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The concept of energy storage in capacitors, including the calculation of potential energy U, the work required to charge capacitors, and the advantages of using capacitors. It also covers capacitance in parallel and series combinations. Students will learn about the relationship between voltage V, charge q, and capacitance C, as well as the differences between capacitors in parallel and series.
Typology: Exams
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z^ What is the potential energy,
of a
charged capacitor? z Think of
as being stored in
field
between plates z Calculate
required to charge plates to
potential
z^ Recover energy by discharging capacitor
z^ Charge capacitor by transferring electronswith a battery z^ More charge moved,
field between
plates gets bigger, harder to movecharges so takes positive work to chargecapacitor
z^ Work required from 0 to total charge
is
z^ Potential energy = work z^ Or, use
q^ C qd q C W^
q
2
0
∫
q^ C
U^
2
2 1 CV 2 U^
=
CV q^
=
z^ Advantage of capacitor
z^ Get more power than from just a battery z^ Slowly charge capacitor with battery and thendischarge quickly z^ Examples – photo flash, medical defibrillator
2 1 CV 2 U
=
z^ Capacitors in parallel z^ Capacitors are directlywired together at eachplate and
applied
is same across all capacitors
V V V V^
=^
3 2 1
z^ Capacitors in parallel z^ Total
stored on
has total charge
and same
as original
capacitors
3 2 1
q q q q^
=
q V
C^ eq
=
z^ Capacitors in series z^ Capacitors are wired oneafter the other and
is
applied across the two endsof the series z Capacitors have identical
z^ Battery produces
only on
top and bottom plates,induced
on other plates
q q q q^
=^
3 2 1
z^ Capacitors in series z^ Sum of
across all capacitors
is equal to applied
eq^
has same
and total
as original capacitors
3
2
1
V
V
V
V^
=
q V
C^ eq
=
eq^
is always less than smallest capacitance
n i^
i
eq^
C
C
1
1
z^ Capacitors in parallel
z^ V
across each is equal z^ Total
q^
is sum
z^ Capacitors in series
z^ q
is equal on each z^ Total
V^
is sum
n i
i
eq
n i^
i
eq^
These are allthe same
z^ A battery with
stores total charge
on
two identical capacitors z a) What is
across and
on either
is same for each and equal to
of
battery. • Total charge conserved and
1
2 1
2 q q q q^
=
=^
q 2
qcap
=
2 1
q q^
=
