Effect of Dielectric and Dielectric Inside Capacitor and Polarisation PYQs: JEE Mains Physics

Showing 1–50 of 54 questions

1. 1. A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
   A sheet having thickness \(\left(\frac{1}{3}\right)^{ rd }\) of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is : 2026 Medium
2. 2. A parallel plate capacitor is having separation between plates \(0.885\) mm. It has a capacitance of \(1\,\mu\)F when the space between the plates is filled with an insulating material of resistivity \(1\times 10^{13}\,\Omega\)m and resistance \(17.7\times 10^{14}\,\Omega\). Relative permittivity of the insulating material is \(\alpha\times 10^7\). The value of \(\alpha\) is ________. (Take permittivity of free space \(=8.85\times 10^{-12}\) F/m) 2026 Hard
3. 3. 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 ___________ . 2026 Easy
4. 4. 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. 2026 Medium
5. 5. 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 the figure). If new capacitance is \(\frac{ n }{3} C\) then the value of \(n\) is ___________.
   2026 Medium
6. 6. Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( \(k _1\) and \(k _2\) ) in the following fashion. Which of the following is true? \(\left( k _1> k _2\right)\)
   2026 Easy
7. 7. A parallel plate capacitor has charge \(5 \times 10^{-6} \mathrm{C}\). A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is \(4 \times 10^{-6} \mathrm{C}\) then the dielectric constant of the slab is ________. 2025 Medium
8. 8. A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant \(\varepsilon_1\) and \(\varepsilon_2\), as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are \(C_1\) and \(C_2\) respectively, then \(\frac{C_1}{C_2}\) is :
   
   2025 Hard
9. 9. A parallel-plate capacitor of capacitance \(40 \mu \mathrm{~F}\) is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant \(\mathrm{K}=2\). Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are 2025 Medium
10. 10. Three parallel plate capacitors \(\mathrm{C}_1, \mathrm{C}_2\) and \(\mathrm{C}_3\) each of capacitance \(5 \mu \mathrm{~F}\) 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 :
    2025 Easy
11. 11. A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\) 2024 Hard
12. 12. A capacitor of \(10 \mu \mathrm{F}\) capacitance whose plates are separated by \(10 \mathrm{~mm}\) through air and each plate has area \(4 \mathrm{~cm}^2\) is now filled equally with two dielectric media of \(\mathrm{K}_1=2, \mathrm{~K}_2=3\) respectively as shown in figure. If new force between the plates is \(8 \mathrm{~N}\). The supply voltage is _______ \(\times 10^{-4}\)V.
    2024 Hard
13. 13. A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\). 2024 Hard
14. 14. A parallel plate capacitor with plate separation \(5\) \(\mathrm{mm}\) is charged up by a battery. It is found that on introducing a dielectric sheet of thickness \(2 \mathrm{~mm}\), while keeping the battery connections intact, the capacitor draws \(25 \%\) more charge from the battery than before. The dielectric constant of the sheet is _______. 2024 Hard
15. 15. Two identical charged spheres are suspended by string of equal lengths. The string make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If density of material of the sphere is \(1.4 \mathrm{~g} / \mathrm{cm}^3\), the dielectric constant of the liquid is _______\(\left(\tan 37^{\circ}=\frac{3}{4}\right)\). 2024 Hard
16. 16. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle \(\theta\) with each other. When suspended in water the angle remains the same. If density of the material of the sphere is \(1.5 \mathrm{~g} / \mathrm{cc}\), the dielectric constant of water will be _______. (Take density of water \(=1 \mathrm{~g} / \mathrm{cc}\) ) 2024 Hard
17. 17. A capacitor has capacitance \(5 \mu F\) when it's parallel plates are separated by air medium of thickness \(d\). A slab of material of dielectric constant \(1.5\) having area equal to that of plates but thickness \(\frac{ d }{2}\) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be \(..........\mu F\) 2023 Medium
18. 18. A parallel plate capacitor has plate area \(40\,cm ^2\) 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 : 2023 Medium
