Capacitors and capacitance, combinations in series and parallel, parallel plate capacitor with and without dielectric, energy stored in a capacitor - Question Bank

1. What is the capacitance of a capacitor if a charge of 0.001 Coulomb is stored on it when a potential difference of 10 Volts is applied across it?
A) 100 microfarad
B) 10 microfarad
C) 1 microfarad
D) 0.1 microfarad
2. If the capacitance of a conductor is C, and it stores charge Q, then the potential energy stored is given by:
A) Q²/2C
B) C²/2Q
C) Q²/2
D) C²/2
3. The capacitance of a spherical conductor of radius R is:
A) 4πε₀R
B) R/(4πε₀)
C) 4πε₀/R
D) 1/(4πε₀R)
4. A parallel plate capacitor has a capacitance of 1 microfarad in vacuum. If a dielectric with K=4 is inserted, what is the new capacitance?
A) 0.25 microfarad
B) 1 microfarad
C) 4 microfarad
D) 16 microfarad
5. Two capacitors, 2 microfarad and 3 microfarad, are connected in parallel. What is the equivalent capacitance?
A) 5 microfarad
B) 1.2 microfarad
C) 6 microfarad
D) 0.6 microfarad
6. Two capacitors, 2 microfarad and 3 microfarad, are connected in series. What is the equivalent capacitance?
A) 5 microfarad
B) 1.2 microfarad
C) 6 microfarad
D) 0.6 microfarad
7. A capacitor stores 50 J of energy when charged to 200 V. What is its capacitance?
A) 2.5 mF
B) 25 mF
C) 5 mF
D) 50 mF
8. A capacitor of 10 microfarad is connected to a 100V battery. What is the charge stored on the capacitor?
A) 1000 C
B) 1 C
C) 0.001 C
D) 10 C
9. When a dielectric is inserted into a charged capacitor connected to a battery, the energy stored:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
10. When a dielectric is inserted into a charged capacitor connected to a battery, the potential difference between the plates:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
11. When a dielectric is inserted into a charged capacitor connected to a battery, the electric field between the plates:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
12. When a dielectric is inserted into a charged capacitor connected to a battery, the charge on the plates:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
13. When a dielectric is inserted into a charged capacitor disconnected from the battery, the energy stored:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
14. When a dielectric is inserted into a charged capacitor disconnected from the battery, the potential difference between the plates:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
15. When a dielectric is inserted into a charged capacitor disconnected from the battery, the electric field between the plates:
A) Increases
B) Decreases
C) Remains unchanged
D) Becomes zero
16. Which of the following is NOT a factor affecting the capacitance of a parallel plate capacitor?
A) Area of the plates
B) Distance between the plates
C) Material between the plates
D) Charge on the plates
17. If three capacitors of capacitances C1, C2, and C3 are connected in parallel, the equivalent capacitance Ceq is given by:
A) 1/Ceq = 1/C1 + 1/C2 + 1/C3
B) Ceq = C1 + C2 + C3
C) Ceq = (C1*C2*C3)/(C1+C2+C3)
D) Ceq = 1/(C1+C2+C3)
18. If three capacitors of capacitances C1, C2, and C3 are connected in series, the equivalent capacitance Ceq is given by:
A) 1/Ceq = 1/C1 + 1/C2 + 1/C3
B) Ceq = C1 + C2 + C3
C) Ceq = (C1*C2*C3)/(C1+C2+C3)
D) Ceq = 1/(C1+C2+C3)
19. The dielectric strength of a material is the maximum electric field it can withstand before:
A) It conducts electricity
B) It melts
C) It becomes an insulator
D) It explodes
20. For a given voltage, a larger capacitance means:
A) Less charge stored
B) More charge stored
C) No charge stored
D) Negative charge stored
21. What happens to the capacitance of a parallel plate capacitor if a metal sheet of negligible thickness is inserted between the plates?
A) Capacitance increases
B) Capacitance decreases
C) Capacitance becomes infinite
D) Capacitance remains unchanged
22. A capacitor is essentially a device used to store:
A) Charge
B) Energy
C) Electric field
D) All of the above
23. What is the unit of energy stored in a capacitor?
A) Joule
B) Watt
C) Coulomb
D) Volt
24. What is the dimension of capacitance?
A) [M⁻¹L⁻²T⁴A²]
B) [M¹L²T⁻³A²]
C) [M⁰L⁰T⁰A⁰]
D) [M¹L¹T¹A¹]
25. A capacitor of capacitance C is charged to voltage V. If the battery remains connected and the distance between the plates is doubled, what happens to the energy stored in the capacitor?
