Combination of Capacitor and Sharing of Charge PYQs: JEE Mains Physics

Showing 1–38 of 38 questions

1. 1. A capacitor P with capacitance \( 10\times10^{-6} F \) is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance \( 20\times10^{-6} F \). The charge on capacitor Q when equilibrium is established will be \( \alpha\times10^{-5} C \).(assume capacitor \(Q\) does not have any charge initially),The value of \( \alpha \) is __________ . 2026 Hard
2. 2. A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF) 2026 Hard
3. 3. From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
   (take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)
   2026 Hard
4. 4. A capacitor, \(C_1=6 \mu \mathrm{~F}\) is charged to a potential difference of \(\mathrm{V}_0=5 \mathrm{~V}\) using a 5 V battery. The battery is removed and another capacitor, \(\mathrm{C}_2=12 \mu \mathrm{~F}\) is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \(\left(q_1\right.\) and \(\left.q_2\right)\) on the capacitors \(C_1\) and \(C_2\) when equilibrium condition is reached.
   
   2025 Medium
5. 5. Four capacitor each of capacitance \(16 \mu \mathrm{~F}\) are connected as shown in the figure. The capacitance between points A and B is : ______ (in \(\mu \mathrm{F}\)).
   2025 Easy
6. 6. 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) 2025 Medium
7. 7. A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.
   2024 Hard
8. 8. As shown in the figure, two parallel plate capacitors having equal plate area of \(200\,cm ^2\) are joined in such a way that \(a \neq b\). The equivalent capacitance of the combination is \(x \varepsilon_0 F\). The value of \(x\) is \(..........\).
   2023 Hard
9. 9. In the given circuit, \(C _1=2\,\mu F , C _2=0.2\,\mu F\), \(C _3=2\,\mu F , C _4=4\,\mu F,\) \(C _5=2\,\mu F , C _6=2\,\mu F\), the charge stored on capacitor \(C _4\) is \(.....\mu C\).
   2023 Medium
10. 10. In the given figure the total charge stored in the combination of capacitors is \(100\,\mu C\). The value of ' \(x\) ' is \(............\).
    2023 Medium
11. 11. The distance between two plates of a capacitor is \(d\) and its capacitance is \(C _1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac{2 d }{3}\) and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C _2\). The ratio \(\frac{ C _2}{ C _1}\) is: 2023 Medium
12. 12. The equivalent capacitance of the combination shown is
    2023 Medium
13. 13. A capacitor \(C _{1}\) of capacitance \(5\,\mu F\) is charged to a potential of \(30\,V\) using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor \(C _{2}\) of capacitance \(10\,\mu F\) as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor \(C _{2}\) is________ \(\mu C\)
    2022 Hard
14. 14. A paralle plate capacitor is made up of stair like structure with a palte area \(A\) of each stair and that is connected with a wire of length \(b\), as shown in the figure. The capacitance of the arrangement is \(\frac{ x }{15} \frac{\varepsilon_{0} A }{ b }\). The value of \(x\) is ............
    2022 Hard
15. 15. The charge on capacitor of capacitance \(15 \mu F\) in the figure given below is \(\dots \; \mu c\)
    2022 Medium
16. 16. The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).
    2022 Hard
17. 17. The total charge on the system of capacitance \(C _{1}=1\,\mu F , C _{2}=2\,\mu F , C _{3}=4\,\mu F\) and \(C _{4}=3\,\mu F\) connected in parallel is \(......\mu C\) (Assume a battery of \(20\,V\) is connected to the combination) 2022 Medium
18. 18. Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is
    2022 Medium
19. 19. 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 \(?\) 2022 Medium
20. 20. A \(2\, \mu F\) capacitor \(C _{1}\) is first charged to a potential difference of \(10\, V\) using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor \(C _{2}\) of \(8\, \mu F\). The charge in \(C _{2}\) on equilibrium condition is \(\ldots\,\mu C\). (Round off to the Nearest Integer)
    2021 Hard
21. 21. A simple pendulum of mass \('m',\) length \('I'\) and charge \('+q'\) suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be -
    2021 Hard
22. 22. Calculate the amount of charge on capacitor of \(4\, \mu\, {F}\). The internal resistance of battery is \(1\, \Omega\) : (in \(\mu {C}\))
    2021 Hard
23. 23. Consider the combination of \(2\) capacitors \(C _{1}\) and \(C _{2},\) with \(C _{2}> C _{1},\) when connected in parallel, the equivalent capacitance is \(\frac{15}{4}\) time the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, \(\frac{ C _{2}}{ C _{1}}\) 2021 Hard
24. 24. Four identical rectangular plates with length, \(l=2\, cm\) and breadth, \(b =\frac{3}{2}\, cm\) are arranged as shown in figure. The equivalent capacitance between \(A\) and \(C\) is \(\frac{ x \varepsilon_{0}}{ d } .\) The value of \(x\) is (Round off to the Nearest Integer)
    2021 Medium
25. 25. Three capacitors \({C}_{1}=2\, \mu {F}, {C}_{2}=6 \, \mu {F}\) and \({C}_{3}=12 \, \mu {F}\) are connected as shown in figure. Find the ratio of the charges on capacitors \({C}_{1}, {C}_{2}\) and \({C}_{3}\) respectively:
    2021 Hard
26. 26. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be 2021 Medium
27. 27. A \(10\, \mu F\) capacitor is fully charged to a potential difference of \(50\, V\). After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes \(20\, V\). The capacitance of the second capacitor is......\(\mu F\) 2020 Hard
28. 28. In the circuit shown, charge on the \(5\, \mu F\) capacitor is\(........\mu C\)
    2020 Hard
29. 29. In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)
    2020 Medium
30. 30. Two isolated conducting spheres \(S_{1}\) and \(S_{2}\) of radius \(\frac{2}{3} R\) and \(\frac{1}{3} R\) have \(12\, \mu C\) and \(-3\, \mu C\) charges, respectively, and are at a large distance from each other. They are now  onnected by a conducting wire. A long time after this is done the charges on \(S_{1}\) and \(S_{2}\) are respectively 2020 Hard
31. 31. Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are
    2019 Hard
32. 32. In the circuit shown, find \(C\) if the effective capacitance of the whole circuit is to be \(0.5\,\mu F.\) All values in the circuit are in \(\mu F.\)
    2019 Hard
33. 33. In the figure shown below, the charge on the left plate of the \(10\, \mu F\) capacitor is \(-30\,\mu C.\) The charge on the right place of the \(6\,\mu F\) capacitor is.....\(\mu C\)
    2019 Hard
34. 34. In the given circuit, the charge on \(4\, \mu F\) capacitor will be.....\(\mu C\)
    2019 Hard
35. 35. The equivalent capacitance between \(A\) and \(B\) in the circuit given below is.....\(μF\)
    2018 Hard
36. 36. A capacitance of \(2\ μF\) is required in an electrical circuit across a potential difference of \(1.0\ kV\). A large number of \(1\ μF\) capacitors are available which can withstand a potential difference of not more than \(300\ V\). The minimum number of capacitors required to achieve this is 2017 Medium
37. 37. Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance \(C\) if the equivalent capacitance between point \(A\) and \(B\) is to be \(1\,\mu F\) is 
    2016 Hard
38. 38. Three capacitors each of \(4\,\,\mu F\)  are to be connected in such a way that the effective capacitance is \(6\,\,\mu F.\)  This can be done by connecting thern 2016 Hard

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