Chapter 24-capacitance
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This document discusses capacitors and dielectrics. It defines capacitance as the amount of charge stored between two charged regions divided by the voltage. Capacitors are electronic components that can store electric charge. Common units for capacitors are microfarads, nanofarads, and picofarads. The document discusses different capacitor geometries including parallel plates, cylindrical, and spherical. It also explains how dielectrics can increase the capacitance of a capacitor by decreasing the voltage needed to store a given charge through induced dipole moments in the dielectric material. The energy stored in a capacitor is defined as one-half the capacitance times the voltage squared. Formulas are provided for calculating the capacitance of components connected in
![Capacitance of simple systems
Type Capacitance Comment
Parallel-plate capacitor
A: Area
d: Distance
Coaxial cable
a1: Inner radius
a2: Outer radius
l: Length
Pair of parallel wires[17]
a: Wire radius
d: Distance, d > 2a
l: Length of pair
Wire parallel to wall[17]
a: Wire radius
d: Distance, d > a
l: Wire length
Concentric spheres
a1: Inner radius
a2: Outer radius
Two spheres,
equal radius[18][19]
a: Radius
d: Distance, d > 2a
D = d/2a
γ: Euler's constant
Sphere in front of wall[18]
a: Radius
d: Distance, d > a
D = d/a
Sphere a: Radius
Circular disc a: Radius
Thin straight wire,
finite length[20][21][22]
a: Wire radius
l: Length
Λ: ln(l/a)](https://image.slidesharecdn.com/chapter-24-capacitance-160501121122/85/Chapter-24-capacitance-27-320.jpg)
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Chapter 24-capacitance
- 1. Chapter 24 Capacitors and Dielectrics
- 2. What is Capacitance? • Capacitance (C) is equal to the Charge (Q ) between two charges or charged “regions” divided by the Voltage (V) in those regions. • Here we assume equal and opposite charges (Q) • Thus C = Q/V or Q = CV or V=Q/C • The units of Capacitance are “Farads” after Faraday denoted F or f • One Farad is one Volt per Coulomb • One Farad is a large capacitance in the world of electronics • “Capacitors” are electronic elements capable of storing charge • Capacitors are very common in electronic devices • All cell phones, PDA’s, computers, radio, TV’s … have them • More common units for practical capacitors are micro-farad (10-6 f = μf), nano-farad (10-9 f = nf) and pico-farads (10-12 f = pf)
- 3. A classic parallel plate capacitor
- 4. General Surfaces as Capacitors The Surfaces do not have to be the same
- 5. Cylindrical – “Coaxial” Capacitor
- 7. How most practical cylindrical capacitors are constructd
- 8. Dielectrics – Insulators – Induced and Aligned Dipole Moments
- 9. Aligning Random Dipole Moments
- 10. Creating Dipole Moments – Induced Dipoles
- 11. Adding Dielectric to a Capacitor INCREASES its Capacitance since it DECREASES the Voltage for a GIVEN Charge
- 12. Induced Dipole Moments in a Normally Unpolarized Dielectric
- 14. Electrostatic Attraction – “Cling” Forced on Induced Dipole Moments
- 15. Energy Stored in a Capacitor • Capacitors store energy in their electric fields • The force on a charge in E field E is F=qE • The work done moving a charge q across a potential V is qV • Lets treat a capacitor as a storage device we are charging • We start from the initial state with no charge and start adding charge until we reach the final state with charge Q and Voltage V. • Total work done W = ∫ V(q) dq (we charge from zero to Q) • BUT V = q/C • We assume here the Capacitance in NOT a function of Q and V BUT only of Geometry • Thus the energy stored is W = 1/C ∫q dq = ½ Q2/C = ½ CV2
- 16. Calculating Parallel Capacitor Capacitance • Assume two metal plates, area A each, distance d apart, Voltage V between them, Charge +-Q on Plates • σ = Q/A V = ∫Edx = Ed E = σ/є0 (from Gauss) • Therefore C = Q/V = σA/ (Ed) = є0 A/d • Note – As d decreases C increases
- 18. Force on a Dielectric inserted into a Capacitor
- 19. Force on Capacitor Plates F=QE V=Ed (d separation distance) F=QV/d Q=CV -> F =CV2/d Recall W (Stored Energy) = ½ CV2 Hence F = 2W/d or W = ½ Fd
- 22. Series and Parallel Capacitors
- 23. Dielectric Constants of Some Common Materials
- 24. Two Dielectric Constants – As if capacitors in Series
- 25. Two Dielectric Constants – As if two capacitors in Parallel
- 26. Dielectric Plus Vacuum (Air) Treat is if three capacitors in Series
- 27. Capacitance of simple systems Type Capacitance Comment Parallel-plate capacitor A: Area d: Distance Coaxial cable a1: Inner radius a2: Outer radius l: Length Pair of parallel wires[17] a: Wire radius d: Distance, d > 2a l: Length of pair Wire parallel to wall[17] a: Wire radius d: Distance, d > a l: Wire length Concentric spheres a1: Inner radius a2: Outer radius Two spheres, equal radius[18][19] a: Radius d: Distance, d > 2a D = d/2a γ: Euler's constant Sphere in front of wall[18] a: Radius d: Distance, d > a D = d/a Sphere a: Radius Circular disc a: Radius Thin straight wire, finite length[20][21][22] a: Wire radius l: Length Λ: ln(l/a)