$ (4) $Zero$ 221. $A parallel plate capacitor has plates of area A separated by distance d between them. It is filled with a dielectric a dielectric which has a dielectric constant that varies as k (x) = k_{0} (1 + αx) where 'x' is the distance measured from one of the plates. If (αd) << 1, the total capacitance of the system is best given by the expression:$ (1) $\frac{k _{0} ϵ _{0} A}{d} (1 + α^{2} d^{2})$ (2) $\frac{k _{0} ϵ _{0} A}{d} (1 + \frac{α d}{2})$ (3) $\frac{k _{0} ϵ _{0} A}{2 d} (1 + αd)$ (4) $\frac{k _{0} ϵ _{0} A}{2 d} (1 + \frac{αd}{2})$ 222. $A parallel plate capacitor was made with two rectangular plates, each with a length of l 3 cm and breath of b=1 cm. The distance between the plates is 3μ m. Out of the following, which are the ways to increase the capacitance by a factor of 10? (A) l = 30 cm, b = 1 cm, d = 1 μ m (B) l = 3 cm, b = 1 cm, d = 30 μ m (C) l = 6 cm, b = 5 cm, d = 3 μ m (D) l = 1 cm, b = 1 cm, d = 10 μ m (E) l = 5 cm, b = 2 cm, d = 1 μ m Choose the correct answer from the options given below:$ (1) $A only$ (2) $C only$ (3) $B and D only$ (4) $C and E only$ 223. $The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II. List-I P. E is independent of d Q. E μ 1/d R. E μ 1/ d^{2} S. E μ 1/ d^{3} List-II 1. A point charge Q at the origin 2. A small dipole with point charges Q at (0, 0, l) and -Q at (0, 0, -l) Take 2l << d 3. An infinite line charge coincident with the x-axis, with uniform linear charge density l. 4. Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along (y = 0, z = l) has a charge density +l and the one along (y = 0, z = -l) has a charge density -l. Take 2l << d 5. Infinite plane charge coincident with the xy-plane with uniform surface charge density.$ (1) $P \to 5, Q \to 3, 4, R \to 1, S \to 2$ (2) $P \to 5, Q \to 3, R \to 1, 4, S \to 2$ (3) $P \to 5, Q \to 3, R \to 1, 2, S \to 4$ (4) $P \to 4, Q \to 2, 3, R \to 1, S \to 5$ 224. $Four charge Q_{1}, Q_{2}, Q_{3}, and Q_{4}, of same magnitude are fixed along the x axis at x = -2a -a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List-I. The direction of the forces on the charge q is given in List- II Match List-1 with List-II and select the correct answer using the code given below the lists. List-I (P) Q_{1}, Q_{2}, Q_{3}, Q_{4}, all positive (Q) Q_{1}, Q_{2} positive Q_{3}, Q_{4} negative (R) Q_{1}, Q_{4} positive Q_{2}, Q_{3} negative (S) Q_{1}, Q_{3} positive Q_{2}, Q_{4} negative List-II (1) +x (2) -x (3) +y (4) -y$ (1) $P-3, Q-1, R-4, S-2$ (2) $P-4, Q-2, R-3, S-1$ (3) $P-3, Q-1, R-2, S-4$ (4) $P-4, Q-2, R-1, S-3$ 225. $This question has statement-I and statement-II. Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero. Statement-I: When a charge ‘q’ is taken from the center to the surface of the sphere its potential energy changes by \frac{q ρ}{3 ϵ _{0}} . Statement-II: The electric field at a distance r (r < R) from the center of the sphere is \frac{ρ r}{3 ϵ _{0}}$ (1) $Statement-I is true, Statement-II is true; Statement-II is not the correct explanation of statement-I.$ (2) $Statement I is true Statement II is false.$ (3) $Statement I is false Statement II is true.$ (4) $Statement I is true, Statement II is true, Statement II is the correct explanation of Statement I.