Capacitance Problems

This section provides 100 problems to test your understanding of capacitance, including calculations of capacitance for various geometries, series and parallel combinations, energy stored in capacitors, and the effects of dielectrics. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering electrostatics, a key topic for JEE/NEET success.

Numerical Problems

1. A parallel plate capacitor has plates of area $A=0.02{\text{m}}^2$ and separation $d=0.002\text{m}$ in vacuum (${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N·m}}^2$). Calculate the capacitance.

   • (a) $8.84\times {10}^{-11}\text{F}$
   • (b) $8.85\times {10}^{-11}\text{F}$
   • (c) $8.86\times {10}^{-11}\text{F}$
   • (d) $8.87\times {10}^{-11}\text{F}$

2. A capacitor with capacitance $C=15\mu \text{F}$ is charged to a potential difference $V=100\text{V}$. Calculate the charge stored on the capacitor.

   • (a) $1.49\times {10}^{-3}\text{C}$
   • (b) $1.50\times {10}^{-3}\text{C}$
   • (c) $1.51\times {10}^{-3}\text{C}$
   • (d) $1.52\times {10}^{-3}\text{C}$

3. A spherical capacitor has inner radius $a=0.1\text{m}$ and outer radius $b=0.2\text{m}$. Calculate the capacitance (${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N·m}}^2$).

   • (a) $2.21\times {10}^{-11}\text{F}$
   • (b) $2.22\times {10}^{-11}\text{F}$
   • (c) $2.23\times {10}^{-11}\text{F}$
   • (d) $2.24\times {10}^{-11}\text{F}$

4. A cylindrical capacitor has inner radius $a=0.01\text{m}$, outer radius $b=0.02\text{m}$, and length $L=0.5\text{m}$. Calculate the capacitance.

   • (a) $4.01\times {10}^{-11}\text{F}$
   • (b) $4.02\times {10}^{-11}\text{F}$
   • (c) $4.03\times {10}^{-11}\text{F}$
   • (d) $4.04\times {10}^{-11}\text{F}$

5. Two capacitors $C_1=3\mu \text{F}$ and $C_2=6\mu \text{F}$ are connected in series. Calculate the equivalent capacitance.

   • (a) $1.99\mu \text{F}$
   • (b) $2.00\mu \text{F}$
   • (c) $2.01\mu \text{F}$
   • (d) $2.02\mu \text{F}$

6. Three capacitors $C_1=2\mu \text{F}$, $C_2=4\mu \text{F}$, and $C_3=8\mu \text{F}$ are connected in parallel. Calculate the equivalent capacitance.

   • (a) $13.9\mu \text{F}$
   • (b) $14.0\mu \text{F}$
   • (c) $14.1\mu \text{F}$
   • (d) $14.2\mu \text{F}$

7. Two capacitors $C_1=5\mu \text{F}$ and $C_2=10\mu \text{F}$ are in series, connected to a potential difference of $150\text{V}$. Calculate the potential difference across $C_1$.

   • (a) $99.9\text{V}$
   • (b) $100.0\text{V}$
   • (c) $100.1\text{V}$
   • (d) $100.2\text{V}$

8. A capacitor $C=25\mu \text{F}$ is charged to $V=60\text{V}$. Calculate the energy stored in the capacitor.

   • (a) $4.49\times {10}^{-2}\text{J}$
   • (b) $4.50\times {10}^{-2}\text{J}$
   • (c) $4.51\times {10}^{-2}\text{J}$
   • (d) $4.52\times {10}^{-2}\text{J}$

9. A parallel plate capacitor has $A=0.03{\text{m}}^2$, $d=0.001\text{m}$, and an electric field $E=4000\text{N/C}$ between the plates. Calculate the energy density.

   • (a) $7.07\times {10}^{-2}{\text{J/m}}^3$
   • (b) $7.08\times {10}^{-2}{\text{J/m}}^3$
   • (c) $7.09\times {10}^{-2}{\text{J/m}}^3$
   • (d) $7.10\times {10}^{-2}{\text{J/m}}^3$

10. A parallel plate capacitor has $C=10\mu \text{F}$. A dielectric with $\kappa =2$ is inserted while keeping the charge constant at $Q=20\mu \text{C}$. Calculate the new potential difference across the capacitor.

