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Goal: To understand the basics of capacitors. Objectives: To learn about what capacitors are To learn about the Electric fields inside a capacitor To learn about Capacitance To understand how a Dielectric can make a better Capacitor

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goal to understand the basics of capacitors

Goal: To understand the basics of capacitors

Objectives:

To learn about what capacitors are

To learn about the Electric fields inside a capacitor

To learn about Capacitance

To understand how a Dielectric can make a better Capacitor

To be able to calculate the Energy stored inside a capacitor

what are capacitors
What are capacitors?
  • Much like we build reservoirs to hold water you can build a device which holds onto charge.
  • These are capacitors.
  • They work by separating + and – charges so that you have an electric field between them.
  • Most commonly this is done on a pair of plates which are parallel to each other.
electric field inside a capacitor
Electric field inside a capacitor
  • The electric field is usually a constant between the plates of the capacitor.
  • This makes the math fairly straight forward.
  • The voltage across the capacitor is therefore V = E d where d is the separation between the plates.
  • Now we just need to find E.
electric field
Electric Field
  • Each plate will have some amount of charge spread out over some area.
  • This creates a density of charge which is denoted by the symbol σ
  • σ = Q / A where Q is the total charge and A is the area
  • And E = 4π k σ
  • Also, E = σ / ε0 where ε0 is a constant (called the permittivity of free space)
  • ε0 = 8.85 * 10-12 C2/(N*m2)
capacitance
Capacitance
  • Capacitance is a measure of how much charge you can store based on an electrical potential difference.
  • Basically it is a measure of how effectively you can store charge.
  • The equation is:
  • Q = C V where Q is the charge, C is the capacitance (not to be confused with units of charge), and V is the voltage (not to be confused with a velocity)
  • C is in units of Farads (F).
quick question
Quick question
  • You have a 10 F capacitor hooked up to a 8 V battery. What is the maximum charge that you can hold on the capacitor?
quick question1
Quick question
  • You have a 10 F capacitor hooked up to a 8 V battery. What is the maximum charge that you can hold on the capacitor?
  • Q = C V = (to be done on board)
finding the capacitance of a capacitor
Finding the Capacitance of a Capacitor
  • For this we have a few steps:
  • E = σ / ε0
  • Since σ = Q/A, E = Q / (ε0 * A)
  • V = E * d, so V = Q d / (ε0 * A)
  • Or, just moving things around:
  • Q/V = ε0 * A / d
  • Since C = Q / V = ε0 * A / d
wake up time
Wake up time!
  • Sample problem.
  • Two parallel plates are separated by 0.01 m.
  • The plates are 0.1 m wide and 1 m long.
  • If you add 5 C of charge to this plate then find:
  • A) the Electric field between the plates.
  • B) The Capacitance of the plate.
  • C) The voltage across the 2 plates.
wake up time1
Wake up time!
  • Two parallel plates are separated by 0.01 m.
  • The plates are 0.1 m wide and 1 m long.
  • If you add 5 C of charge to this plate then find:
  • A) the Electric field between the plates.
  • E = σ / (ε0 )
  • σ = Q / A, Q = 5 C, and A = 0.1 m * 1 m = 0.1 m2
  • So, σ = (Done on Board)
  • And E = (Done on Board)
wake up time2
Wake up time!
  • Two parallel plates are separated by 0.01 m.
  • The plates are 0.1 m wide and 1 m long.
  • If you add 5 C of charge to this plate then find:
  • B) The Capacitance of the plate.
  • C = A ε0 / d = (Done on Board)
wake up time3
Wake up time!
  • Two parallel plates are separated by 0.01 m.
  • The plates are 0.1 m wide and 1 m long.
  • If you add 5 C of charge to this plate then find:
  • C) The voltage across the 2 plates.
  • V = Q / C or E * d
  • Lets use E * d
limits
Limits
  • There are limits to what you can do with a normal capacitor (just like limits to what you can do with a dam).
  • Eventually the charges will overflow the capacitor and will leak out.
  • How would you solve this problem?
fill it with substance
Fill it with substance
  • One solution is to place a material in between the plates which prohibit the flow of charge (an insulator).
  • This allows you to build up more charge.
  • A substance that allows you to do this is called a dielectric.
dielectrics
Dielectrics
  • The dielectric has the effect of increasing the capacitance.
  • The capacitance is increased by a factor of the dielectric constant of the material (κ).
  • So, C = κA / (4π k d) or κε0 * A / d
lightning
Lightning!
  • One natural example of a discharging capacitor is lightning.
  • Somehow the + charges are removed from the – ones in the updraft of the cloud.
  • So, the bottom of the cloud has – charge.
  • This induces a + charge on the ground.
  • Now they do a dance. The – charges step down randomly. The + charges step up randomly.
  • If they meet it forms a pathway for a large amount of charge to flow very quickly – a lightning strike!
energy
Energy
  • Lightning of course contains a LOT of energy.
  • So, clearly capacitors don’t just keep charge, but energy as well.
  • How much energy?
  • For a plate capacitor the energy it stores is simply:
  • U = ½ Q V or ½ Q E d or ½ C V2
  • Note this is half of what we had for individual charges – be careful not to mix up the equations for particles and capacitors.
sample
Sample
  • You hook up a small capacitor to an 8 volt battery.
  • If the charge on the plates are 5 C then how much energy does the capacitor contain?
sample1
Sample
  • You hook up a small capacitor to an 8 volt battery.
  • If the charge on the plates are 5 C then how much energy does the capacitor contain?
  • U = ½ Q V = (Done on Board)
conclusion
conclusion
  • We learn that capacitors act as dams for charge – allowing them to store charge.
  • Store too much though, and they flood.
  • The maximum charge storable is Q = VC
  • Dielectrics can increase this by increasing the capacitance.
  • We learn the equations for capacitance and the E field inside a capacitor.
  • The energy a capacitor holds is U = ½ Q V