Capacitance PYQs Set 6 (PDF)

Set 6 of 8 · Questions 151-180 of 239

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Mere Teacher · Previous Year Questions NEET Physics · Capacitance · Set 6 (Q151-180)
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151. $Three uncharged capacitors of capacities C_{1}, C_{2} and C_{3} are connected as shown in the figure. A, B and C are at potentials V_{1}, V_{2} and V_{3}, respectively, then the potential at O is$ (1) $\frac{C _{1} V _{1} + C _{2} V _{2} + C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$ (2) $\frac{C _{1} V _{1} + C _{2} V _{2} - C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$ (3) $\frac{C _{1} V _{1} - C _{2} V _{2} - C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$ (4) $zero$ 152. $A capacitor of 2µF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:$ (1) $80%$ (2) $0%$ (3) $20%$ (4) $75%$ 153. $A capacitor is charged with a battery and energy stored is U . After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is$ (1) $U /2$ (2) $U /4$ (3) $4 U$ (4) $2 U .$ 154. $A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is:$ (1) $zero every where$ (2) $is not zero but uniform$ (3) $nonuniform$ (4) $is zero at center only$ 155. $In the figure shown, after the switch 'S' is turned position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:$ (1) $\frac{3}{8} \frac{Q ^{2}}{C}$ (2) $\frac{5}{8} \frac{Q ^{2}}{C}$ (3) $\frac{1}{8} \frac{Q ^{2}}{C}$ (4) $\frac{3}{4} \frac{Q ^{2}}{C}$ 156. $Two identical capacitors A and B are connected as shown in the circuit. Initially the switch ' S ' is closed. Now the switch is opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. The ratio of total electrostatic energy stored in the capacitors before and after introduction of the dielectric is$ (1) $3 : 1$ (2) $5 : 1$ (3) $3 : 5$ (4) $5 : 3$ 157. $A capacitor is connected to a 20V battery through a resistance of 10Ω . It is found that the potential difference across the capacitor rises to 2V in 1 μ s . The capacitance of the capacitor is μ F . Given: ln (\frac{10}{9}) = 0.105$ (1) $9.52$ (2) $0.95$ (3) $0.105$ (4) $1.85$ 158. $In the given circuit, a charge of +80 µC is given to the upper plate of the 4µF capacitor. Then in the steady state, the charge on the upper plate of the 3µF capacitor is:$ (1) $+32 µC$ (2) $+40 µC$ (3) $+48 µC$ (4) $+80 µC$ 159. $For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points A and B is (capacitance of each capacitor is 4 μF)$ (1) $4 μF$ (2) $2 μF$ (3) $1 μF$ (4) $8 μF$ 160. $Consider an electric field E = E_{0} x, where E_{0} is a constant. The flux through the shaded area (as shown in the figure) due to this field is:$ (1) $2E0a2$ (2) $2 E0a2$ (3) $E0a2$ (4) $\frac{E _{0} a ^{2}}{2}$ 161. $A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system:$ (1) $increases by a factor of 4$ (2) $decreases by a factor 2$ (3) $remains the same$ (4) $increases by a factor of 2$ 162. $The network of 4 capacitors is connected to a battery as shown. The ratio of charges on capacitors ' C_{2}' and ' C_{4}' is$ (1) $\frac{3}{22}$ (2) $\frac{5}{21}$ (3) $\frac{1}{16}$ (4) $\frac{4}{17}$ 163. $Five capacitors each of value 1 μF are connected as shown in the figure. The equivalent capacitance between A and B is$ (1) $3 μF$ (2) $1 μF$ (3) $2 μF$ (4) $5 μF$ 164. $The effective capacitance between points A and B shown in the figure is$ (1) $10 μF$ (2) $15 μF$ (3) $20 μF$ (4) $25 μF$ 165. $Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be -$ (1) $2 : 1$ (2) $1 : 4$ (3) $4 : 1$ (4) $1 : 2$ 166. $Four metal plates are arranged as shown. Capacitance between X and Y (A \to Area of each plate, d \to distance between the plates)$ (1) $\frac{3}{2} \frac{ϵ _{0} A}{d}$ (2) $\frac{2 ϵ _{0} A}{d}$ (3) $\frac{2}{3} \frac{ϵ _{0} A}{d}$ (4) $\frac{3 ϵ _{0} A}{d}$ 167. $A parallel plate capacitor has 1 μF capacitance. One of its two plates is given + 2 μC charge and the other plate, + 4 μC charge. The potential difference developed across the capacitor is$ (1) $3V$ (2) $1V$ (3) $5V$ (4) $2V$ 168. $A network of four capacitors of capacity equal to C_{1} = C, C_{2} = 2 C C_{3} = 3 C and C_{4} = 4 C are connected to a battery as shown in the figure. The ratio of the charges on C_{2} and C_{4} is$ (1) $4/7$ (2) $3/22$ (3) $7/4$ (4) $22/3$ 169. $In figure, charge on the capacitor is plotted against potential difference across the capacitor: The capacitance and energy stored in the capacitor are respectively$ (1) $12 μF, 1200 μJ$ (2) $12 μF, 600 μJ$ (3) $24 μF, 600 μJ$ (4) $24 μF, 1200 μJ$ 170. $The equivalent capacitance between A and B in the given circuit is$ (1) $3 μF$ (2) $1 μF$ (3) $2 μ$ (4) $1.5 μF$ 171. $A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to$ (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) $\frac{1}{ϵ _{0}} \frac{σ ^{2}}{R ^{2}}$ 172. $Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)$ (1) $600$ (2) $100$ (3) $400$ (4) $200$ 173. $A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4µF and 9µF capacitors), at a point distance 30 m from it, would equal:$ (1) $360 N/C$ (2) $420 N/C$ (3) $480 N/C$ (4) $240 N/C$ 174. $A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k_{1} = 3 and thickness d/3 while the other one has dielectric constant k_{2} = 6 and thickness 2d/3. Capacitance of the capacitor is now:$ (1) $45 pF$ (2) $40.5 pF$ (3) $20.25 pF$ (4) $1.8 pF$ 175. $Four metal plates, each with surface area A on one side, are placed with separation ' d ' as shown in the figure. The capacitance between a and b is (ϵ_{0} -) permittivity of free space)$ (1) $\frac{3 ϵ _{0} A}{d}$ (2) $\frac{2 ϵ _{0} A}{d}$ (3) $\frac{2 ϵ _{0} A}{3 d}$ (4) $\frac{3 ϵ _{0} A}{2 d}$ 176. $The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = \frac{A}{r}, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:$ (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) $\frac{Q}{2 π a ^{2}}$ 177. $In the following circuit, the equivalent capacitance between terminal A and terminal B is [NEET 2024]$ (1) $2 μF$ (2) $1 μF$ (3) $0.5 μF$ (4) $4 μF$ 178. $The following figure shows a 9 V battery and 3 uncharged capacitors of capacitances C_{1} = C_{2} = C_{3} = 1 μF . The switch is thrown to the right side until capacitor C_{1} is fully charged, then the switch is thrown fo the left. The final charge on capacitor C_{2} is$ (1) $1 μC$ (2) $2 μC$ (3) $3 μC$ (4) $4 μC$ 179. $A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is E_{1} . Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E_{2} . The ratio E_{1} / E_{2} will be:$ (1) $\frac{1}{10}$ (2) $\frac{2}{5}$ (3) $\frac{5}{13}$ (4) $\frac{5}{26}$ 180. $A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?$ (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) $The potential difference between the plates decreases K times.$