Capacitance PYQs Set 6 (PDF)

Set 6 of 11 · Questions 151-180 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 6 (Q151-180)
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151. $The total energy stored in the condenser system shown in the figure will be$ (1) $8 μJ$ (2) $16 μJ$ (3) $2 μJ$ (4) $4 μJ$ 152. $A capacitor of capacitance C_{1} = 1 μF is charged using a 9 V battery. C_{1} is then removed from the battery & connected to capacitors C_{2} and C3 of 2 μF and 3 μF respectively as shown in the figure. Find the charge on C3 after equilibrium has reached is$ (1) $4.5 \times 10^{- 6} C$ (2) $3.5 \times 10^{- 6} C$ (3) $2.5 \times 10^{- 6} C$ (4) $1.5 \times 10^{- 5} C$ 153. $Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30º with each other. When suspended in a liquid of density 0.8 g c m^{-3}, the angle remains the same. If density of the material of the sphere is 1.6 g c m^{-3}, the dielectric constant of the liquid is$ (1) $4$ (2) $3$ (3) $2$ (4) $1$ 154. $In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C2 is 20V. Then the charge on capacitor C2 is:$ (1) $650 μC$ (2) $590 μC$ (3) $160 μC$ (4) $450 μC$ 155. $A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:$ (1) $\frac{CV}{ϵ _{0}}$ (2) $Zero$ (3) $\frac{2 CV}{ϵ _{0}}$ (4) $\frac{CV}{2 ϵ _{0}}$ 156. $An electron with kinetic energy K_{1} enters between parallel plates of a capacitor at an angle 'α' with the plates. It leaves the plates at angle 'β' with kinetic energy K_{2} . Then the ratio of kinetic energies K_{1} : K_{2} will be:$ (1) $\frac{sin ^{2} β}{cos ^{2} α}$ (2) $\frac{cos ^{2} β}{cos ^{2} α}$ (3) $\frac{cos β}{sin α}$ (4) $\frac{cos β}{cos α}$ 157. $Two identical charged spheres of material density ρ, suspended from the same point by inextensible strings of equal length make an angle θ between the strings. When suspended in a liquid of density σ the angle θ remains the same. The dielectric constant K of the liquid is$ (1) $\frac{ρ}{ρ - σ}$ (2) $\frac{ρ - σ}{ρ}$ (3) $\frac{ρ}{ρ + σ}$ (4) $\frac{ρ + σ}{ρ}$ 158. $In the figure shown below, the charge on the left plate of the 10 µF capacitor is -30 µC. The charge on the right plate of the 6 µF capacitor is$ (1) $-12 µC$ (2) $+12 µC$ (3) $-18 µC$ (4) $+ 18 µC$ 159. $A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E at the center O is:$ (1) $\frac{q}{4 π ^{2} ϵ _{0} r ^{2}} j$ (2) $- \frac{q}{4 π ^{2} ϵ _{0} r ^{2}} j$ (3) $- \frac{q}{2 π ^{2} ϵ _{0} r ^{2}} j$ (4) $\frac{q}{2 π ^{2} ϵ _{0} r ^{2}} j$ 160. $The electrostatic potential inside a charged spherical ball is given by φ = a r^{2} + b where r is the distance from the center; a, b are constants. Then the charge density inside the ball is:$ (1) $- 24 π a ε_{0} r$ (2) $- 6 π a ε_{0} r$ (3) $- 24 π a ε_{0}$ (4) $- 6 a ε_{0}$ 161. $Two capacitors C_{1} and C_{2} are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U_{1} and U_{2}, respectively. Which of the given statements is true?$ (1) $C_{2} > C_{1}, U_{2} < U_{1}$ (2) $C_{1} > C_{2}, U_{1} > U_{2}$ (3) $C_{1} > C_{2}, U_{1} < U_{2}$ (4) $C_{2} > C_{1}, U_{2} > U_{1}$ 162. $Identify the valid statements relevant to the given circuit at the instant when the key is closed. (A) There will be no current through resistor R. (B). There will be maximum current in the connecting wires. (C) Potential difference between the capacitor plates A and B is minimum. (D) Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:$ (1) $A, C Only$ (2) $A, B, D Only$ (3) $C, D Only$ (4) $B, C, D Only$ 163. $A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates. Now, an insulating slab of same