📘 Chapter 30: Energy Stored in a Capacitor (Class XII)
🔷 1. Introduction
A capacitor not only stores electric charge but also stores energy. This energy is stored in the form of an electric field between the plates of the capacitor.
Understanding this concept is essential for analyzing energy storage systems, circuits, and modern electronic devices.
🔷 2. Work Done in Charging a Capacitor
When a capacitor is charged, work is done in moving charges from one plate to another against the electric field.
If at any instant charge is q and potential is V:
dW = V dq
Since:
V = q / C
So:
dW = (q/C) dq
🔷 3. Derivation of Energy Stored
Total work done:
W = ∫ (q/C) dq
Integrating from 0 to Q:
U = Q² / 2C
Using Q = CV:
U = ½ CV²
Another form:
U = ½ QV
📦 4. Important Results (Must Remember)
- Energy stored: U = ½ CV²
- Also: U = Q²/2C = ½ QV
- Unit: Joule
- Energy stored in electric field
- Depends on capacitance and voltage
🔷 5. Energy Density
Energy per unit volume is called energy density.
u = ½ ε₀ E²
This shows energy is stored in electric field itself.
🔷 6. Physical Interpretation
The energy stored in a capacitor is not located on the plates but in the electric field between them.
Electric field acts as energy storage medium
🔷 7. Effect of Dielectric on Energy
🔹 Case 1: Battery Connected
- Voltage constant
- Capacitance increases
- Energy increases
🔹 Case 2: Battery Disconnected
- Charge constant
- Capacitance increases
- Energy decreases
🔷 8. Energy in Terms of Electric Field
Using field:
U = ½ ε₀ E² × Volume
This connects electrostatics with field theory.
🔷 9. Applications
- Energy storage devices
- Power electronics
- Flash cameras
- Defibrillators
🧠 10. Solved Numerical Problems
🔹 Q1
Find energy stored in capacitor C = 2F, V = 5V.
Solution:
U = ½ CV²
= ½ × 2 × 25
U = 25 J
Answer: 25 Joule
🔹 Q2
What is energy density formula?
Answer:
u = ½ ε₀ E²
🔹 Q3
Where is energy stored?
Answer:
In electric field
🔹 Q4
What happens when dielectric is inserted (battery connected)?
Answer:
Energy increases.
🔹 Q5
What are three forms of energy equation?
Answer:
U = ½ CV², Q²/2C, ½ QV
🔷 11. Advanced Conceptual Insight
Energy storage in capacitors is fundamental to modern electronics, renewable energy systems, and pulsed power technology. Supercapacitors are advanced devices capable of storing large amounts of energy.
This concept also bridges electrostatics with electromagnetic field theory.
🔷 12. Summary
Energy stored in a capacitor is the work done in charging it and is stored in the electric field. It depends on capacitance and voltage and plays a crucial role in modern technology.
✨ End of Chapter 30: Energy Stored in Capacitor ✨
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