Capacitance PYQs Set 1 (PDF)

Set 1 of 11 · Questions 1-30 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 1 (Q1-30)
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1. $An uncharged capacitor is connected to a battery. While charging the capacitor, how much is the energy lost, from the energy supplied by the battery?$ (1) $50 %$ (2) $75 %$ (3) $100 %$ (4) $25 %$ 2. $Let there be a spherically symmetric charge distribution with charge density varying as ρ (r) = ρ_{0} (\frac{5}{4} - \frac{r}{R}) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by$ (1) $\frac{4 π ρ _{0} r}{3 ϵ _{0}} (\frac{5}{3} - \frac{r}{R})$ (2) $\frac{ρ _{0} r}{4 ϵ _{0}} (\frac{5}{3} - \frac{r}{R})$ (3) $\frac{4 ρ _{0} r}{3 ϵ _{0}} (\frac{5}{4} - \frac{r}{R})$ (4) $\frac{ρ _{0} r}{3 ϵ _{0}} (\frac{5}{4} - \frac{r}{R})$ 3. $The space between the plates of a parallel plate capacitor is filled with a mica sheet of thickness 1 \times 1 0^{- 3} m and a fiber sheet of thickness 0.5 \times 1 0^{- 3} m . The dielectric constants of mica and fiber are 8 and 2.5 respectively. If the fiber breaks down at an electric field of 6.4 \times 1 0^{6} V m^{- 1} then the maximum voltage that can be applied to the capacitor is$ (1) $3400 V$ (2) $5200 V$ (3) $2700 V$ (4) $4800 V$ 4. $A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will:$ (1) $increase by 50%$ (2) $decrease by 15%$ (3) $increase by 25%$ (4) $increase by 33%$ 5. $The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is [NEET 2018]$ (1) $proportional to the square root of the distance between the plates$ (2) $linearly proportional to the distance between the plates$ (3) $independent of the distance between the plates$ (4) $inversely proportional to the distance between the plates$ 6. $Two square shaped metal plates of side 1 m, kept 0.01 m apart in air form a parallel plate capacitor. It is connected to a battery of 500 V . The plates of the capacitor are then immersed in an insulting oil by lowering the plates vertically with a speed of 0.001 ms^{- 1} . If the dielectric constant of the oil is 11 , then current drawn from the battery during this process is$ (1) $4.425 \times 10^{- 6} A$ (2) $4.425 \times 10^{- 5} A$ (3) $4.425 \times 10^{- 9} A$ (4) $4.425 \times 10^{- 2} A$ 7. $Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. Then the net charge on the sphere is:$ (1) $negative and distributed uniformly over the surface of the sphere.$ (2) $negative and appears only at the point on the sphere closest to the point charge.$ (3) $negative and distributed non-uniformly over the entire surface of the sphere.$ (4) $zero.$ 8. $A parallel plate capacitor with pates of area 1 m^{2} each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate. (Take I^_{0} = 8.85 \times 1 0^{-12} \frac{C ^{2}}{N - m ^{2}})$ (1) $6.85 \times 1 0^{-10} C$ (2) $7.85 \times 1 0^{-10} C$ (3) $9.85 \times 1 0^{-10} C$ (4) $8.85 \times 1 0^{-10} C$ 9. $A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and the area of each plate is A, the energy stored in the capacitor is (ϵ_{0} = permittivity of free space). [NEET 2021]$ (1) $\frac{1}{2} ϵ_{0} E^{2}$ (2) $ϵ_{0} EAd$ (3) $\frac{1}{2} ϵ_{0} E^{2} Ad$ (4) $\frac{E ^{2} Ad}{ϵ _{0}}$ 10. $Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C - R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time needed for reducing the voltage of the fully charged series combination by half is:$ (1) $10 second$ (2) $5 second$ (3) $2.5 second$ (4) $20 second$ 11. $A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E (r) produced by the shell in the range 0 < r < ¥, where r is the distance from the center of the shell?$ (1) (2) (3) (4) 12. $Two capacitors of 10 pF and 20 pF are connected to 200 V and 100 V sources respectively. If they are connected by the wire, what is the common potential of the capacitors?$ (1) $300 volt$ (2) $133.3 volt$ (3) $400 volt$ (4) $150 volt$ 13. $Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area \frac{A}{3} and the separation between the plates is d, 2 d and 3d respectively. The equivalent capacity of combination is (ϵ_{0} = absolute permittivity of free space)$ (1) $\frac{7 ϵ _{0} A}{18 d}$ (2) $\frac{11 \in _{0} A}{18 d}$ (3) $\frac{13 \in _{0} A}{18 d}$ (4) $\frac{17 ϵ _{0} A}{18 d}$ 14. $Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness \frac{d}{2} and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?