19. 19. A parallel plate capacitor with air between the plate has a capacitance of \(15 pF\). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \(3.5.\) Then the capacitance becomes \(\frac{ x }{4}\,pF\).The value of \(x\) is \(............\) 2023 Medium
20. 20. A parallel plate capacitor with plate area \(A\) and plate separation \(d\) is filled with a dielectric material of dielectric constant \(K =4\). The thickness of the dielectric material is \(x\), where \(x < d\). Let \(C_1\) and \(C_2\) be the capacitance of the system for \(x =\frac{1}{3} d\) and \(x =\frac{2 d }{3}\), respectively. If \(C _1=2 \mu F\) the value of \(C _2\) is \(........... \mu F\)
    2023 Hard
21. 21. A composite parallel plate capacitor is made up of two different dielectric materials with different thickness \(\left(t_{1}\right.\) and \(\left.t_{2}\right)\) as shown in figure. The two different dielectric material are separated by a conducting foil \(F\). The voltage of the conducting foil is \(.....V\)
    2022 Hard
22. 22. 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 ...................... 2022 Hard
23. 23. A parallel plate capacitor is formed by two plates each of area \(30 \pi\, cm ^{2}\) separated by \(1\, mm\). A material of dielectric strength \(3.6 \times 10^{7} \,Vm ^{-1}\) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \(7 \times 10^{-6}\, C\), the value of dielectric constant of the material is \(\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}\) 2022 Medium
24. 24. A parallel plate capacitor with plate area \(A\) and plate separation \(d =2 \,m\) has a capacitance of \(4 \,\mu F\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K =3\) (as shown in figure) will be .........\( \mu \,F\)
    2022 Hard
25. 25. A parallel plate capacitor with width \(4\,cm\), length \(8\,cm\) and separation between the plates of \(4\,mm\) is connected to a battery of \(20\,V\). A dielectric slab of dielectric constant \(5\) having length \(1\,cm\), width \(4\,cm\) and thickness \(4\,mm\) is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be......... \(\in_{0}\,J\). (Where \(\epsilon_{0}\) is the permittivity of free space) 2022 Medium
26. 26. A slab of dielectric constant \(K\) has the same crosssectional area as the plates of a parallel plate capacitor and thickness \(\frac{3}{4}\,d\), 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.) 2022 Hard
27. 27. 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 :
    2022 Hard
28. 28. Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be. 2022 Medium
29. 29. Two parallel plate capacitors of capacity \(C\) and \(3\,C\) are connected in parallel combination and charged to a potential difference \(18\,V\). The battery is then disconnected and the space between the plates of the capacitor of capacity \(C\) is completely filled with a material of dielectric constant \(9\). The final potential difference across the combination of capacitors will be \(V\) 2022 Hard
30. 30. A parallel plate capacitor has plate area \(100\, m ^{2}\) and plate separation of \(10\, m\). 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 system is \('x'\) \(pF\). The value of \(\varepsilon_{0}=8.85 \times 10^{-12} F \cdot m ^{-1}\) The value of \('x'\) to the nearest integer is............ 2021 Hard
31. 31. A parallel plate capacitor of capacitance \(200 \,\mu {F}\) is connected to a battery of \(200 \, {V} .\) 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 ......\( J.\) 2021 Hard
32. 32. A parallel plate capacitor with plate area \('A'\) and distance of separation \('d'\) is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : \(\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)\) \(\varepsilon(x)=\varepsilon_{0}+k(d-x)\), for \(\left(\frac{d}{2} \leq x \leq d\right)\) 2021 Hard
33. 33. A parallel - plate capacitor with plate area \(A\) has separation \(d\) between the plates. Two dielectric slabs of dielectric constant \({K}_{1}\) and \({K}_{2}\) of same area \(\frac A2\) and thickness \(\frac d2\) are inserted in the space between the plates. The capacitance of the capacitor will be given by :
    2021 Hard
