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CIRCUIT ELEMENT: CAPACITOR
PROF SIRIPONG POTISUKPROF. SIRIPONG POTISUK
ELEC 308
Types of Circuit Elements
Two broad types of circuit elements
A ti l t bl f ti l t i Active elements - capable of generating electric energy from nonelectric energy (chemical, mechanical, nuclear, etc.)
e.g. generators, batteries, operational amplifiers
Passive elements – consume or store energy i d f h l i h i ireceived from other elements in the circuit
e.g. resistors, capacitors, inductors
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Capacitors
consists of two conducting (metal) plates separated by an insulating gapan insulating gap
Circuit symbol with reference
voltage and current assignment
Physics of the Capacitor
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Example
If the voltage of 10 V applied to the capacitor induces 25 mC charge on its plates, what is the capacitance of the mC charge on its plates, what is the capacitance of the capacitor in Farads?
Physics of the Capacitor
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The capacitance can be significantly increased by filling the gap between the plates with so-called dielectric materials.
Physics of the Capacitor
g p p
Air
+Q
Dielectric
+Q
-Q -Q
Relative Permittivity of Selected Materials
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Example
Determine the plate size of a square parallel-plate air-gap capacitor that has the capacitance of 1 F and air gap capacitor that has the capacitance of 1 F and plate spacing of 1 mm.
Example
A parallel-plate capacitor has the plate size of 500 μm × 200 μm. The plates are separated by 2 μm thick dielectric film μ p p y μwith relative permittivity εr = 10. What is the capacitance of this capacitor in Farads?
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Physics of the Capacitor
Accumulation of charges on the plates is not instantaneous → the voltage across the terminals of a capacitor cannot g pchange abruptly
Gradual rise or fall in voltage is referredto as the charging and discharging of thecapacitor
Physics of the Capacitor
The transition period known as the transient state
During transient, the amount of charge changes with time During transient, the amount of charge changes with time → a flow of electric current
As time progresses until VC = VB , charging stops and the steady state is reached with no current flow
→ Capacitor acts like an open circuit to DC voltage
Q = CV
Q = 0
Time
QC = CVC
Transient state
Steady state
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Q = 0
QC = CVC
Transient state
Steady state
VCIVB
Time
TimeTime
Electrical Characteristics
v-i characteristics:
dvdQ 1∫t
The instantaneous power delivered to the capacitor is
dtdvC
dtdQi C
C == )(1)( ∫ +=t
oc
o
tvdiC
tv τ
tddvCvvip ==
The energy stored in the capacitor is
[ ])()(21
21)( 22)(
)(
2o
tv
tv
t
t
t
t
tvtvCvCdddvvCdpw
ooo
−==== ∫∫ ττ
ττ
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Energy Stored in Capacitor
Capacitance is the circuit property that accounts for energy stored in electric fields established by the accumulated ycharge on both plates
The E field is the Coulomb force per unit charge directed from positive to negative charge and distributed as shown
Effect of Dielectric on the E field
Alignment of dipoles in the dielectric (Polarization)
→ A flow of ‘displacement’ current→ A flow of displacement current
The more dipoles the dielectric material contains, the more additional charges it induces on the capacitor plates
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Example
Calculate the amount of charge stored on a 3-pF capacitor with 20 V across it. Find also the energy stored in it.with 20 V across it. Find also the energy stored in it.
Example
The voltage across 0.5 nF capacitor changes with time as shown. What is the current through the capacitor?shown. What is the current through the capacitor?
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Example
The current as shown flows through an initially uncharged 1-mF capacitor . Calculate the voltage across it at t = 2 ms1 mF capacitor . Calculate the voltage across it at t 2 msand t = 5 ms.
Example
Obtain the energy stored in each capacitor under DC steady-state conditionssteady state conditions
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For steady-state conditions with DC sources, capacitorsbehave as open circuits.
Series Capacitance Combination
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Parallel Capacitance Combination
Example
For the circuit shown, find the voltage across each capacitor.
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Electrolytic Capacitors
High capacitance per unit volume
Only voltages of proper polarity should be applied Only voltages of proper polarity should be applied (polarized capacitors)
One plate is oxide-coated metallic aluminum or tantalum immersed in the electrolytic solution
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Ceramic Capacitors (Non-polarized)
High-voltage Capacitors
11 kV capacitors
Capacitor bank
Ultra-capacitor battery
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Variable Capacitors
Capacitance of the variable air capacitor is changed by turning the shaft at the end of the unitby turning the shaft at the end of the unit.
Semiconductor technology allows making variable capacitor without moving parts, e.g., semiconductor diode capacitance is controlled by applied voltage