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Physics
Capacitors
Capacitors
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Cards (21)
What is a
capacitor
?
A component used to store
electrical charge
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How does a
capacitor
work?
There are two conductive metal plates connected to a voltage supply with a
dielectric
between them. Charge builds up on the two plates creating a
potential difference
between them.
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What is the equation for
Capacitance
, C
C =
Q
/
V
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What is the unit of
Capacitance
?
Farad
(F)
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What is the
equation
for energy in a
capacitor
?
E =
1/2
QV
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What are the alternate equations for energy in a
capacitor
?
E = 1/2 C V^2 and E = Q^2 / 2C
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How is total
Capacitance
in
series
calculated?
1/Ct
=
1/C1
+
1/C2
....
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How is
total Capacitance
in parallel
calculated
?
Ct
= C1 + C2 ....
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How does current change when a
capacitor
is charging?
The current decreases
exponentially
to zero
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How does
voltage
change when a
capacitor
is charging?
The voltage increases to a maximum
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How does current change when a
capacitor
discharges?
The current decreases
exponentially
to zero
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How does
potential difference
change when a capacitor discharges?
The potential difference decreases to zero by
exponential decay
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What is a
capacitor
used for?
Charge is stored creating a build-up of
electrical potential energy
which is used for a backup release of energy if the power fails.
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What is the
time constant
,
τ
?
The time constant τ is the time taken for the current, charge stored, or p.d. to fall to
1/e
(about
37%
) of its initial value.
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What is the equation for the
time constant
?
τ
= RC
Time constant =
Resistance
x
Capacitance
.
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What is the general
equation
for
capacitors
discharging
?
x = x₀(1 - e^(-t/
CR
))
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Proof that
total capacitance
in
parallel
is the sum of capacitance of
individual capacitors
- Total
charge stored
,
Q
is equal to the sum of individual charges (Qt = Q1 +Q2 + Q3).
-
P.d.
across each capacitor is the same as they are in parallel V1 = V2 = V3
-
C
= Q/V -> Q = CV therefore:
VCt
= VC1 + VC2 + VC3....
V cancels out leaving Ct = C1 + C2 + C3...
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Proof of the result for
total capacitance
in
series
-
Kirchhoff's second law
:
Vt = V1 + V2 + V3
-
charge
stored by each capacitor is the same
Q = Q1 = Q2
- C = Q/V -> V = Q/C
-
Q/Ct
= Q/C1 + Q/C2 ....
Q cancels leaving
1/Ct
=
1/C1
+
1/C2
....
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How is energy stored in a
capacitor
?
- Work must be done to push
electrons
onto the negative plate
- Work must also be done to pull electrons from the
positive
plate
- This work is stored as energy in the capacitor
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Plotting a graph of V against Q, what is the area under the graph?
Electrical potential energy
as area =
1/2
QV
= E
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What are the main uses of
capacitors
?
- capacitors can be used to smooth
output voltage
when arranged in a certain way
- capacitors are used in
mobile phone screens
to detect touch
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