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C 0 A
d
C Q
V
Capacitors: Store Electric Energy
To calculate:
1) Put on arbitrary ±Q
2) Calculate E
3) Calculate V
Parallel Plate Capacitor:
P8-
Ideal Battery
Fixes potential difference between its terminals
Sources as much charge as necessary to do so
Think: Makes a mountain
P8- 3
Equivalent Capacitance
1 2C1 C2V Q , V Q
V V1 V2
(voltage adds in series)
V = Q Q QC1 C2Ceq
C1 C2
1 1 1 Ceq
P8- 11
PRS Question: Capacitors in Series and Parallel
When capacitors are combined, they behave in an opposite way comparing to resistors.
P8- 13
Dielectrics
P8- 14
A dielectric is a non-conductor or insulator
Examples: rubber, glass, waxed paper
When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates
HOW???
Molecular View of Dielectrics
Polar Dielectrics :
Dielectrics with permanent electric dipole moments
Example: Water
P8- 15
Molecular View of Dielectrics
Non-Polar Dielectrics
Dielectrics with induced electric dipole moments
Example: CH4
P8- 16
Dielectric in Capacitor
Potential difference decreases because dielectric polarization decreases Electric Field!
P8- 17
Gauss’s Law for Dielectrics
Upon inserting dielectric, a charge density ’ is induced at its surface
0 0 S
insideqE dA EA
E '
0
' A
P8- 18
What is ’?
Dielectric Constant Dielectric weakens original field by a factor
E ' E0
0
0 ' ⎛1 1 ⎞
⎠⎜⎟⎝
P8- 19
Bound charge = free charge (1-1/ )k
Total net charge = free charge – bound charge = free charge/k
' /
Dielectric Constant Dielectric weakens original field by a factor
Very often, people use e instead of k to represent dielectric constant.
Dielectric constants
P8- 20
Vacuum 1.0Paper 3.7
Pyrex Glass 5.6
Water 800
0
AC
d
For a vacuum(air)-filled capacitor
For a dielectric-filled capacitor
?C
=1 k for vacuum. >1 k for other insulators (dielectrics).
Dielectric in a CapacitorQ0= constant after battery is disconnected
Upon inserting a dielectric:
Q0 Q0 C0
0 0
C Q VV /
VP8- 21Dielectric filling will increase C by a factor of , k when free charge
Q is unchanged, E field and DV will reduce by a factor of . k
E and V reducesdue to bounded charges.
Dielectric in a CapacitorV0 = constant when battery remains connected
Upon inserting a dielectric: Q Q0
C Q C Q0
P8- 22
0V0V
Dielectric filling increases C by a factor of ,kWhen DV is constant, Q increase by a factor of .k
Capacitors & DielectricsTo calculate:
1) Put on arbitrary ±Q
2) Calculate E
3) Calculate VC Q
VEnergy
2
Capacitance
21
2
Q 1
2C 2C V
P10-
Q V U 2
3 3
2o
E
Eu d r d r
Dielectrics
When DV is fixed, adding dielectric filling increases U by a factor of k. When Q (free charge) is unchanged, adding dielectric filling decreases U by a factor of k.