$ 226. $Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K_{1}, K_{2} and K_{3} . The first capacitors is filled as shown in Fig. I, and the second one is filled as shown in Fig. II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two would be (E_{1} refers to capacitors (I) and E_{2} to capacitors (II):$ (1) $\frac{E _{1}}{E _{2}} = \frac{K _{1} K _{2} K _{3}}{( K _{1} + K _{2} + K _{3} ) ( K _{2} K _{3} + K _{3} K _{1} + K _{1} K _{2} )}$ (2) $\frac{E _{1}}{E _{2}} = \frac{( K _{1} + K _{2} + K _{3} ) ( K _{2} K _{3} + K _{3} K _{1} + K _{1} K _{2} )}{K _{1} K _{2} K _{3}}$ (3) $\frac{E _{1}}{E _{2}} = \frac{9 K _{1} K _{2} K _{3}}{( K _{1} + K _{2} + K _{3} ) ( K _{2} K _{3} + K _{3} K _{1} + K _{1} K _{2} )}$ (4) $\frac{E _{1}}{E _{2}} = \frac{( K _{1} + K _{2} + K _{3} ) ( K _{2} K _{3} + K _{3} K _{1} + K _{1} K _{2} )}{9 K _{1} K _{2} K _{3}}$ 227. $A capacitor, C_{1} = 6 μ F is charged to a potential difference of V_{0} = 5 V using a 5 V battery. The battery is removed and another capacitor, C_{2} = 12 μ F is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (q_{1} and q_{2}) on the capacitors C_{1} and C_{2} when equilibrium condition is reached.$ (1) $q_{1} = 10 μC, q_{2} = 20 μC$ (2) $q_{1} = 30 μC, q_{2} = 15 μC$ (3) $q_{1} = 20 μC, q_{2} = 10 μC$ (4) $q_{1} = 15 μC, q_{2} = 30 μC$ 228. $A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its center at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = \pm a/2, y = \pm a/2, z = \pma/2. The electric flux through this cubical surface is:$ (1) $\frac{- 2 C}{ϵ _{0}}$ (2) $\frac{2 C}{ϵ _{0}}$ (3) $\frac{10 C}{ϵ _{0}}$ (4) $\frac{12 C}{ϵ _{0}}$ 229. $What is the effective capacitance between points X and Y?$ (1) $12$ (2) $18 μ F$ (3) $24 μ F$ (4) $6 μ F$ 230. $An electric dipole has a fixed dipole moment p, which makes angle θ with respect to x-axis. When subjected to an electric field E_{1} = E i, it experiences a torque T_{1} = τ k . When subjected to another electric field E_{2} = 3 E_{1} j it experiences a torque T_{2} = - T_{1} . The angle θ is:$ (1) $90°$ (2) $30°$ (3) $45°$ (4) $60°$ 231. $A capacitor is made of two square plates each of side 'a' making a very small angle α between them, as shown in figure. The capacitance will be close to:$ (1) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{α a}{2 d})$ (2) $\frac{ϵ _{0} a ^{2}}{d} (1 + \frac{α a}{2 d})$ (3) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{α a}{4 d})$ (4) $\frac{ϵ _{0} a ^{2}}{d} (1 - \frac{3 α a}{2 d})$ 232. $In the arrangement of capacitors shown in the figure, if each capacitor is 9 pF, then the effective capacitance between the points A and B is$ (1) $10 pF$ (2) $15 pF$ (3) $20 pF$ (4) $5 pF$ 233. $In the given network, the value of C, so that an equivalent capacitance between A and B is 3 μF, is$ (1) $\frac{1}{5} μF$ (2) $\frac{31}{5} μF$ (3) $48 μF$ (4) $36 μF$ 234. $In the reported figure, a capacitor is formed by placing a compound dielectric (three layers in series) between the plates of a parallel plate capacitor: layer 1 of dielectric constant K and thickness d, layer 2 of dielectric constant 3 K and thickness 2 d, layer 3 of dielectric constant 5 K and thickness 3 d . The expression for the capacity of the said capacitor will be : (Given area of plate = A)$ (1) $\frac{15}{34} \frac{K ϵ _{0} A}{d}$ (2) $\frac{15}{6} \frac{K ϵ _{0} A}{d}$ (3) $\frac{25}{6} \frac{K ϵ _{0} A}{d}$ (4) $\frac{9}{6} \frac{K ϵ _{0} A}{d}$ 235. $The energy stored in a capacitor of capacity C and potential V is given by$ (1) $\frac{CV}{2}$ (2) $\frac{C ^{2} V ^{2}}{2}$ (3) $\frac{C ^{2} V}{2}$ (4) $\frac{C V ^{2}}{2}$ 236. $25 capacitors each of capacitance 1 μF are connected in series to a battery of 100 V . The total charge stored on capacitors is$ (1) $2.0 \times 10^{- 5} C$ (2) $2.5 \times 10^{- 3} C$ (3) $4.0 \times 10^{- 6} C$ (4) $1.5 \times 10^{- 6} C$ 237. $Consider a thin spherical shell of radius R with its center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field (E (r)) and the electric potential V(r) with the distance r from the centre, is best represented by which graph?$ (1) (2) (3) (4) 238. $The equivalent capacitance between points A and B is$ (1) $5/6 C$ (2) $11/5 C$ (3) $6C$ (4) $5/11 C$ 239. $The effective capacitance between points A and B shown in the circuit is$ (1) $2C$ (2) $C$ (3) $\frac{C}{2}$ (4) $5C$