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Capacitance
A capacitor is a device used to store energy using charges
and electric field.
They are a number of uses for capacitors in our modern world: Pulsed Lasers/Weapons Help engines run Touch screens (like this SMARTboard) Filters for electrical circuits
Capacitors work using the physics of capacitance.
Capacitors
Capacitance – the ratio of charges on a
conductive plate to the voltage between the conductive plates.
Capacitance is like Capacity The Capacity of a milk carton is the volume it
holds Heat Capacity is the amount of energy an
object can store without an increase in temp.
Capacitance
Basic capacitance equation:
Capacitance of different objects: Isolated sphere
Parallel Plates
Capacitance
Capacitance 𝐶=𝑄∆𝑉
Charge on Plate
Potential Difference (Voltage)
8.854 x 10-12 C2/Nm2
Radius
Area
Separation
Unit: Farad Scalar Quantity
Since charges are being held in place there is
also potential energy that is being stored (which can then be turned into kinetic energy of the moving electrons!)
Capacitance
Parallel Plate Capacitor
We can change the capacitance by affecting the area of the plates, the distance between the plates, or the voltage of the battery.
How a Capacitor Works
Battery+ -
Electric Field in Wire
Electric Field in Wire
+++++
-----
Electrons move from the plate leaving it positively charged Electrons build up on the
plate leaving it negatively charged
The separation between the two charged
plates creates potential energy.
The potential energy comes from the chemically stored potential energy in the battery.
Parallel Plate Capacitors
+++++
-----
One way to increase the capacitance of a
parallel plate capacitor is to insert an insulator (like glass) between the two conductive plates.
This insulator is called a dielectric.
Dielectrics
This slightly changes our equation for a
parallel plate capacitor to look like this:
Dielectric cont.
Dielectric Constant
Capacitor with dielectric
Capacitor without dielectric
Basic Circuit Symbols
Wire
Capacitor
Battery
Switch
Combinations of Capacitors
Parallel Circuits are ‘stacked like pancakes.’
Capacitors in Parallel
C1
C2
C3
Battery
Parallel Circuits have two important
characteristics:
The Current varies over each component in the circuit:
The Voltage stays constant over each component in the circuit:
Parallel Circuits
To find the equivalent capacitance (a single
capacitor to replace all of the capacitors), we use the following equation:
Capacitors in Parallel
C1
C2
C3
Battery
Battery
CEQUIV
Series Circuits are placed next to each other.
Capacitors in Series
C2 C3C1
Battery
Series Circuits have two important
characteristics:
The Current stays constant over each component in the circuit:
The Voltage varies over each component in the circuit:
Series Circuits
To find the equivalent capacitance (a single
capacitor to replace all of the capacitors), we use the following equation:
Capacitors in Series
C2 C3C1
Battery
CEQUIV
What is the potential difference between the
plates of a 3.3 F capacitor that stores sufficient energy to operate a 75 W light bulb for 30 seconds?
Remember: Power =
Practice Problem