Transcript 2 Combinations of Capacitors, Energy of Capacitors

-Combinations of Capacitors
-Energy Stored in a Charged
Capacitor
AP Physics C
Mrs. Coyle
Circuit Symbols used in Circuit
Diagrams
Resistor
Capacitors in
Parallel
•The potential difference
across the capacitors is the
same.
V  V1  V2
•The flow of charges ceases
when the voltage across the
capacitors equals that of the
battery.
•The total charge of the
capacitors in series is the
sum of the individual
charges.
Qtotal = Q1 + Q2
Equivalent Capacitance for
Capacitors in Parallel
Qtotal  Q1  Q2
Ceq V  C1V  C2 V
Ceq = C1 + C2 + ....


Ceq is greater than
any of the individual
capacitors C.
It is as if the areas of
the capacitors were
combined.
Capacitors in Series
Qtotal  Q1  Q2



Electrons are transferred from
the left plate of C1 to the right
plate of C2 through the battery
An equal amount of negative
charge is removed from the left
plate of C2, leaving it with an
excess positive charge
All of the right plates gain
charges of –Q and all the left
plates have charges of +Q
Equivalent Capacitance
for Capacitors in Series
V  V1  V2
Qtotal  Q1  Q2
1
1
1



Ceq C1 C2
The equivalent capacitance of a
series combination is always less
than any individual capacitor in the
combination.
Ex: Find the equivalent capacitance,
the charge and the voltage across in
one of the 2μF capacitors.
2 F
6V
3 F
Ans: 8 μF, 6 μC
4 F
2 F
Ex 26.4: Find the Equivalent
Capacitance
Answer: 6F
Work to Charge a Capacitor


The work needed to transfer a charge, q,
from one plate to the other through the
battery is:
q
dW  Vdq  dq
C
The total work required to charge the
capacitor from q=0 to Q is:
q
W 
dq
0 C
2
1Q
W 
2 C
Q
Energy Stored in a Capacitor

The work done in charging the capacitor is
stored as electric potential energy U:
Q2 1
1
U
 QV  C(V )2
2C 2
2



This applies to a capacitor of any geometry.
The energy stored increases as the charge
increases and as the potential difference
increases.
At a certain maximum voltage, corona discharge
occurs between the plates.
Energy and Energy density for a
Parallel Plate Capacitor
V  Ed
o A
C
d

1
2
U  C ( V )
2
1  oA 2 2
U=
(d E )
2 d
1
2
U   o AdE
2
Energy density (energy per unit volume)
U
uE =
Ad
1
2
uE = oE
2