A) It doubles
B) It becomes four times
C) It remains the same
D) It halves
26. A capacitor of capacitance C is charged to voltage V. If the battery remains connected and the distance between the plates is doubled, what happens to the potential difference across the capacitor?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
27. A capacitor of capacitance C is charged to voltage V. If the battery remains connected and the distance between the plates is doubled, what happens to the electric field between the plates?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
28. A capacitor of capacitance C is charged to voltage V. If the battery remains connected and the distance between the plates is doubled, what happens to the charge on the capacitor?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
29. A capacitor of capacitance C is charged to voltage V. If the battery is removed and the distance between the plates is doubled, what happens to the energy stored in the capacitor?
A) It doubles
B) It becomes four times
C) It remains the same
D) It halves
30. A capacitor of capacitance C is charged to voltage V. If the battery is removed and the distance between the plates is doubled, what happens to the potential difference across the capacitor?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
31. A capacitor of capacitance C is charged to voltage V. If the battery is removed and the distance between the plates is doubled, what happens to the electric field between the plates?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
32. A capacitor of capacitance C is charged to voltage V. If the battery is removed and the distance between the plates is doubled, what happens to the charge on the capacitor?
A) It doubles
B) It halves
C) It remains the same
D) It becomes zero
33. If the area of the plates of a parallel plate capacitor is doubled, its capacitance will:
A) Halve
B) Double
C) Remain the same
D) Become four times
34. If the distance between the plates of a parallel plate capacitor is halved, its capacitance will:
A) Halve
B) Double
C) Remain the same
D) Become four times
35. The capacitance of a parallel plate capacitor is inversely proportional to:
A) The distance between the plates
B) The area of the plates
C) The square of the distance between the plates
D) The square of the area of the plates
36. The capacitance of a parallel plate capacitor is directly proportional to:
A) The distance between the plates
B) The area of the plates
C) The square of the distance between the plates
D) The inverse of the area of the plates
37. When capacitors are connected in parallel, the voltage across each capacitor is:
A) Different
B) The same
C) Zero
D) Equal to the total voltage
38. When capacitors are connected in series, the charge on each capacitor is:
A) Different
B) The same
C) Zero
D) Equal to the total charge
39. If a capacitor is charged to a voltage V, and then the voltage is doubled, by what factor does the stored energy increase?
A) 2
B) 3
C) 4
D) 8
40. What is the formula for the energy stored in a capacitor (U) in terms of charge (Q) and voltage (V)?
A) U = ½ QV
B) U = QV
C) U = Q/(2V)
D) U = 2QV
41. What is the formula for the energy stored in a capacitor (U) in terms of voltage (V) and capacitance (C)?
A) U = ½ CV²
B) U = CV²
C) U = ½ C/V²
D) U = C²V/2
42. What is the formula for the energy stored in a capacitor (U) in terms of charge (Q) and capacitance (C)?
A) U = Q² / (2C)
B) U = Q² * C
C) U = C / (2Q²)
D) U = 2Q² * C
43. If a dielectric material with dielectric constant K is inserted between the plates of a parallel plate capacitor, what is the new capacitance?
A) K * C₀
B) C₀ / K
C) C₀ + K
D) C₀ - K
44. What is the dielectric constant (K) of a material?
A) The ratio of capacitance with dielectric to capacitance in vacuum
B) The ratio of capacitance in vacuum to capacitance with dielectric
C) The product of capacitance with dielectric and capacitance in vacuum
D) The difference between capacitance with dielectric and capacitance in vacuum
45. When a dielectric material is introduced between the plates of a parallel plate capacitor, its capacitance:
A) Decreases
B) Increases
C) Remains unchanged
D) Becomes zero
46. A parallel plate capacitor has plates of area A and separation d. What is its capacitance in vacuum?
A) ε₀A/d
B) ε₀d/A
C) A/(ε₀d)
D) d/(ε₀A)
47. Two capacitors C1 and C2 are connected in parallel. What is their equivalent capacitance?
A) C1 + C2
B) C1 * C2 / (C1 + C2)
C) 1 / (C1 + C2)
D) (C1 + C2) / (C1 * C2)
48. Two capacitors C1 and C2 are connected in series. What is their equivalent capacitance?
A) C1 + C2
B) C1 * C2 / (C1 + C2)
C) 1 / (C1 + C2)
D) (C1 + C2) / (C1 * C2)
49. Which of the following represents the relationship between charge (Q), capacitance (C), and voltage (V) for a capacitor?
A) Q = CV
B) C = QV
C) V = CQ
D) Q = C/V
50. What is the unit of capacitance?
A) Volt
B) Ampere
C) Farad
D) Ohm