    • (a) $0.999\text{V}$
    • (b) $1.000\text{V}$
    • (c) $1.001\text{V}$
    • (d) $1.002\text{V}$

11. A parallel plate capacitor has $C=8\mu \text{F}$, connected to a battery with $V=50\text{V}$. A dielectric with $\kappa =3$ is inserted while maintaining constant $V$. Calculate the new capacitance.

    • (a) $23.9\mu \text{F}$
    • (b) $24.0\mu \text{F}$
    • (c) $24.1\mu \text{F}$
    • (d) $24.2\mu \text{F}$

12. A parallel plate capacitor has $A=0.05{\text{m}}^2$, $d=0.003\text{m}$. Calculate the capacitance in vacuum.

    • (a) $1.47\times {10}^{-10}\text{F}$
    • (b) $1.48\times {10}^{-10}\text{F}$
    • (c) $1.49\times {10}^{-10}\text{F}$
    • (d) $1.50\times {10}^{-10}\text{F}$

13. A capacitor $C=12\mu \text{F}$ is charged to $V=80\text{V}$. Calculate the charge stored on the capacitor.

    • (a) $9.59\times {10}^{-4}\text{C}$
    • (b) $9.60\times {10}^{-4}\text{C}$
    • (c) $9.61\times {10}^{-4}\text{C}$
    • (d) $9.62\times {10}^{-4}\text{C}$

14. A spherical capacitor has $a=0.05\text{m}$, $b=0.1\text{m}$. Calculate the capacitance.

    • (a) $1.11\times {10}^{-11}\text{F}$
    • (b) $1.12\times {10}^{-11}\text{F}$
    • (c) $1.13\times {10}^{-11}\text{F}$
    • (d) $1.14\times {10}^{-11}\text{F}$

15. Two capacitors $C_1=4\mu \text{F}$ and $C_2=8\mu \text{F}$ are in series. Calculate the equivalent capacitance.

    • (a) $2.66\mu \text{F}$
    • (b) $2.67\mu \text{F}$
    • (c) $2.68\mu \text{F}$
    • (d) $2.69\mu \text{F}$

16. Three capacitors $C_1=1\mu \text{F}$, $C_2=2\mu \text{F}$, $C_3=3\mu \text{F}$ are in parallel, connected to $V=60\text{V}$. Calculate the total charge stored.

    • (a) $3.59\times {10}^{-4}\text{C}$
    • (b) $3.60\times {10}^{-4}\text{C}$
    • (c) $3.61\times {10}^{-4}\text{C}$
    • (d) $3.62\times {10}^{-4}\text{C}$

17. Two capacitors $C_1=6\mu \text{F}$ and $C_2=12\mu \text{F}$ are in series, connected to $V=120\text{V}$. Calculate the potential difference across $C_2$.

    • (a) $39.9\text{V}$
    • (b) $40.0\text{V}$
    • (c) $40.1\text{V}$
    • (d) $40.2\text{V}$

18. A capacitor $C=30\mu \text{F}$ is charged to $V=40\text{V}$. Calculate the energy stored.

    • (a) $2.39\times {10}^{-2}\text{J}$
    • (b) $2.40\times {10}^{-2}\text{J}$
    • (c) $2.41\times {10}^{-2}\text{J}$
    • (d) $2.42\times {10}^{-2}\text{J}$

19. A parallel plate capacitor has $A=0.04{\text{m}}^2$, $d=0.002\text{m}$, $E=3000\text{N/C}$. Calculate the energy density.

    • (a) $3.97\times {10}^{-2}{\text{J/m}}^3$
    • (b) $3.98\times {10}^{-2}{\text{J/m}}^3$
    • (c) $3.99\times {10}^{-2}{\text{J/m}}^3$
    • (d) $4.00\times {10}^{-2}{\text{J/m}}^3$

20. A capacitor $C=5\mu \text{F}$ has $Q=15\mu \text{C}$. A dielectric with $\kappa =2$ is inserted (constant $Q$). Calculate the new potential difference.

