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CAPACITORS
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A capacitor is a device used to “store” electric charge.
It can store energy and release it very quickly!!
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Some hybrid buses uses capacitors instead of batteries
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So do some other new vehicles
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Kinetic torches store energy in a capacitor
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Speakers use capacitors to direct current to the correct
speaker
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What determines the amount of air you can squeeze in a
bottle?
More pressure
More volume
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What affects the amount of charge in a capacitor?
More voltage
More capacitance
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A resistor is an object.Its resistance is how much it opposes
the flow of charge. (measured in Ω)
A capacitor is an object. Its capacitance is how much charge it
can store. (measured in Farads (F))
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Charge stored = Capacitance x Voltage
Q = C x V
A 1 Farad capacitor will store one Coulomb of charge if connected to a one Volt cell.
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Pumping Air Into a Bottle
pressure
time time
Air flow
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Charging a Capacitor
What happens when the switch is closed?
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Charging a Capacitor
voltage
time time
current
batteryvoltage
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electron flow
electron flow
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time
Battery voltage
voltage
0.63 Vmax
1 time constant
0.37 Vmax
max
t
RCV V e
max
1
2.71878V V
max 0.37V V
When t = RC
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time
Battery voltage
voltage
0.63 Vmax
1 time constant
0.37 Vmax
2 time constants
0.37 x 0.37 Vmax
2 time constants
3 time constants
0.37 x 0.37 x 0.37 Vmax
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Time Constant
A measure of the time to charge a capacitor is called the time constant.
It is the time taken to rise to 63% of the maximum voltage…
…… ordrop to 37% of the maximum voltage or
drop 63% of the maximum voltage.
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time
Vmax
voltage
0.63 Vmax
1 τ 2τ 3 τ
0.372 Vmax
0.37 Vmax{ {0.373 Vmax {
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Which capacitor charges faster?
Which circuit has the bigger time constant?
Which capacitor has the bigger capacitance?
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Do Now
The time constant for a capacitor charging circuit is 2.0 s. Find out:The time taken for the voltage of the capacitor to reach 50% and 99% of its maximum respectively.
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Ans.
9.3s 2.063.4t
4.63 log0.37
log0.01n
log0.01 nlog0.37
0.010.37
charged be to1% is There (1)
1.4s 2.00.70t
0.70 log0.37
log0.5n
log0.5 nlog0.37
0.50.37
charged be to(0.5) 50% be willThere
requiredconstant timeofnumber theben Let (1)
n
n
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How and why do R and C affect the time constant
τ is directly proportional to R and C.
If R increases, the current to charge/discharge the capacitor decreases. It will take longer time to charge/discharge a capacitor to/from the maximum voltage.
If C increases, it needs more charge to charge/discharge the capacitor, as Q =CV. It will take longer time to charge/discharge a capacitor to/from the same voltage.
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Do Now: Calculate time constant:
(1) R=2.26MΩ, C=100μF(2) R=3.2kΩ, C=10000μF(3) R=1.1MΩ, C=100μF(4) R=1.02MΩ, C=100μF(5) R=132kΩ, C=1000μF(6) R=65kΩ, C=1000μF
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Battery voltage
Capacitor voltage
Electron flow continues until the capacitor voltage is equal (and opposite) to battery voltage
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VB
What is the relationship between VB VC and
VR
VC
VR
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VB
VB = VC + VR
VC
VR
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As the capacitor charges, what happens to VB ?
VB
VC
VR
As the capacitor charges, what happens to VC ?
As the capacitor charges, what happens to VR ?
VB VC VR
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Charging CurvesWhich curve represents charging voltage of the capacitor and which the resistor?
voltage
time
Vmax
VB
VC
VR
VC
VR
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Discharging a Capacitor
What happens when the switch is closed?
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VC
VR
As the capacitor discharges, what happens to VC ?
As the capacitor discharges, what happens to VR ?
Vmax VC VR
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Discharging CurvesWhich curve represents discharging voltage of the capacitor and which the resistor?
voltage
time
Vmax
VC
VR
VCVR
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VB
QTOT = C x V
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V
Capacitors in parallel
C2
C1 Q1
Q2
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VCapacitors in parallel have the same voltage
QTOT = Q1 + Q2
CTOT V= C1V + C2V
CTOT = C1 + C2
Q1
Q2
VB = VC1 = VC2
Capacitors in parallel store more charge
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V
Capacitors in Series
V1 V2
C1 C2
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V
V = V1 + V2
Total capacitance is less than any of individual’s
Capacitors in series have the same charge, total voltage is the sum of individuals’.
V1 V2
C1 C2
Q = Q1 = Q2
C
QV
2
2
1
1
C
Q
C
Q
C
Q
21 C
1
C
1
C
1
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Connecting capacitors:
A capacitor is connected to a battery.
VB
QTOT = C x V
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The battery is disconnected.• What happens to the charge on the
capacitor?
QTOT = C x V
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The capacitor is connected to an uncharged capacitor. What happens?
QTOT = C x V
elecrons elecrons
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Closed loop so charge redistributes until the capacitors have the same voltage
QTOT = C x V
V1=V2
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Capacitor Construction
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The Capacitance depends on:
• The Area of the plates• The separation of the
plates.
d
AC
d
AC o
εo is absolute permittivity of free space (vacuum or air)εo =8.84x10-12 F m-1
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eg. Find the area needed to construct a 1 F capacitor using two parallel plates of 1 mm apart in air.
It is an area of 10000m x 10000m
d
AC o
2812
101.11084.8
001.01m
CdA
o
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DielectricPutting an insulator between the plates increases the capacitance
εr is called dielectric constant, dimensionless.
o
dr C
C
d
ACC orord
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What does a dielectric do??
-------
+++++++
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Dielectric becomes polarised
-------
+++++++
++++
- ----
The charges of the polarised dielectric attract more charges to the plates. Since the voltage does not change, the capacitance increases.
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More charge can be stored.Capacitance increases
-------
+++++++
++++
- ----
More elecrons
More elecrons
-
-
-
--
+++++++
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Capacitors
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Ceramic capacitor
Electrolytic capacitor
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When the capacitor is fully charged:•The flow of electrons stops;•Both plates have equal and opposite amount of charge;•The potential difference across the plates equals the supply voltage;•An electric field exists between the plates;•The strength of the electric field between the plates:
d
VE
eg. A two parallel plate capacitor of 1mm apart is connected to a 12V battery. The electric field strength between the plates is:E=12/0.001 =12000Vm-1
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Energy stored in a capacitor
When a capacitor is charged, it gains energy from the power source. The energy is stored as electric potential energy. When the capacitor is discharged, the potential energy is dissipated in the resistance of the circuit as heat and light.
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When a capacitor is charged to voltage V, with charge Q, the energy provided by the power =QV.
Voltage of Capacitor V
Q Charge
The electric potential energy stored by the capacitor
C
Q
CV
QVEp
2
2
2
1
2
12
1
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• A capacitor is labelled:100 V 200 μF
What does this mean?
How much charge can it store?
How much energy can it store?
JCVEp 0.1100102002
1
2
1 262
CCVQ 020.010010200 6