area but thickness d/2 is inserted between the plates as shown in figure having dielectric constant K (= 4) . The ratio of new capacitance to its original capacitance will be [NEET 2020]$ (1) $2 : 1$ (2) $8 : 5$ (3) $6 : 5$ (4) $4 : 1$ 164. $Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is$ (1) $\frac{3}{2} C V^{2}$ (2) $\frac{9}{2} C V^{2}$ (3) $Zero$ (4) $\frac{25}{6} C V^{2}$ 165. $The equivalent capacitance of the system shown in the following circuit is [NEET 2023]$ (1) $3 μF$ (2) $6 μF$ (3) $9 μF$ (4) $2 μF$ 166. $The equivalent capacitance of the combination shown in the figure is [NEET 2021]$ (1) $3 C$ (2) $2 C$ (3) $\frac{C}{2}$ (4) $\frac{3 C}{2}$ 167. $Two non-conducting spheres of radii R_{1} and R_{2} and carrying uniform volume charge densities +ρ and -ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region:$ (1) $the electrostatic field is zero$ (2) $the electrostatic potential is constant$ (3) $the electrostatic field is constant in magnitude$ (4) $the electrostatic field has same direction$ 168. $Three parallel plate capacitors C_{1}, C_{2} and C_{3} each of capacitance 5 μ F are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of C_{1} capacitor is filled with a dielectric medium having dielectric constant of 4, is:$ (1) $9 μ F$ (2) $30 μ F$ (3) $7.5 μ F$ (4) $22.5 μ F$ 169. $In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:$ (1) $CE \frac{r _{1}}{( r _{1} + r )}$ (2) $CE$ (3) $CE \frac{r _{1}}{( r _{2} + r )}$ (4) $CE \frac{r _{2}}{( r + r _{2} )}$ 170. $A parallel plate capacitor has plate area 40 c m^{2} and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is:$ (1) $24 ϵ_{0} F$ (2) $\frac{3}{10} ϵ_{0} F$ (3) $\frac{10}{3} ϵ_{0} F$ (4) $10 ϵ_{0} F$ 171. $Two condensers one of capacity \frac{C}{2} and other capacity C are connected to a battery of voltage V as shown. The work done in charging fully both the condensers is$ (1) $1 2 CV^{2}$ (2) $\frac{3}{4} C V^{2}$ (3) $3 2 CV^{2}$ (4) $2 CV^{2}$ 172. $If q_{f} is the free charge on the capacitor plates and q_{b} is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge q_{b} can be expressed as:$ (1) $q_{b} = q_{f} (1 - \frac{1}{k})$ (2) $q_{b} = q_{f} (1 - \frac{1}{k})$ (3) $q_{b} = q_{f} (1 + \frac{1}{k})$ (4) $q_{b} = q_{f} (1 + \frac{1}{k})$ 173. $Two thin dielectric slabs of dielectric constants K_{1} and K_{2} (K_{1} < K_{2}) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate P is correctly shown by:$ (1) (2) (3) (4) 174. $A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:$ (1) $increases$ (2) $decreases$ (3) $remains same$ (4) $becomes zero$ 175. $In the following figure C_{1} = 5 μF, C_{2} = C_{3} = 10 μF and ϵ = 20 V . Initially the switch S is connected to point A until capacitor C_{1} is fully charged. Afterwards switch is thrown to left side and connected to point B. The charge on capacitor C_{3} after equilibrium is reached will be$ (1) $40 μC$ (2) $100 μC$ (3) $50 μC$ (4) $20 μC$ 176. $As shown in the figure, two parallel plate capacitors having equal plate area of 200 c m^{2} are joined in such a way that a \neq = b. The equivalent capacitance of the combination is x ϵ_{0} F. The value of x is_____.$ 177. $In an electrical circuit drawn below the amount of charge stored in the capacitor is____μC .$ 178. $The equivalent capacitance between points A and B in below shown figure will be_____µF.$ 179. $In the given figure the total charge stored in the combination of capacitors is 100 µC. The value of ‘x’ is______________.$ 180. $In the circuit shown, the energy stored in the capacitor is nµJ. The value of n is_____.$