Cylindrical Capacitor Problems In Physics -Multiple Choice Questions Quiz

Question 1: What is the capacitance of a cylindrical capacitor with length L, radius R, and vacuum (air) between the plates?

(a) C = ε₀ * L / (2πR)
(b) C = 2πR / (ε₀ * L)
(c) C = ε₀ * (2πR / L)
(d) C = (ε₀ * L) / (2πR)

Question 2: What is the SI unit of capacitance?

(a) Volt (V)
(b) Ohm (Ω)
(c) Farad (F)
(d) Coulomb (C)

Question 3: In a cylindrical capacitor, if the distance between the plates is halved, what happens to the capacitance?

(a) The capacitance is halved.
(b) The capacitance is doubled.
(c) The capacitance remains the same.
(d) The capacitance becomes zero.

Question 4: Two cylindrical capacitors with capacitances C₁ and C₂ are connected in parallel. What is the equivalent capacitance (C_eq) of the combination?

(a) C_eq = C₁ + C₂
(b) C_eq = C₁ - C₂
(c) C_eq = 2C₁C₂ / (C₁ + C₂)
(d) C_eq = C₁C₂ / (C₁ + C₂)

Question 5: Two cylindrical capacitors with capacitances C₁ and C₂ are connected in series. What is the equivalent capacitance (C_eq) of the combination?

(a) C_eq = C₁ + C₂
(b) C_eq = C₁ - C₂
(c) C_eq = 2C₁C₂ / (C₁ + C₂)
(d) C_eq = C₁C₂ / (C₁ + C₂)

Question 6: A cylindrical capacitor has a capacitance of 20 picofarads (pF). If the length between the plates is doubled while the radius remains the same, what is the new capacitance?

(a) 5 pF
(b) 10 pF
(c) 20 pF
(d) 40 pF

Question 7: If the voltage across a 5 picofarad (pF) cylindrical capacitor is 10 volts, what is the charge stored in the capacitor?

(a) 5 × 10^(-12) C
(b) 10 × 10^(-12) C
(c) 50 × 10^(-12) C
(d) 100 × 10^(-12) C

Question 8: A cylindrical capacitor has a capacitance of 12 picofarads (pF) and a voltage of 60 volts across its plates. What is the energy stored in the capacitor?

(a) 12 × 10^(-9) J
(b) 36 × 10^(-9) J
(c) 72 × 10^(-9) J
(d) 120 × 10^(-9) J

Question 9: What happens to the capacitance of a cylindrical capacitor if a dielectric material is inserted between the plates?

(a) The capacitance increases.
(b) The capacitance decreases.
(c) The capacitance remains the same.
(d) It depends on the dielectric constant of the material.

Question 10: If a cylindrical capacitor is submerged in a liquid dielectric, what happens to the capacitance compared to the capacitance in a vacuum?

(a) The capacitance increases.
(b) The capacitance decreases.
(c) The capacitance remains the same.
(d) It depends on the specific heat capacity of the liquid.

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Total score: /10

Answer key:

Question 1: d

Question 2: c

Question 3: b

Question 4: c

Question 5: d

Question 6: b

Question 7: c

Question 8: a

Question 9: a

Question 10: a