Capacitors and Capacitance
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Section 1: Introduction to Capacitors
A capacitor is a device that stores electric charge and electrostatic energy. It consists of two conductors separated by an insulating medium.
Section 2: Capacitance
Capacitance is the ability of a conductor system to store charge per unit potential difference.
It depends on geometry, medium, area, separation and arrangement, not directly on Q or V alone.
Section 3: Parallel Plate Capacitor
Section 4: Effect of Dielectric
A dielectric polarizes in an electric field and reduces the effective field inside the capacitor.
Section 5: Capacitors in Series
In series, charge on each capacitor is same and total potential is sum of individual potentials.
Section 6: Capacitors in Parallel
In parallel, potential difference across each capacitor is same and total charge is sum of charges.
Section 7: Equivalent Capacitance Problems
Section 8: Partially Filled Dielectric
Sections 9-10: Dielectric Slab and Conducting Slab
For a dielectric, thickness t behaves like t/K air thickness. For a conductor, electric field inside is zero, so thickness t is removed from effective separation.
Sections 11-13: Battery Connected vs Battery Disconnected
| Parameter | Battery Connected | Battery Disconnected |
|---|---|---|
| Voltage | Constant | Changes |
| Charge | Changes | Constant |
| Capacitance | Increases with dielectric | Increases with dielectric |
| Electric Field | May remain fixed by V/d in simple full-fill case | Reduces inside dielectric |
| Energy | U = ½CV² increases | U = Q²/(2C) decreases |
Section 14: Force on Dielectric
The dielectric is pulled into the capacitor because insertion increases capacitance and lowers/increases energy depending on the source condition. The force points in the direction of increasing capacitance.
Sections 15-16: Energy Stored and Energy Density
Sections 17-18: Two Charged Plates and Field of Charged Conductor
For two conducting plates carrying net charges q₁ and q₂, electrostatic equilibrium and field cancellation inside conductors give inner surface charges equal and opposite.
Sections 19-20: Multiple Dielectric Combinations and JEE Advanced Theory
Sections 21-24: CBSE, NEET, JEE Main, JEE Advanced Questions
Section 25: Formula Sheet
Section 26: Revision Notes
Capacitors store charge and energy. Geometry controls capacitance. Series reduces capacitance; parallel increases it. Dielectrics increase capacitance. Conductors remove active field region. Energy depends on whether Q or V is constant.
Section 27: FAQ
Section 28: Chapter Summary
This chapter connects electric field, potential, dielectric polarization, equivalent circuits, capacitor energy and advanced electrostatic boundary conditions. It is highly important for CBSE, NEET and JEE.
Section 29: Dielectric Slab of Thickness t Inside Parallel Plate Capacitor
Consider a parallel plate capacitor with plate area A, separation d, dielectric slab thickness t, and dielectric constant K.
Physical Explanation
The dielectric reduces the electric field only in the part of thickness t. The remaining air gap behaves normally. So the capacitor acts like two capacitors in series: one air part and one dielectric part.
Effective Separation Concept
The dielectric thickness t behaves like an equivalent air thickness t/K.
Equivalent Capacitor Approach
Alternative Derivation Using Potential Difference
Section 30: Conducting Slab of Thickness t Inserted Inside Capacitor
For a conducting slab of thickness t inserted between plates, electric field inside the conductor is zero in electrostatic equilibrium.
Inside a conductor, charges rearrange until the internal electric field becomes zero. Therefore no potential drop occurs across the conducting slab.
Physical interpretation: A conducting slab effectively brings the plates closer by thickness t.
Section 31: Comparison Table
| Parameter | Air Capacitor | Dielectric Slab Capacitor | Conducting Slab Capacitor |
|---|---|---|---|
| Electric Field | E = σ/ε₀ | Reduced inside dielectric: E = σ/(Kε₀) | Zero inside conductor |
| Potential Difference | V = Ed | V = E(d − t) + (E/K)t | V = E(d − t) |
| Capacitance | C = ε₀A/d | C = ε₀A/(d − t + t/K) | C = ε₀A/(d − t) |
| Energy | U = ½CV² or Q²/2C | Depends on battery connected/disconnected | Increases due to reduced effective separation |
| Applications | Basic capacitor model | Practical capacitors, insulation, tuning capacitance | JEE Advanced effective distance problems |
Section 32: Energy Density of Electric Field
CBSE Derivation
Since volume between plates is Ad:
Dielectric Medium
NEET and JEE Advanced Meaning
Energy is stored in the electric field, not literally inside the plates. In advanced problems, integrate energy density over volume when field is non-uniform.