Download Chapter 24: Capacitance and Dielectrics

Chapter 24: Capacitance and Dielectrics
• When you compress/stretch a spring, we are storing potential energy … This is the mechanical method to store energy
It is also possible to store electric energy as electric potential energy using capacitors
• In this chapter: we will study electric devices (capacitors) used to store electric energy
‐We Will Learn The Followings‐
• The nature of capacitors (how we can make them) and their ability to store energy There are various types of capacitors, we will define the physical quantity (capacitance) which is a measure of ability to store energy and learn how to calculate this quantity for various capacitor like the – plate type – cylindrical – spherical …
• Analysis of capacitors connected in a network (connected in parallel and series)
There might be more than one capacitor connected in a circuit …
• Calculation of energy stored in a capacitor (how to calculate the stored energy)
We will drive an expression that gives the total amount of stored energy in a capacitor.
• Study of dielectrics in more details and how they used to make capacitors more effective
We will learn how we can use the dielectrics to increase the efficiency of capacitors.
Capacitors and Capacitance
• Capacitors are the devices that store electrical energy as electric potential energy
• A capacitor can be made using two conductors insulated from each other
Q = 0 (uncharged – empty)
no charge means the capacitors are not charged or empty
Q ≠ 0 (charged)
One can charge this capacitor by using a battery by applying a potential difference – which will reveal +Q and –Q on each conductor. This process is called charging the capacitor.
The battery doesn’t produce any charged. It just does move the charges from one conductor to another through chemical process until the potential difference becomes equal to potential difference along the battery.
Capacitors in Circuit Diagrams
The amount of charge on each conductor Q is proportional to potential difference between the conductors. This proportionality constant / ratio between Q and Vab is called capacitance: Capacitance
*** Q ~ Vab ***
proportionality constant is called capacitance, C .
When potential difference increases Q increases, but C remains the same.
C is a CONSTANT that ONLY depends on the physical properties of the capacitor ‐ mostly the geometry
C is a measure of ability to store energy. Greater C
means that it can hold/store more charge and energy Unit for capacitance
The SI‐unit of capacitance is called one farad (1 F), named after 19th century English physicist Michael Faraday. Attention: Don’t confuse C with C
C is used for coulomb (unit for charge) but C (italic C) is for capacitance.
Calculating Capacitance: Capacitors in Vacuum
There are various type of capacitors commonly used in applications
Parallel‐plate Capacitors – formed using two conducting parallel plates
Spherical Capacitors ‐ formed using two conducting spherical shells
Cylindrical Capacitors ‐ formed using two conducting cylindrical shells
Calculation of Capacitance for these capacitors is simple.
For a capacitor, we can calculate the capacitance by considering a charge Q then calculate the potential difference between them and then applying formula that describes the capacitance. Here, we will consider the capacitors in vacuum where the space between the conductors are empty. Later we will learn using the dielectrics to increase the capacitance (measure of efficiency in storing energy) of a capacitor. Parallel‐Plate Capacitors ‐ Calculation
What is the capacitance of a capacitor which is formed using two parallel plates?
The separation between the plates is d and surface area for the plates is A.
In order to determine the capacitance
Consider plates are charged with +Q and –Q
Determine the potential between + and – plates
Apply capacitance formula C = Q/Vab
If the d << size of the plates then the field is uniform directed from + to – plate.
From Gauss’s Law: which can be expressed in terms of Q:
Potential difference: yields to
Now, Apply capacitance Formula: C = Q /Vab
Q
Q
A
C

 C  0
Ed  Q  0 A  d
d
Parallel‐Plate Capacitors ‐ Interpretation
As mentioned before, capacitance of any capacitor only depends on physical properties of the plate and vacuum (that fills the space between the pates)
A
C  0
d
‐ Capacitance ‐
Increases with increasing A
Decreases with increasing d
Capacitance also depends on ε0 (electric permittivity of free space) which is the nature of space between the plates. Later, we will see that we can use some dielectric materials to increase the capacitance instead of using vacuum.
Let’s now do a unit analysis for the expression that we have found.
As you remember from Coulomb’s law, unit for ε0:
plug this into eq.
Remember Joule/Coulomb = Volt – So F = Coulomb/Volt is dimensionally correct
Therefore, we can take the unit for ε0 alternatively in capacitance calculations
Note: Because ε0 is very small, capacitors in industry are usually in microfarads or smaller, like picofarad 1pF = 10‐12 F
Various Types of Commercial Capacitors Capacitance and Break–Down Voltage
are marked on each capacitor
As can be seen in this picture
Capacitance increases with increasing size
Breakdown voltage (6.3V) depends on the
material used in construction, usually the electric properties of the material between the plates
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QUESTIONS AND PROBLEMS
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