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Today’s agenda:
Energy Storage in Capacitors.
You must be able to calculate the energy stored in a capacitor, and apply the energy
storage equations to situations where capacitor configurations are altered.
Dielectrics.
You must understand why dielectrics are used, and be able include dielectric constants in
capacitor calculations.
Dielectrics
If an insulating sheet (“dielectric”) is
placed between the plates of a
capacitor, the capacitance increases by
a factor , which depends on the
material in the sheet.  is the
dielectric constant of the material.
In general, C = 0A / d.  is 1
for a vacuum, and  1 for air.
(You can also define  = 0
and write C =  A / d).
 A
C=
.
d
dielectric
The dielectric is the thin insulating sheet
in between the plates of a capacitor.
A lot of interesting physics happens in the dielectric, but we’ll skip that section.
dielectric
Any reasons to use a dielectric in a capacitor?
Makes your life as a physics student more complicated.
Lets you apply higher voltages (so more charge).
Lets you place the plates closer together (make d
smaller).
Increases the value of C because >1.
Q = CV
  A
C=
d
Gives you a bigger kick when
Gives you a bigger kick when
Gives
you capacitor
a bigger kick when
you discharge
the
you discharge
the
you discharge capacitor
the capacitor
throughthrough
yourthrough
tongue!
your
tongue!
your tongue!
Homework hint: what if the
dielectric fills only half the
space between the plates?
dielectric
This is equivalent to two capacitors in parallel. Each of the
two has half the plate area. The two share the total
charge, and have the same potential difference
Q1 C 1
Q
C
Q2 C 2
Some things for you to ponder…
If you charge a capacitor and then remove the battery and
manipulate the capacitor, Q must stay the same but C, V,
and U may change. (What about E?)
If you charge a capacitor, keep the battery connected, and
manipulate the capacitor, V must stay the same but C, Q,
and U may change. (What about E?)
If exactly two capacitors are connected such that they have
the same voltage across them, they are probably in parallel
(but check the circuit diagram).
If you charge two capacitors, then remove the battery and
reconnect the capacitors with oppositely-charged plates
connected together…
draw a circuit diagram before and after, and use
conservation of charge to determine the total charge on
each plate before and after.