Goal: To understand the basics of capacitors

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# Goal: To understand the basics of capacitors - PowerPoint PPT Presentation

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

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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 understand how a Dielectric can make a better Capacitor

To be able to calculate the Energy stored inside a capacitor

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
• 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
• 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 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
• 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 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
• 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!
• 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 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 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 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
• 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
• 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
• 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!
• 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
• 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
• 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?
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
• 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