Energy Stored in a Capacitor PYQs: JEE Mains Physics

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1. 1. A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____. 2026 Hard
2. 2. A parallel plate capacitor of capacitance \(1 \mu \mathrm{~F}\) is charged to a potential difference of 20 V . The distance between plates is \(1 \mu \mathrm{~m}\). The energy density between plates of capacitor is _________. 2025 Easy
3. 3. Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If \(E\) is the electric field and \(\varepsilon_0\) is the permittivity of free space between the plates, then potential energy stored in the capacitor is 2025 Easy
4. 4. 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?
   
   2025 Medium
5. 5. A \(16\  \Omega\) wire is bend to form a square loop. A \(9 \mathrm{~V}\) battery with internal resistance \(1\  \Omega\) is connected across one of its sides. If a \(4\  \mu \mathrm{F}\) capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \(\frac{x}{2} \ \mu \mathrm{J}\). where \(x=\) ________. 2024 Hard
6. 6. A capacitor of capacitance \(\mathrm{C}\) and potential \(\mathrm{V}\) has energy \(E\). It is connected to another capacitor of capacitance \(2 \mathrm{C}\) and potential \(2 \mathrm{~V}\). Then the loss of energy is \(\frac{x}{3} E\), where \(\mathrm{x}\) is _______. 2024 Hard
7. 7. In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ \(\mu \mathrm{C}\).
   2024 Hard
8. 8. Three capacitors of capacitances \(25 \mu \mathrm{F}, 30 \mu \mathrm{F}\) and \(45 \mu \mathrm{F}\) are connected in parallel to a supply of \(100\) \(V\). Energy stored in the above combination is \(\mathrm{E}\). When these capacitors are connected in series to the same supply, the stored energy is \(\frac{9}{\mathrm{x}} \mathrm{E}\). The value of \(x\) is _______. 2024 Hard
9. 9. Two identical capacitors have same capacitance \(C\). One of them is charged to the potential \(\mathrm{V}\) and other to the potential \(2 \mathrm{~V}\). 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 _______. 2024 Hard
10. 10. A \(600\,pF\) capacitor is charged by \(200\,V\) supply. It is then disconnected from the supply and is connected to another uncharged \(600\,pF\) capacitor. Electrostatic energy lost in the process is \(.........\,\mu J\). 2023 Hard
11. 11. A capacitor of capacitance \(900\,\mu F\) is charged by a \(100\,V\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as \(x \times 10^{-2}\,J\). The value of \(x\) is \(..............\) 2023 Medium
12. 12. A parallel plate capacitor of capacitance \(2\; F\) is charged to a potential \(V\). The energy stored in the capacitor is \(E_1\). The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is \(E _2\). The ratio \(E _2 / E _1\) is 2023 Medium
13. 13. A capacitor of capacitance \(50 \; pF\) is charged by \(100 \; V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is \(\dots \; nJ\). 2022 Hard
14. 14. If the charge on a capacitor is increased by \(2C\), the energy stored in it increases by \(44 \%\). The original charge on the capacitor is (in \(C\) ) 2022 Medium
15. 15. \(27\) similar drops of mercury are maintained at \(10 \,V\) each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop. 2021 Hard
16. 16. A parallel plate capacitor whose capacitance \(C\) is \(14\, pF\) is charged by a battery to a potential difference \(V =12\, V\) between its plates. The charging battery is now disconnected and a porcelin plate with \(k =7\) is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of \(..........pJ\). (Assume no friction) 2021 Medium
17. 17. An electron with kinetic energy \(K _{1}\) enters between parallel plates of a capacitor at an angle \('\alpha'\) with the plates. It leaves the plates at angle \(' \beta '\) with kinetic energy \(K _{2}\). Then the ratio of kinetic energies \(K _{1}: K _{2}\) will be ....... . 2021 Hard
18. 18. The electric field intensity produced by the radiation coming from a \(100\, W\) bulb at a distance of \(3\, m\) is \(E\). The electric field intensity produced by the radiation coming from \(60\, W\) at the same distance is \(\sqrt{\frac{x}{5}} E\). Where the value of \(x=......... .\) 2021 Hard
19. 19. A \(5\, \mu F\) capacitor is charged fully by a \(220\,V\) supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5\;\mu F\) capacitor. If the energy change during the charge redistribution is \(\frac{ X }{100} \;J\) then value of \(X\) to the nearest integer is\(.....\) 2020 Medium
20. 20. A \(60\; pF\) capacitor is fully charged by a \(20\; \mathrm{V}\) supply. It is then disconnected from the supply and is connected to another uncharged \(60 \;pF\) capactior is parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in \(nJ\)) 2020 Medium
21. 21. A capacitor \(C\) is fully charged with voltage \(V _{0}\) After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \(\frac{ C }{2} .\) The energy loss in the process after the charge is distributed between the two capacitors is\(.........\)\(CV _{0}^{2}\) 2020 Hard
22. 22. Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be 2020 Medium
23. 23. Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), 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\(.....CV^2\) 2020 Hard
24. 24. A capacitor with capacitance \(5\,\mu F\) is charged to \(5\,\mu C.\) If the plates are pulled apart to reduce the capacitance to \(2\,\mu F,\) how much work is done? 2019 Medium
25. 25. In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is
    2019 Hard
26. 26. The energy stored in the electric field produced by a metal sphere is \(4.5\, J\). lf the sphere contains \(4\,\mu C\) charge, its radius will be.......\(mm\) : [Take : \(\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N - {m^2}\,/{C^2}\, ]\) 2017 Hard

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