    • (a) $1.499\text{V}$
    • (b) $1.500\text{V}$
    • (c) $1.501\text{V}$
    • (d) $1.502\text{V}$

21. A capacitor $C=4\mu \text{F}$ is connected to $V=200\text{V}$. A dielectric with $\kappa =5$ is inserted (constant $V$). Calculate the new energy stored.

    • (a) $0.799\text{J}$
    • (b) $0.800\text{J}$
    • (c) $0.801\text{J}$
    • (d) $0.802\text{J}$

22. A parallel plate capacitor has $A=0.1{\text{m}}^2$, $d=0.005\text{m}$. Calculate the capacitance in vacuum.

    • (a) $1.76\times {10}^{-10}\text{F}$
    • (b) $1.77\times {10}^{-10}\text{F}$
    • (c) $1.78\times {10}^{-10}\text{F}$
    • (d) $1.79\times {10}^{-10}\text{F}$

23. A capacitor $C=18\mu \text{F}$ is charged to $V=70\text{V}$. Calculate the charge stored.

    • (a) $1.259\times {10}^{-3}\text{C}$
    • (b) $1.260\times {10}^{-3}\text{C}$
    • (c) $1.261\times {10}^{-3}\text{C}$
    • (d) $1.262\times {10}^{-3}\text{C}$

24. A spherical capacitor has $a=0.02\text{m}$, $b=0.04\text{m}$. Calculate the capacitance.

    • (a) $4.42\times {10}^{-12}\text{F}$
    • (b) $4.43\times {10}^{-12}\text{F}$
    • (c) $4.44\times {10}^{-12}\text{F}$
    • (d) $4.45\times {10}^{-12}\text{F}$

25. Two capacitors $C_1=1\mu \text{F}$ and $C_2=2\mu \text{F}$ are in series. Calculate the equivalent capacitance.

    • (a) $0.666\mu \text{F}$
    • (b) $0.667\mu \text{F}$
    • (c) $0.668\mu \text{F}$
    • (d) $0.669\mu \text{F}$

26. Four capacitors $C_1=5\mu \text{F}$, $C_2=10\mu \text{F}$, $C_3=15\mu \text{F}$, $C_4=20\mu \text{F}$ are in parallel, connected to $V=30\text{V}$. Calculate the total charge stored.

    • (a) $1.499\times {10}^{-3}\text{C}$
    • (b) $1.500\times {10}^{-3}\text{C}$
    • (c) $1.501\times {10}^{-3}\text{C}$
    • (d) $1.502\times {10}^{-3}\text{C}$

27. Two capacitors $C_1=2\mu \text{F}$ and $C_2=3\mu \text{F}$ are in series, then in parallel with $C_3=5\mu \text{F}$. Calculate the equivalent capacitance.

    • (a) $6.19\mu \text{F}$
    • (b) $6.20\mu \text{F}$
    • (c) $6.21\mu \text{F}$
    • (d) $6.22\mu \text{F}$

28. A capacitor $C=40\mu \text{F}$ is charged to $V=25\text{V}$. Calculate the energy stored.

    • (a) $1.249\times {10}^{-2}\text{J}$
    • (b) $1.250\times {10}^{-2}\text{J}$
    • (c) $1.251\times {10}^{-2}\text{J}$
    • (d) $1.252\times {10}^{-2}\text{J}$

29. A parallel plate capacitor has $A=0.02{\text{m}}^2$, $d=0.004\text{m}$, $E=2000\text{N/C}$. Calculate the energy density.

    • (a) $1.76\times {10}^{-2}{\text{J/m}}^3$
    • (b) $1.77\times {10}^{-2}{\text{J/m}}^3$
    • (c) $1.78\times {10}^{-2}{\text{J/m}}^3$
    • (d) $1.79\times {10}^{-2}{\text{J/m}}^3$

30. A capacitor $C=6\mu \text{F}$ has $Q=12\mu \text{C}$. A dielectric with $\kappa =4$ is inserted (constant $Q$). Calculate the new potential difference.

    • (a) $0.499\text{V}$
    • (b) $0.500\text{V}$
    • (c) $0.501\text{V}$
    • (d) $0.502\text{V}$

31. In a spacecraft power system, a capacitor has $C=20\mu \text{F}$, $V=150\text{V}$. A dielectric with $\kappa =3$ is inserted (constant $V$). Calculate the new capacitance.

