Download Electric Potential

Capacitance
q  CV
Characteristics of a Capacitor
+ + + + + + + + + + + +
Charge = +q
No Dielectric
d
- - - - - - - - - - - -
Uniform Electric
Field
Charge = -q
Area
Note: Net charge of the system is zero.
Electric Field of a Parallel Plate
Capacitor
A
E-
E+
EA = ½ E+ + -½ E- = 0
- - - - - - - - - - -
B
E-
E+
EB = ½ E+ + ½ E- = E
+ + + + + + + + +
C
E-
E+
EC = -½ E+ + ½ E- = 0
Note that the electric field between the two plates is the sum of
the electric fields due to each plate individually
Electric Field of a Parallel Plate
Capacitor
From
- - - - - - - - - - -
E
+ + + + + + + + +
Gauss’ Law:
E = q/εoA
where:
εo = permittivity of free space
= 8.854 x 10-12 C2/Nm2
A = Area of the plate
Electric Field of a Parallel Plate
Capacitor
 Since:
E = ΔV/d
- - - - - - - - - - -
E
+ + + + + + + + +
And
E = q/εoA
 Set
them equal to each other and
rearrange to get:
 oA
q

C=
V
d
The ratio of charge per volt for any capacitor is call its
capacitance C.
Capacitance

Capacitance is a proportionality constant that is proportional to the
charge (q) between two oppositely charged objects and is inversely
proportional to the potential difference between them (V).
C = q/ΔV




SI Units: 1 Farad = 1 Coulomb/1 Volt.
A capacitor is an electrical device whose purpose is to store
electrical energy which can be used in a controlled manner over a
short period of time.
A capacitor consists of two conductors placed near one another
without touching. One is charged +q while the other is charged –q.
Capacitance is an intrinsic property of the capacitor independent of
charge and voltage.
Charging a Capacitor



When a capacitor is subjected to an electric
potential across its terminals, the electrons
will move accordingly.
When charging a capacitor, it will initially
behave much like a wire, allowing very high
current flow with a very small potential drop.
When a capacitor nears the electric
potential of the external source, the current
flow will slow and eventually come to a halt.

Charging and discharging a capacitor.
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The Dielectric
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+
+
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- - - - - - - - - - - 
Dielectric with
dipole
characteristics
Uniform
Electric Field
The electric field resulting from a dielectric is weaker than it would
be if there was nothing there.
The Dielectric Constant

A dielectric is an insulating material that contains
permanent dipole moments.
Where:
Eo

E
Eo = Electric field without a dielectric medium.
E = Electric field with dielectric.

Eo > E such that κ > 1.
 What does this mean?
• When an insulating material is added to the space
between two charged plates, the electric field is
decreased.
Effects of Adding Dielectric
Material

When dielectric material is added to
the space between the two plates of a
capacitor:
The electric field intensity will
decrease.
 The amount of charge on each of the
plates will increase.
 The capacitance will increase.

Storing Electric Charge on a
Parallel Plate Capacitor
When a 1.2F capacitor has a slab of dielectric
material, 2.6x10-5C of additional charge flows onto
the plates. What is the dielectric constant?
qo = CoV
q = κCoV
The extra charge equals Δq = q – qo
q – qo = κCoV – CoV
κ
=

q – qo
CoV
+1
Leads to
2.8
that the excess charge that the
capacitor can store is exactly equal to the
charge without the dielectric times the
dielectric constant.
q = 2.6x10-5C
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
C = 1.2F
Note
+
V = 12V
-
Effect of Dielectric on
Voltage when q is Constant
A capacitor is charged up by connecting to a
battery. It is then disconnected, and a slab of
dielectric material is inserted between the two
plates. Does the voltage between the plates…
1. increase?
2. decrease?
3. remain
the same?
 Why?

Because q is fixed and q = CV. Since C
increases with addition of the dielectric, V
must decrease.
Applications for Parallel Plate
Capacitors



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
Microphones
Keyboards
RAM
Starters for electric motors
Electronic noise filtering applications
Capacitors in Series and
Parallel Circuits
Parallel
+
V
-
C1
C2
C
3
C1
Series
+
-
V
C
2
C3
Capacitors in Parallel Circuits


The total charge stored on the capacitors in a parallel
circuit is equal to the sum of the charges stored on all of
the capacitors.
Voltage is the same across all of the capacitors.
q1 = C1V; q2 = C2V; q3 = C3V
qtotal = q1 + q2 + q3
Ceq = q/V = C1 + C2 + C3…
+
-
V
+q
2
+q
1
-q
1
C1
-q
2
+q
3
C2
-q
3
C3
Capacitors in Series Circuits


When capacitors are connected in series, the charge on
them is the same irrespective of the capacitance.
When capacitors are connected in series, the sum of the
voltages for each capacitor equals the potential for the
circuit.
V1
+q
+
-
C1
-q
+q
V
V2
-q C
-q
+q
C3
V3
2
Capacitors in Series Circuits
V1 = q/C1; V2 = q/C2; V3 = q/C3
Total voltage in a series circuit is equal to the sum of the
voltages. Therefore:
V = V 1 + V2 + V3
V = q/C1 + q/C2 + q/C3
V = q (1/C1 + 1/C2 + 1/C3)
Ceq = q/V
Solve for V
1/Ceq = 1/C1 + 1/C2 + 1/C3…
V = q/Ceq
Energy Stored in a Capacitor

A capacitor stores charge in the form of electrical energy.


This is why capacitors have features of batteries.
The amount of work required to fully charge a capacitor
is equal to the final charge q multiplied by the average
voltage as follows:
W = ½ qV (V = ½ V)

This work is also equal to the stored potential energy in
the capacitor (U).
Since q = CV, we can substitute this into 1 to obtain:
U = ½CV2
Similarly, since V = q/C:
U = ½ q2/C
Key Ideas

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Capacitors store electrical energy.
Capacitance is dependent on the geometry of the capacitor and
not the voltage or charge.
Capacitance is the ratio of the charge on one of the plates of the
capacitor and the voltage.
The plates in a capacitor are equally and oppositely charged.
A dielectric media gives a capacitor a greater ability to carry
charge.
Current does not flow through capacitors under normal
circumstances.