📘 Chapter 27: Capacitors and Capacitance (Class XII)

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🔷 1. Introduction

In electrostatics, devices that store electric charge and energy are called capacitors. The ability of a capacitor to store charge is known as capacitance.

Capacitors are fundamental components in electronics, power systems, and communication devices.

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🔷 2. What is a Capacitor?

A capacitor consists of:

• Two conducting plates
• Separated by an insulating medium (dielectric)

When connected to a battery, charges accumulate on plates:

• One plate becomes positively charged
• Other plate becomes negatively charged

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🔷 3. Capacitance

Capacitance is defined as:

C = Q / V

Where:

• C = capacitance
• Q = charge stored
• V = potential difference

Unit:

Farad (F)

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📦 4. Important Results (Must Remember)

• Capacitance: C = Q/V
• Unit: Farad
• Depends on geometry and medium
• Independent of charge and voltage
• Stores electrical energy

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🔷 5. Parallel Plate Capacitor

For a parallel plate capacitor:

C = ε₀ A / d

Where:

• A = area of plates
• d = separation
• ε₀ = permittivity of free space

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🔷 6. Effect of Dielectric

When dielectric is inserted:

C = K ε₀ A / d

Where K = dielectric constant

• Capacitance increases
• Electric field decreases

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🔷 7. Combination of Capacitors

🔹 Series Combination

1/C = 1/C₁ + 1/C₂ + ...

• Capacitance decreases

🔹 Parallel Combination

C = C₁ + C₂ + ...

• Capacitance increases

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🔷 8. Energy Stored in Capacitor

Energy stored:

U = ½ C V²

Other forms:

U = ½ QV = Q² / 2C

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🔷 9. Physical Interpretation

A capacitor stores energy in the form of an electric field between its plates.

This energy can be released when required in circuits.

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🔷 10. Factors Affecting Capacitance

• Area of plates (↑A → ↑C)
• Distance between plates (↑d → ↓C)
• Nature of dielectric

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🧠 11. Solved Numerical Problems

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🔹 Q1

Find capacitance of capacitor with A = 1 m² and d = 0.01 m.

Solution:

C = ε₀ A / d

= (8.85×10⁻¹² × 1) / 0.01

C = 8.85 × 10⁻¹⁰ F

Answer: 8.85 × 10⁻¹⁰ Farad

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🔹 Q2

What happens when dielectric is inserted?

Answer:

Capacitance increases.

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🔹 Q3

Which combination gives higher capacitance?

Answer:

Parallel

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🔹 Q4

What is energy stored formula?

Answer:

U = ½ CV²

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🔹 Q5

Does capacitance depend on voltage?

Answer:

No, it depends on geometry.

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🔷 12. Advanced Conceptual Insight

Capacitance is a fundamental concept in electronics, signal processing, and power systems. It is used in filters, memory devices, and energy storage systems.

Modern capacitors include ceramic, electrolytic, and supercapacitors.

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🔷 13. Applications

• Energy storage
• Power supply smoothing
• Signal filtering
• Electronic circuits

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🔷 14. Summary

Capacitors store charge and energy, and their capacitance depends on geometry and dielectric medium. They are essential components in modern electrical and electronic systems.

✨ End of Chapter 27: Capacitors and Capacitance ✨