1. PHYS 221 Recitation
Kevin Ralphs
Week 3

2. Overview
HW Questions
Capacitance
Capacitors
Dielectrics

3. HW Questions
Ask Away….

4. Capacitance 𝑄=𝐶∆𝑉 What does it tell me? Why do I care?
The charge that accumulates on two conductors is proportional to the voltage between them
𝑄=𝐶∆𝑉
Q: charge on the capacitor’s plates, C: capacitance,
ΔV: potential difference across the capacitor
Why do I care?
Capacitors are vital components in electronics
They can be used to temporarily store charge and energy, and play an even more important role when we move to alternating current systems
Camera flashes, touch screen devices, modern keyboards all exploit capacitance

5. Capacitance What does capacitance depend on?
Geometry of the plates
Material between the plates
For parallel plates: 𝐶= 𝜀𝐴 𝑑
C: capacitance, ε: permittivity of the material between the plates, A: area of the plates (may or may not be square), d: distance between the plates
Unit of capacitance is the Farad
To demystify this, units are (meters*permittivity)

6. Capacitance The permittivity of free space has no physical meaning
It merely changes physical quantities into their appropriate SI units
Physical Units
SI Units
Length
Farads
Length/Charge
Volts
Length^2/Charge^2
Newtons
Length/Charge^2
Joules

7. Capacitance Dielectric
Put simply, a dielectric is a material (an insulator) that in all, but very rare cases weakens the electric field around it
This allows more charge to be placed on the plates for the same voltage (i.e. capacitance is increased)
The permittivity of a dielectric tells you how it affects the capacitance
The ratio of the permittivity of a dielectric and the permittivity of free space is the dielectric constant
𝜅= 𝜀 𝜀 𝑜 = 𝐶 𝑑 𝐶 𝑣𝑎𝑐
κ: dielectric constant, ε: permittivity of a material, εo : permittivity of free space, Cd : capacitance with a dielectric, Cvac: capacitance in the vacuum

8. Capacitance A charged capacitor has potential energy
𝑈= 𝑄 2 2𝐶 = 1 2 𝐶( ∆𝑉) 2 = 1 2 𝑄∆𝑉
U: stored potential energy, Q: charge on the capacitor,
C: capacitor’s capacitance, ΔV: voltage across the capacitor

9. Capacitance In circuits
In well-behaved configurations, capacitors may be combined into a single equivalent capacitor
Parallel
𝐶 𝑒𝑞 = 𝐶 𝑖
* This is like increasing the area of the plates *
Series
𝐶 𝑒𝑞 = 𝐶 𝑖 −1
* This is like increasing the separation distance *

10. Capacitance Capacitors are in equilibrium
Series: when they have the same charge
Parallel: when they have the same voltage