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Class 12  »  Physics  »  Electrostatic Potential and Capacitance

Capacitor and Capacitance - UNSOLVED PRACTICE SET

Class 12

Chapter: Electrostatic Potential and Capacitance | Topic: Capacitor and Capacitance

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Study Material.
Class 12

CAPACITOR AND CAPACITANCE - UNSOLVED PRACTICE SET

Topic: Capacitor and Capacitance

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The capacitance of a capacitor is defined as:

  1. The ratio of charge to potential difference
  2. The ratio of potential difference to charge
  3. The product of charge and potential difference
  4. The difference between charge and potential difference

Q2. The SI unit of capacitance is:

  1. Coulomb
  2. Volt
  3. Farad
  4. Ohm

Q3. For a parallel plate capacitor, the capacitance depends on:

  1. Only the plate area
  2. Only the plate separation
  3. Plate area, plate separation, and the medium between plates
  4. Only the charge on the plates

Q4. The capacitance of a parallel plate capacitor with air between the plates is C. If the space between the plates is completely filled with a dielectric of constant K, the new capacitance becomes:

  1. C/K
  2. KC
  3. C
  4. K²C

Q5. A spherical capacitor consists of two concentric spherical conductors. Its capacitance depends on:

  1. Only the inner radius
  2. Only the outer radius
  3. Both inner and outer radii
  4. The charge on the conductors

Q6. The energy stored in a capacitor is given by:

  1. ½CV
  2. ½CV²
  3. CV²
  4. ½C²V

Short Answer Questions

Q7. Define capacitance. Why is it called a "geometric property" of a capacitor?

Q8. Write the expression for the capacitance of a parallel plate capacitor. On what factors does it depend?

Q9. A capacitor is connected to a battery. What happens to the capacitance if the battery voltage is doubled? Explain.

Q10. Why is the unit of capacitance called the "Farad"? Is 1 Farad a practical value for everyday capacitors? Explain.

Q11. A parallel plate capacitor has circular plates of radius 5 cm separated by 2 mm in air. Calculate its capacitance.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q12. What is an isolated sphere capacitor? Write the expression for its capacitance.

Long Answer Questions

Q13. Derive the expression for the capacitance of a parallel plate capacitor. Explain each step clearly and state the assumptions made.

Q14. Derive the expression for the capacitance of a spherical capacitor consisting of two concentric spherical shells of radii a and b (b > a). What happens to the capacitance when b → ∞?

Q15. A parallel plate capacitor has square plates of side 10 cm separated by 1 mm in air. It is connected to a 100 V battery.

(a) Calculate the capacitance of the capacitor.

(b) Find the charge on each plate.

(c) Calculate the electric field between the plates.

(d) If a dielectric slab of thickness 1 mm and K = 5 is inserted, what is the new capacitance?

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Numerical / Application-Based Problems

Q16. A parallel plate capacitor has plates of area 500 cm² separated by 2 mm in air.

(a) Calculate its capacitance.

(b) It is connected to a 200 V battery. Calculate the charge stored and the energy stored.

(c) The battery is now disconnected and the plate separation is doubled to 4 mm. Find the new potential difference, charge, and energy.

(d) Explain why the energy increases when the plate separation is increased with the battery disconnected.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q17. In your kitchen, you use a microwave oven that contains a high-voltage capacitor. A typical microwave capacitor has capacitance C = 1 μF and is charged to V = 2000 V.

(a) Calculate the charge stored on the capacitor.

(b) Calculate the energy stored in the capacitor.

(c) Even after the microwave is unplugged, the capacitor can hold this charge for a long time. Why is this dangerous, and why do technicians discharge capacitors before repairing appliances?

(d) If this energy were released in 1 millisecond, what would be the average power? Compare this to a 100 W light bulb.

Q18. A spherical capacitor has inner sphere radius a = 4 cm and outer sphere radius b = 6 cm. The space between them is filled with a dielectric of constant K = 3.

(a) Calculate the capacitance of the spherical capacitor.

(b) It is connected to a 500 V battery. Calculate the charge and energy stored.

(c) Find the electric field at r = 5 cm from the center.

(d) If the outer sphere is grounded, what is the potential of the inner sphere?

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Total: 30 Marks | Time: 40 mins

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