STD 12 - Electric potential and capacitance PYQs: JEE Mains Physics

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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 parallel plate air capacitor has a capacitance \(C\). When it is half filled as show in figure with a dielectric constant \(K = 5\), the percentage increase in the capacitance is _______.
   2026 Medium
3. 3. 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
4. 4. 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
5. 5. 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
6. 6. 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
7. 7. A point charge of \(10^{-8} C\) is placed at origin. The work done in moving a point charge \(2 \mu C\) from point \(A (4,4,2) m\) to \(B (2,2,1) m\) is _________ J. 2026 Easy
8. 8. 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
9. 9. A three coulomb charge moves from the point \((0, -2, -5)\) to the point \((5, 1, 2)\) in an electric field expressed as \(\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\) N/C. The work done in moving the charge is _______ J. 2026 Hard
10. 10. Consider two identical metallic spheres of radius \(R\) each having charge \(Q\) and mass \(m\). Their centers have an initial separation of \(4 R\). Both the spheres are given an initial speed of \(u\) towards each other. The minimum value of \(u\), so that they can just touch each other is:
    (Take \(k=\frac{1}{4 \pi \epsilon_0}\) and assume \(k Q^2>G m^2\) where G is the Gravitational constant) 2026 Easy
11. 11. Electric field in a region is given by \( \vec{E}=Ax\hat{i}+By\hat{j} \), where \( A=10~V/m^{2} \) and \( B=5~V/m^{2} \). If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is __________ V. 2026 Medium
12. 12. Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field \((\vec{E})\) at the center O of the pentagon due to these five positive charges are:
    2026 Hard
13. 13. 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
14. 14. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    
    Assertion A: In electrostatics, a conductor does not store any net charge inside.
    
    Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
    
    Choose the correct answer from the options given below 2026 Medium
15. 15. 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
16. 16. The electric potential as a function of \(x, y\) is given by \(V = 5(x^2 - y^2)\) V. The electric field at a point \((2, 3)\) m is __________ V/m. 2026 Medium
17. 17. The electrostatic potential in a charged spherical region of radius \(r\) varies as \(V=a r^3+b\), where \(a\) and b are constants. The total charge in the sphere of unit radius is \(\alpha \times \pi a \in_0\). The value of \(\alpha\) is _________ . 2026 Medium
18. 18. The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _________ A.
    2026 Easy
19. 19. 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
20. 20. The stored charge in the capacitor in steady state of the following circuit is ________ \(\mu\)C.
    2026 Medium
21. 21. There are three co-centric conducting spherical shells \(A , B\) and C of radii \(a , b\) and c respectively. The potential of the spheres \(A , B\) and C respectively, are : 2026 Hard
22. 22. 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
23. 23. Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is: 2026 Hard
24. 24. Two charged conducting spheres \(S_1\) and \(S_2\) of radii \(8\) cm and \(18\) cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \(S_1\) and \(S_2\) spheres are \(E_{S_1}\) and \(E_{S_2}\) respectively. The value of \(\dfrac{E_{S_1}}{E_{S_2}}\) is _______. 2026 Medium
25. 25. Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
    Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J . 2026 Medium
26. 26. Two metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right)\) cm, with plate A on the top. An atomizer jet sprays oil (density \(1.5\) g/cm\(^3\)) droplets of radius \(1\) mm horizontally. All oil droplets carry a charge \(5\) nC. The potentials \(V_A\) and \(V_B\) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \(V_A\) and \(V_B\) are _______.
    (Neglect the air resistance to the droplets and take \(g = 10\) m/s\(^2\)) 2026 Hard
27. 27. Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ________ \(\mu\)J.
    (\(\frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9}\ N.m^{2}/C^{2}\)) 2026 Hard
28. 28. Under steady state condition the potential difference across the capacitor in the circuit is _______ V.
    2026 Medium
29. 29. Which one of the following is not a measurable quantity ? 2026 Medium
30. 30. 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
31. 31. A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is 2025 Easy
32. 32. 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
33. 33. 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
34. 34. 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
35. 35. 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
36. 36. A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
    A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
    B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
    C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
    D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
    E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
    Choose the correct answer from the options given below: 2025 Hard
37. 37. At steady state the charge on the capacitor, as shown in the circuit below, is _________ \(\mu \mathrm{C}\).
    
    2025 Medium
38. 38. 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
39. 39. Electric charge is transferred to an irregular metallic disk as shown in figure. If \(\sigma_1, \sigma_2, \sigma_3\) and \(\sigma_4\) are charge densities at given points then, choose the correct answer from the options given below:
    
    2025 Medium
40. 40. For a short dipole placed at origin \(O\), the dipole moment \(P\) is along \(x\)-axis, as shown in the figure. If the electric potential and electric field at A are \(\mathrm{V}_0\) and \(\mathrm{E}_0\), respectively, then the correct combination of the electric potential and electric field, respectively, at point \(B\) on the \(y\)-axis is given by...
    2025 Medium
41. 41. 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
42. 42. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\) Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
    Reason \(\mathrm{R}\) : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below 2025 Medium
43. 43. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.
    Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.
    In the light of the above statements, chose the most appropriate answer from the options given below : 2025 Easy
44. 44. 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: 2025 Easy
45. 45.
    In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by : 2025 Hard
46. 46.
    Space between the plates of a parallel plate capacitor of plate area \(4 \mathrm{~cm}^2\) and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ________ pF. \(\left(\right.\) Given \(\left.\varepsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\) 2025 Hard
47. 47. The electrostatic potential on the surface of uniformly charged spherical shell of radius \(\mathrm{R}=10 \mathrm{~cm}\) is 120 V. The potential at the centre of shell, at a distance \(\mathrm{r}=5 \mathrm{~cm}\) from centre, and at a distance \(\mathrm{r}=15 \mathrm{~cm}\) from the centre of the shell respectively, are : 2025 Easy
48. 48. The net current flowing in the given circuit is_______ A.
    2025 Medium
49. 49. Three infinitely long wires with linear charge density \(\lambda\) are placed along the \(x-a x i s, y\)-axis and \(z-\) axis respectively. Which of the following denotes an equipotential surface? 2025 Hard
50. 50. 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

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