$ (1) $2 : 1$ (2) $l : 2$ (3) $1 : 4$ (4) $4 : l$ 15. $The difference in the effective capacity of two similar capacitors when joined in series and then in parallel is 6 μF . The capacity of each capacitor is$ (1) $2 μF$ (2) $4 μF$ (3) $8 μF$ (4) $16 μF$ 16. $Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2 V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :$ (1) $\frac{1}{4} CV^{2}$ (2) $2 CV^{2}$ (3) $1 2 CV^{2}$ (4) $\frac{3}{4} CV^{2}$ 17. $Assume that an electric field E = 30 x^{2} i exists in space. Then the potential difference VA - VO, where VO is the potential at the origin and VA the potential at x = 2 m is:$ (1) $120 J$ (2) $-120 J$ (3) $- 80 J$ (4) $80 J$ 18. $Consider the combination of 2 capacitors C_{1} and C_{2}, with C_{2} > C_{1}, when connected in parallel, the equivalent capacitance is \frac{15}{4} times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, \frac{C _{2}}{C _{1}}$ (1) $\frac{15}{11}$ (2) $\frac{29}{15}$ (3) $\frac{15}{4}$ (4) $None of the above$ 19. $The potential energy of charged parallel plate capacitor is v_{0} . If a slab of dielectric constant K is inserted between the plates, then the new potential energy will be$ (1) $\frac{v _{0}}{K}$ (2) $v_{0} K^{2}$ (3) $\frac{v _{0}}{K ^{2}}$ (4) $v_{0}^{2}$ 20. $A parallel plate capacitor of capacitance 1 μ F is charged to a potential difference of 20 V. The distance between plates is 1 μ m . The energy density between plates of capacitor is.$ (1) $2 \times 10^{- 4} J / m^{3}$ (2) $1.8 \times 10^{5} J / m^{3}$ (3) $1.8 \times 10^{3} J / m^{3}$ (4) $2 \times 10^{2} J / m^{3}$ 21. $The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is:$ (1) $independent of the distance between the plates$ (2) $inversely proportional to the distance between the plates$ (3) $proportional to the square root of the distance the plates$ (4) $linearly proportional to the distance between the plates$ 22. $A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are$ (1) $increases, decreases, decreases$ (2) $constant, increases, decreases$ (3) $constant, decreases, decreases$ (4) $constant, decreases, increases.$ 23. $A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes$ (1) $\frac{C}{2}$ (2) $2C$ (3) $2 C$ (4) $\frac{C}{2}$ 24. $A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?$ (1) $The potential difference between the plates decreases K times.$ (2) $The energy stored in the capacitor decreases K times.$ (3) $The change in energy stored is \frac{1}{2} C V^{2} (\frac{1}{K} - 1) .$ (4) $The charge on the capacitor is not conserved.$ 25. $The material filled between the plates of a parallel plate capacitor has resistivity 200 Ωm . The value of capacitance of the capacitor is 2 pF . If a potential difference of 40V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permitivity of material is 50)$ (1) $9.0 μA$ (2) $9.0mA$ (3) $0.9mA$ (4) $0.9 μA$ 26. $A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge -σ in the lower half. The electric field lines around the cylinder will look like figure given in :(figures are schematic and not drawn to scale)$ (1) (2) (3) (4) 27. $A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25 % more charge from the battery. The dielectric constant of mica is____.$ (1) $1.0$ (2) $2.5$ (3) $2.0$ (4) $1.5$ 28. $Let E_{1} (r), E_{2} (r) and E_{3} (r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density σ. if E_{1} (r_{0}) = E_{2} (r_{0}) = E_{3} (r_{0}) at a given distance r_{0}, then$ (1) $Q = 4 σπ r_{0}^{2}$ (2) $r_{0} = \frac{λ}{2 πσ}$ (3) $E_{1} (r_{0} /2) = 2 E_{2} (r_{0} /2)$ (4) $E_{2} (r_{0} /2) = 4 E_{3} (r_{0} /2)$ 29. $A parallel plate capacitor of capacitance 200 μF is connected to a battery of 200V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be ..... J.$ 30. $Three capacitors of capacitances 25 μF, 30 μF and 45 μF are connected in parallel to a supply of 100 V . Energy stored in the above combination is E . When these capacitors are connected in series to the same supply, the stored energy is \frac{9}{x} E . The value of x is_____$