    • (a) $59.9\mu \text{F}$
    • (b) $60.0\mu \text{F}$
    • (c) $60.1\mu \text{F}$
    • (d) $60.2\mu \text{F}$

32. A parallel plate capacitor has $A=0.08{\text{m}}^2$, $d=0.004\text{m}$. Calculate the capacitance in vacuum.

    • (a) $1.76\times {10}^{-10}\text{F}$
    • (b) $1.77\times {10}^{-10}\text{F}$
    • (c) $1.78\times {10}^{-10}\text{F}$
    • (d) $1.79\times {10}^{-10}\text{F}$

33. A capacitor $C=50\mu \text{F}$ is charged to $V=20\text{V}$. Calculate the charge stored.

    • (a) $9.99\times {10}^{-4}\text{C}$
    • (b) $1.00\times {10}^{-3}\text{C}$
    • (c) $1.01\times {10}^{-3}\text{C}$
    • (d) $1.02\times {10}^{-3}\text{C}$

34. Two capacitors $C_1=7\mu \text{F}$ and $C_2=14\mu \text{F}$ are in series, connected to $V=180\text{V}$. Calculate the potential difference across $C_1$.

    • (a) $119.9\text{V}$
    • (b) $120.0\text{V}$
    • (c) $120.1\text{V}$
    • (d) $120.2\text{V}$

35. A capacitor $C=10\mu \text{F}$ is charged to $V=300\text{V}$. A dielectric with $\kappa =2$ is inserted (constant $V$). Calculate the new energy stored.

    • (a) $0.899\text{J}$
    • (b) $0.900\text{J}$
    • (c) $0.901\text{J}$
    • (d) $0.902\text{J}$

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Conceptual Problems

36. What does capacitance measure?

• (a) Charge stored per unit area
• (b) Charge stored per unit potential difference
• (c) Energy stored per unit charge
• (d) Potential difference per unit energy

37. What happens to the capacitance of a parallel plate capacitor if the separation between plates doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Quarters

38. What is the key difference between capacitors in series and parallel?

• (a) Series: same charge, parallel: same voltage
• (b) Series: same voltage, parallel: same charge
• (c) Series: same energy, parallel: same capacitance
• (d) Series: same capacitance, parallel: same energy

39. What happens to the energy stored in a capacitor if a dielectric is inserted while keeping the charge constant?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

40. What is the unit of capacitance in SI units?

• (a) Farad
• (b) Volt
• (c) Joule
• (d) Ohm

41. What does a zero electric field inside a conductor imply for a capacitor?

• (a) No charge on plates
• (b) Uniform potential on plates
• (c) Non-uniform potential on plates
• (d) No field lines

42. What is the physical significance of $\frac{1}{2}{ϵ}_0{E}^2$?

• (a) Energy stored in a capacitor
• (b) Energy density in an electric field
• (c) Capacitance of a capacitor
• (d) Charge on a capacitor

43. What does a dielectric do to the electric field inside a capacitor?

• (a) Increases it
• (b) Decreases it
• (c) No effect
• (d) Makes it zero

44. What happens to the potential difference across a capacitor when a dielectric is inserted while keeping the voltage constant?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

45. What is the dimension of capacitance?

• (a) $[{\text{M}}^{-1}{\text{L}}^{-2}{\text{T}}^4{\text{A}}^2]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does a high capacitance indicate?

• (a) High charge storage for a given voltage
• (b) Low charge storage
• (c) High voltage for a given charge
• (d) No charge storage

47. What is the significance of $\frac{{ϵ}_{0}A}{d}$?

• (a) Capacitance of a spherical capacitor
• (b) Capacitance of a parallel plate capacitor
• (c) Energy stored in a capacitor
• (d) Charge on a capacitor

48. What happens to the total charge in a series combination of capacitors?

• (a) Same on each capacitor
• (b) Different on each capacitor
• (c) Zero on each capacitor
• (d) Infinite on each capacitor

49. What does the energy density in a capacitor depend on?

• (a) Charge on the plates
• (b) Electric field between the plates
• (c) Area of the plates
• (d) Separation between plates

