Capacitance Class 12 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Capacitance — Competishun
Capacitance Class 12 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Capacitance is one of the most important and scoring chapters in Class 12 Physics. It carries significant weightage in JEE and NEET, with 2-3 questions appearing every year from this chapter. Capacitance is the ability of a system to store electric charge per unit potential difference.
This guide covers isolated conductors, parallel plate capacitors, spherical and cylindrical capacitors, dielectrics, energy stored in capacitors, and combinations of capacitors (series and parallel). Understanding these concepts is essential for solving problems in electrostatics and for understanding more advanced topics like RC circuits.
This page gives you the complete guide to Capacitance with all concepts explained in depth. You will find clear definitions, formulas, visual diagrams, and practice questions. Download the free PDF below and keep it handy for quick revision before your JEE Main, JEE Advanced, or NEET exam.
Download the Capacitance Complete Guide PDF
Get all Capacitance concepts, formulas, parallel plate, spherical and cylindrical capacitors, dielectrics, energy stored, and combinations in one clean PDF, free. Perfect for JEE and NEET revision.
Download Free PDFWhat is Capacitance?
Capacitance depends only on the geometry (size, shape, separation) of the conductors and the medium between them. It never depends on the charge Q or the potential V. Doubling the charge doubles the potential, leaving C unchanged.
Glossary of Capacitance Terms — Complete A to Z
| Term | Definition |
|---|---|
| Capacitance (C) | The ability to store charge per unit potential difference. C = Q/V. Unit: farad (F). Dimensions: M⁻¹L⁻²T⁴A². |
| Dielectric | An insulating material placed between the plates of a capacitor that increases capacitance by a factor equal to its dielectric constant K. |
| Dielectric Constant (K) | The factor by which a dielectric increases the capacitance. Also called relative permittivity: K = ε/ε₀. |
| Energy Stored (U) | The energy stored in a capacitor is U = ½QV = ½CV² = Q²/2C. It is stored in the electric field between the plates. |
| Energy Density (u) | Energy per unit volume in the electric field. u = ½ε₀E². |
| Series Combination | Capacitors connected end-to-end. The charge on each capacitor is the same. 1/Ceq = 1/C₁ + 1/C₂ + ... |
| Parallel Combination | Capacitors connected side-by-side. The voltage across each capacitor is the same. Ceq = C₁ + C₂ + ... |
| Mastering these terms is essential for understanding Capacitance. | |
Parallel Plate Capacitor — The Most Common Type
Capacitance
With Dielectric
Electric Field
Potential Difference
Charge on Faces
Fringing
Spherical Capacitor — Two Concentric Spheres
Capacitance
With Dielectric
Isolated Sphere
Thin-Gap Limit
Field in the Gap
Inner Earthed
Cylindrical Capacitor — The Coaxial Cable
Capacitance
With Dielectric
Field in the Gap
Thin-Gap Limit
Dielectrics — How They Increase Capacitance
With Dielectric
Electric Field
Potential Difference
Relative Permittivity
Energy Stored in a Capacitor — Where Does the Energy Go?
Energy Stored
Energy Density
Total Energy
With Dielectric
Combinations of Capacitors — Series and Parallel
Series
Parallel
Two in Series
Two in Parallel
Practice Questions — From JEE and NEET
| Question | Answer |
|---|---|
| Q1: Find the capacitance of a parallel plate capacitor with A = 0.5 m², d = 2 mm. (ε₀ = 8.85 × 10⁻¹²) | C = ε₀A/d = 8.85×10⁻¹² × 0.5 / 0.002 = 2.21 × 10⁻⁹ F. |
| Q2: What is the capacitance of an isolated sphere of radius 10 cm? | C = 4πε₀R = 4π × 8.85×10⁻¹² × 0.1 = 1.11 × 10⁻¹¹ F. |
| Q3: Two capacitors of 2 µF and 4 µF are connected in series. Find the equivalent capacitance. | Ceq = (2×4)/(2+4) = 8/6 = 1.33 µF. |
| Q4: Find the energy stored in a capacitor of 5 µF charged to 100 V. | U = ½CV² = ½ × 5×10⁻⁶ × 100² = 0.025 J. |
| Q5: What is the capacitance of a spherical capacitor with a = 2 cm, b = 5 cm? | C = 4πε₀ab/(b−a) = 4π×8.85×10⁻¹² × 0.02×0.05 / 0.03 = 3.71 × 10⁻¹² F. |
| Q6: A parallel plate capacitor has C = 10 µF. What is C if a dielectric of K = 5 is inserted? | C = K C₀ = 5 × 10 = 50 µF. |
| Q7: What is the energy density in a field of E = 10⁶ V/m? (ε₀ = 8.85 × 10⁻¹²) | u = ½ε₀E² = ½ × 8.85×10⁻¹² × 10¹² = 4.425 J/m³. |
| Q8: Two capacitors of 3 µF and 6 µF are connected in parallel. Find the equivalent capacitance. | Ceq = 3 + 6 = 9 µF. |
| Practise these types of questions to become comfortable with applying Capacitance concepts in exam scenarios. | |
All Capacitance Formulas at a Glance
| Category | Formula |
|---|---|
| Definition | C = Q/V |
| Parallel Plate | C = ε₀A/d |
| With Dielectric | C = Kε₀A/d |
| Spherical | C = 4πε₀ab/(b−a) |
| Cylindrical | C = 2πε₀L / ln(b/a) |
| Isolated Sphere | C = 4πε₀R |
| Energy Stored | U = ½CV² = Q²/2C |
| Energy Density | u = ½ε₀E² |
| Series | 1/Ceq = Σ1/Cᵢ |
| Parallel | Ceq = ΣCᵢ |
| Memorise these formulas for Capacitance. They are the key to scoring full marks in this chapter. | |
Common Mistakes in Capacitance
- Confusing capacitance with charge: Capacitance is a property of geometry, not of charge. C = Q/V is a definition, not a dependency.
- Forgetting dielectric constant: When a dielectric is inserted, the capacitance increases by a factor of K.
- Using the wrong formula for energy: U = ½CV², not CV². The factor of ½ is essential.
- Confusing series and parallel: In series, the charge is the same; in parallel, the voltage is the same.
- Forgetting field direction: The field between plates is from positive to negative. A plate never feels its own field.
- Ignoring fringing: For accurate calculations, assume d << √A to ignore fringing.
Why Capacitance Matters for JEE and NEET
- High weightage: This chapter appears in 2-3 questions in every JEE Main, JEE Advanced, and NEET physics paper.
- Foundation for circuits: Understanding capacitance is essential for understanding RC circuits, time constants, and AC circuits.
- Conceptual clarity: This chapter rewards students who understand the concepts rather than just memorizing formulas.
- Practical relevance: Capacitors are used everywhere — from power supplies and filters to touchscreens and memory devices.
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Download the full Capacitance guide with all concepts, definitions, formulas, and practice questions. Perfect for last-minute revision before JEE and NEET.
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