Capacitance PYQs Set 7 (PDF)

Set 7 of 11 · Questions 181-210 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 7 (Q181-210)
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181. $A parallel plate capacitor having plates of area S and plate separation d, has capacitance C_{1} in air. When two dielectrics of different relative permittivities (e_{1} = 2 and e_{2} = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C_{2} . The ratio \frac{C _{2}}{C _{1}} is$ (1) $6/5$ (2) $5/3$ (3) $7/5$ (4) $7/3$ 182. $Two positive charges of magnitude ‘q’ are placed at the ends of a side (side 1) of a square of side ‘2a’. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge Q moves from the middle of side 1 to the center of square, its kinetic energy at the center of square is:$ (1) $zero$ (2) $\frac{1}{4 π ϵ _{0}} \frac{2 qQ}{a} (1 + \frac{1}{5})$ (3) $\frac{1}{4 π ϵ _{0}} \frac{2 qQ}{a} (1 - \frac{2}{5})$ (4) $\frac{1}{4 π ϵ _{0}} \frac{2 qQ}{a} (1 - \frac{1}{5})$ 183. $A capacitor of 2 μF is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is [NEET 2016]$ (1) $20 %$ (2) $75 %$ (3) $80 %$ (4) $0 %$ 184. $Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are:$ (1) $40μF and 10 μF$ (2) $60 μF and 40μF$ (3) $50 μF and 30μF$ (4) $20 μF and 30μF$ 185. $The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density λ are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x-direction only. If they are given a small displacement about their equilibrium positions, then the correct statement (s) is (are)$ (1) $Both charges execute simple harmonic motion.$ (2) $Both charges will continue moving in the direction of their displacement.$ (3) $Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement.$ (4) $Charge -q executes simple harmonic motion while charge +q continues moving in the direction of its displacement.$ 186. $Three uncharged capacitors of capacities C_{1}, C_{2} and C_{3} are connected as shown in the figure. A, B and C are at potentials V_{1}, V_{2} and V_{3}, respectively, then the potential at O is$ (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) $zero$ 187. $A capacitor of 2µF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:$ (1) $80%$ (2) $0%$ (3) $20%$ (4) $75%$ 188. $A capacitor is charged with a battery and energy stored is U . After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is$ (1) $U /2$ (2) $U /4$ (3) $4 U$ (4) $2 U .$ 189. $A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is:$ (1) $zero every where$ (2) $is not zero but uniform$ (3) $nonuniform$ (4) $is zero at center only$ 190. $In the figure shown, after the switch 'S' is turned position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:$ (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) $\frac{3}{4} \frac{Q ^{2}}{C}$ 191. $Two identical capacitors A and B are connected as shown in the circuit. Initially the switch ' S ' is closed. Now the switch is opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. The ratio of total electrostatic energy stored in the capacitors before and after introduction of the dielectric is$ (1) $3 : 1$ (2) $5 : 1$ (3) $3 : 5$ (4) $5 : 3$ 192. $A capacitor is connected to a 20V battery through a resistance of 10Ω . It is found that the potential difference across the capacitor rises to 2V in 1 μ s . The capacitance of the capacitor is μ F . Given: ln (\frac{10}{9}) = 0.105$ (1) $9.52$ (2) $0.95$ (3) $0.105$ (4) $1.85$ 193. $In the given circuit, a charge of +80 µC is given to the upper plate of the 4µF capacitor. Then in the steady state, the charge on the upper plate of the 3µF capacitor is:$ (1) $+32 µC$ (2) $+40 µC$ (3) $+48 µC$ (4) $+80 µC$ 194. $For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points A and B is (capacitance of each capacitor is 4 μF)$ (1) $4 μF$ (2) $2 μF$ (3) $1 μF$ (4) $8 μF$ 195. $Consider an electric field E = E_{0} x, where E_{0} is a constant. The flux through the shaded area (as shown in the figure) due to this field is:$ (1) $2E0a2$ (2) $2 E0a2$ (3) $E0a2$ (4) $\frac{E _{0} a ^{2}}{2}$ 196. $A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system:$ (1) $increases by a factor of 4$ (2) $decreases by a factor 2$ (3) $remains the same$ (4) $increases by a factor of 2$ 197. $The network of 4 capacitors is connected to a battery as shown. The ratio of charges on capacitors ' C_{2}' and ' C_{4}' is$ (1) $\frac{3}{22}$ (2) $\frac{5}{21}$ (3) $\frac{1}{16}$ (4) $\frac{4}{17}$ 198. $Five capacitors each of value 1 μF are connected as shown in the figure. The equivalent capacitance between A and B is$ (1) $3 μF$ (2) $1 μF$ (3) $2 μF$ (4) $5 μF$ 199. $The effective capacitance between points A and B shown in the figure is$ (1) $10 μF$ (2) $15 μF$ (3) $20 μF$ (4) $25 μF$ 200. $Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be -$ (1) $2 : 1$ (2) $1 : 4$ (3) $4 : 1$ (4) $1 : 2$ 201. $Four metal plates are arranged as shown. Capacitance between X and Y (A \to Area of each plate, d \to distance between the plates)$ (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) $\frac{3 ϵ _{0} A}{d}$ 202. $A parallel plate capacitor has 1 μF capacitance. One of its two plates is given + 2 μC charge and the other plate, + 4 μC charge. The potential difference developed across the capacitor is$ (1) $3V$ (2) $1V$ (3) $5V$ (4) $2V$ 203. $In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S_{1} is pressed first to fully charge the capacitor C_{1} and then released. The switch S_{2} is then pressed to charge the capacitor C_{2} . After some time, S_{2} is released and then S_{3} is pressed. After some time.$ (1) $the charge on the upper plate of C_{1} is 2 C V_{0}$ (2) $the charge on the upper plate of C_{1} is C V_{0}$ (3) $the charge on the upper plate of C_{2} is 0$ (4) $the charge on the upper plate of C_{2} is - C V_{0}$ 204. $A network of four capacitors of capacity equal to C_{1} = C, C_{2} = 2 C C_{3} = 3 C and C_{4} = 4 C are connected to a battery as shown in the figure. The ratio of the charges on C_{2} and C_{4} is$ (1) $4/7$ (2) $3/22$ (3) $7/4$ (4) $22/3$ 205. $In figure, charge on the capacitor is plotted against potential difference across the capacitor: The capacitance and energy stored in the capacitor are respectively$ (1) $12 μF, 1200 μJ$ (2) $12 μF, 600 μJ$ (3) $24 μF, 600 μJ$ (4) $24 μF, 1200 μJ$ 206. $A 5 μF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected to another uncharged 2.5 μF capacitor. If the energy change during the charge redistribution is \frac{X}{100} J then value of X to the nearest integer is_____.$ 207. $A parallel plate capacitor has plate area 100 m²and plate separation of 10m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the systems 'x' pF. The value of ϵ_{0} = 8.85 \times 10^{- 12} F . m^{- 1} The value of 'x' to the nearest integer is ___$ 208. $A capacitor of 10 μF capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm^{2} is now filled equally with two dielectric media of K_{1} = 2, K_{2} = 3 respectively as shown in figure. If new force between the plates is 8 N . The supply voltage is____\times 10^{- 4} V . (we modified language of question to make it correct)$ 209. $The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K_{1} = 2, K_{2} = 3 and K_{3} = 5 (as shown in figure). If new capacitance is \frac{n}{3} C then the value of n is____.$ 210. $An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m \dots\dots\dots\dots. The total force on a 1C point charge, placed at the origin, is x \times 10^{3} N. The value of x, to the nearest integer, is ___. [Take \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} / C^{2}]$