50. How do capacitors in spacecraft power systems function?

• (a) Reduce charge
• (b) Store energy for ion propulsion
• (c) Increase distance
• (d) Decrease field

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Derivation Problems

51. Derive the capacitance of a parallel plate capacitor $C=\frac{{ϵ}_{0}A}{d}$.

52. Derive the capacitance of a spherical capacitor $C=4\pi {ϵ}_0\frac{ab}{b-a}$.

53. Derive the capacitance of a cylindrical capacitor $C=\frac{2\pi {ϵ}_{0}L}{\ln (b/a)}$.

54. Derive the equivalent capacitance for capacitors in series.

55. Derive the equivalent capacitance for capacitors in parallel.

56. Derive the energy stored in a capacitor $U=\frac{1}{2}C{V}^2$.

57. Derive the energy density in a capacitor $u=\frac{1}{2}{ϵ}_0{E}^2$.

58. Derive the new capacitance of a capacitor with a dielectric $C=\kappa C_0$.

59. Derive the effect of a dielectric on the electric field $E=\frac{E_0}{\kappa }$ (constant $Q$).

60. Derive the potential difference across a capacitor with a dielectric (constant $V$).

61. Derive the total energy in a series combination of capacitors.

62. Derive the total charge in a parallel combination of capacitors.

63. Derive the potential difference across each capacitor in a series combination.

64. Derive the energy stored in a capacitor with a dielectric (constant $V$).

65. Derive the charge distribution in a parallel combination of capacitors.

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NEET-style Conceptual Problems

66. What is the unit of energy density in SI units?

• (a) ${\text{J/m}}^3$
• (b) $\text{N/C}$
• (c) $\text{J}$
• (d) $\text{V}$

67. What does a dielectric constant $\kappa >1$ indicate?

• (a) Decreases capacitance
• (b) Increases capacitance
• (c) No effect on capacitance
• (d) Reduces charge

68. What happens to the total capacitance in a series combination?

• (a) Greater than individual capacitances
• (b) Less than the smallest capacitance
• (c) Equal to the largest capacitance
• (d) Zero

69. What happens to the energy stored in a capacitor if the potential difference doubles?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Quarters

70. What is the dimension of energy density?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

71. What does the area of the plates affect in a parallel plate capacitor?

• (a) Electric field
• (b) Capacitance
• (c) Potential difference
• (d) Energy density

72. What is the role of a dielectric in a capacitor?

• (a) Increases the electric field
• (b) Decreases the electric field
• (c) No effect on the field
• (d) Reduces charge

73. What happens to the charge on a capacitor in a parallel combination?

• (a) Same on each capacitor
• (b) Different, proportional to capacitance
• (c) Zero on each capacitor
• (d) Infinite on each capacitor

74. Why does the energy density depend on the electric field?

• (a) Due to $u=\frac{1}{2}{ϵ}_0{E}^2$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

75. What is the unit of the dielectric constant $\kappa$?

• (a) Unitless
• (b) Farad
• (c) Volt
• (d) Joule

76. What does a constant potential difference across a capacitor indicate?

• (a) Variable charge
• (b) Constant charge
• (c) Variable field
• (d) Zero field

77. Which type of combination results in the same charge on each capacitor?

• (a) Parallel combination
• (b) Series combination
• (c) Mixed combination
• (d) No combination

78. What is the direction of the electric field in a capacitor with a dielectric?

• (a) Same as without dielectric, but reduced
• (b) Opposite to the field
• (c) Perpendicular to the plates
• (d) Random

79. What does a pseudo-force do in a non-inertial frame for capacitors?

• (a) Affects perceived field
• (b) Affects charge distribution
• (c) Creates energy density
• (d) Reduces capacitance

80. What is the dimension of ${ϵ}_0$?

• (a) $[{\text{M}}^{-1}{\text{L}}^{-3}{\text{T}}^4{\text{A}}^2]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of capacitors in spacecraft power systems?