34. 34. For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relation 2021 Medium
35. 35. 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  2021 Hard
36. 36. In a parallel plate capacitor set up, the plate area of capacitor is \(2 \,m ^{2}\) and the plates are separated by \(1\, m\). If the space between the plates are filled with a dielectric material of thickness \(0.5\, m\) and area \(2\, m ^{2}\) (see \(fig.\)) the capacitance of the set-up will be \(.........\, \varepsilon_{0}\) (Dielectric constant of the material \(=3.2\) ) and (Round off to the Nearest Integer)
    2021 Hard
37. 37. In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be (Given area of plate \(=A\) )
    2021 Medium
38. 38. Two capacitors of capacities \(2 {C}\) and \({C}\) are joined in parallel and charged up to potential \({V}\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \({K}\). The potential difference across the capacitors will now be 2021 Medium
39. 39. A parallel plate capacitor has plate of length \('l',\) width \('w'\) and separation of plates is \('d'.\) It is connected to a battery of emf \(V\). A dielectric slab of the same thickness '\(d\)' and of dielectric constant \(k =4\) is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored\(?\) 2020 Hard
40. 40. A parallel plate capacitor has plates of area \(A\) separated by distance \(d\) between them. It is filled with a dielectric which has a dielectric constant that varies as \(\mathrm{k}(\mathrm{x})=\mathrm{K}(1+\alpha \mathrm{x})\) where \(\mathrm{x}\) is the distance measured from one of the plates. If \((\alpha \text {d)}<<1,\) the total capacitance of the system is best given by the expression  2020 Hard
41. 41. A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be
    2019 Hard
42. 42. A parallel plate capacitor having capacitance \(12\, pF\) is charged by a battery to a potential difference of \(10\, V\) between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant \(6.5\) is slipped between the plates. The work done by the capacitor on the slab is.......\(pJ\) 2019 Hard
43. 43. A parallel plate capacitor is made of two square plates of side \(a\), separated by a distance \(d\,(d  < < a)\). The lower triangular portion is filled with a dielectric of dielectric constant \(K\), as shown in the figure. Capacitance of this capacitor is
    2019 Hard
44. 44. A parallel plate capacitor is of area \(6\, cm^2\) 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
    2019 Hard
45. 45. The parallel combination of two air filled parallel plate capacitors of capacitance \(C\) and \(nC\) is connected to a battery of voltage, \(V\). When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant \(K\) is placed between the two plates of the first capacitor. The new potential difference of the combined system is 2019 Hard
46. 46. 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 capacitor 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 capacitor \((I)\) and \(E_2\) to capacitor \((II)\)) 
    2019 Hard
47. 47. Voltage rating of a parallel plate capacitor is \(500\,V\). Its dielectric can withstand a maximum electric field of \({10^6}\,\frac{V}{m}\). The plate area is \(10^{-4}\, m^2\) . What is the dielectric constant if the capacitance is \(15\, pF\) ? (given \({ \in _0} = 8.86 \times {10^{ - 12}}\,{C^2}\,/N{m^2}\)) 2019 Hard
48. 48. A parallel plate capacitor of capacitance \(90\ pF\) is connected to a battery of \(emf\) \(20\ V\). If a dielectric material of dielectric constant \(K = \frac{5}{3}\) is inserted between the plates, the magnitude of the induced charge will be.......\(n \) \(C\) 2018 Medium
49. 49. A combination of parallel plate capacitors is maintained at a certain potential difference When a \(3\, mm\) thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by \(2.4\, mm\). Find the dielectric constant of the slab. 
    2017 Hard
50. 50. A parallel plate capacitor is made of two circular plates separated by a distance \(5\ mm\) and with a dielectric of dielectric constant \(2.2\) between them. When the electric field in the dielectric is \(3 \times 10^4\) \( Vm^{-1}\) the charge density of the positive plate will be close to 2014 Medium

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