• (a) Reduce charge
• (b) Store energy for ion propulsion
• (c) Increase distance
• (d) Decrease field

82. What happens to the potential difference across a capacitor with a dielectric (constant $Q$)?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

83. Why does the capacitance of a parallel plate capacitor depend on the area of the plates?

• (a) Due to $C\propto A$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

84. What is the significance of $\frac{1}{2}\frac{Q^2}{C}$?

• (a) Electric field in a capacitor
• (b) Energy stored in a capacitor
• (c) Capacitance of a capacitor
• (d) Charge on a capacitor

85. What is the unit of energy stored in a capacitor?

• (a) Joule
• (b) Volt
• (c) Farad
• (d) Watt

86. What does a zero energy density in a capacitor indicate?

• (a) No electric field
• (b) Maximum field
• (c) No charge on plates
• (d) Infinite charge

87. What is the physical significance of $4\pi {ϵ}_0\frac{ab}{b-a}$?

• (a) Capacitance of a parallel plate capacitor
• (b) Capacitance of a spherical capacitor
• (c) Energy stored in a capacitor
• (d) Charge on a capacitor

88. Why does the energy stored in a capacitor increase with a dielectric (constant $V$)?

• (a) Due to increased capacitance
• (b) Due to decreased field
• (c) Due to field lines
• (d) Due to charge quantization

89. What is the dimension of $\frac{1}{C}$?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-4}{\text{A}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How do dielectrics help in spacecraft capacitors?

• (a) Reduce charge
• (b) Increase capacitance for energy storage
• (c) Reduce field
• (d) Increase distance

91. What is the role of separation $d$ in a parallel plate capacitor?

• (a) $C\propto d$
• (b) $C\propto \frac{1}{d}$
• (c) No dependence
• (d) Exponential dependence

92. What does a high energy density in a capacitor indicate?

• (a) Low electric field
• (b) High electric field
• (c) No field
• (d) Constant field

93. What is the physical significance of $\frac{V}{d}$ in a parallel plate capacitor?

• (a) Electric field between plates
• (b) Capacitance
• (c) Energy density
• (d) Charge on plates

94. What is the dimension of $\frac{Q}{V}$?

• (a) $[{\text{M}}^{-1}{\text{L}}^{-2}{\text{T}}^4{\text{A}}^2]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does the charge on a capacitor in a series combination remain the same?

• (a) Due to conservation of charge
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

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NEET-style Numerical Problems

96. A parallel plate capacitor has $A=0.06{\text{m}}^2$, $d=0.003\text{m}$. Calculate the capacitance in vacuum.

• (a) $1.76\times {10}^{-10}\text{F}$
• (b) $1.77\times {10}^{-10}\text{F}$
• (c) $1.78\times {10}^{-10}\text{F}$
• (d) $1.79\times {10}^{-10}\text{F}$

97. Two capacitors $C_1=2\mu \text{F}$ and $C_2=4\mu \text{F}$ are in series. Calculate the equivalent capacitance.

• (a) $1.33\mu \text{F}$
• (b) $1.34\mu \text{F}$
• (c) $1.35\mu \text{F}$
• (d) $1.36\mu \text{F}$

98. A capacitor $C=5\mu \text{F}$ is charged to $V=100\text{V}$. Calculate the energy stored.

• (a) $2.49\times {10}^{-2}\text{J}$
• (b) $2.50\times {10}^{-2}\text{J}$
• (c) $2.51\times {10}^{-2}\text{J}$
• (d) $2.52\times {10}^{-2}\text{J}$

99. A capacitor $C=8\mu \text{F}$ has $Q=16\mu \text{C}$. A dielectric with $\kappa =2$ is inserted (constant $Q$). Calculate the new potential difference.

• (a) $0.999\text{V}$
• (b) $1.000\text{V}$
• (c) $1.001\text{V}$
• (d) $1.002\text{V}$

100. A capacitor $C=3\mu \text{F}$ is connected to $V=50\text{V}$. A dielectric with $\kappa =3$ is inserted (constant $V$). Calculate the new energy stored.
     - (a) $1.124\times {10}^{-2}\text{J}$
     - (b) $1.125\times {10}^{-2}\text{J}$
     - (c) $1.126\times {10}^{-2}\text{J}$
     - (d) $1.127\times {10}^{-2}\text{J}$

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