capacitors
DESCRIPTION
NCEA Level 3 Physics Electricity AS91526 CapacitorsTRANSCRIPT
CapacitorsStorage of charge
Introduction
• Read Chapter 14 in ESA and then;
– Write a brief description of what a capacitor is
and what it does, make sure you mention
dielectric
– Describe the maths; capacitance, units,
capacitor formula
– Explain how capacitors behave in DC circuits
in series and parallel
Electronic Components
• Capacitors are electronic components that store charge efficiently
• They can be charged and discharged very quickly and hold their charge indefinitely
• Symbol
The structure of the capacitor
• Capacitors are made
from two parallel
metal plates
separated by an
insulator called a
dielectric
• In practice they
appear a little more
complex
Charging a Capacitor
• In a circuit the capacitor plate closest to the negative terminal of the battery or power supply is “stacked” with electrons (negative charges)
• The opposite plate becomes positively charged
• There is no movement of charge between the plates as they are insulated by the dielectric
Capacitance (symbol C)
• Capacitance is the amount of charge a capacitor can
store when connected across a potential difference of
1V (the larger the capacitance the more charge it can store)
• Units of capacitance are Farads (symbol F)
• 1 Farad = 1 coulomb per volt This is a lot of charge!!
• most capacitors are small;
µF (1 x 10-6 F)
nF (1 x 10-9 F)
pF (1 x 10-12 F)
V
QC
Where;
C=Capacitance in Farads (F)
Q=Charge in Coulombs (C)
V=Voltage in Volts(V)
Exercises
1. Calculate the capacitance of a capacitor
that stores 1.584 10-9 C at 7.2V220 μF
2. A 330μF capacitor is charged by a 9.0V
battery. How much charge will it store?2.97 10-3 C
3. A 0.1μF capacitor stores 1.5 10-7 C of
the charge. What was the voltage used to
charge it?1.5V
Capacitance (C)
Three factors determine
capacitance;
1. The area of the plates
(CA)
2. The distance separating
the plates
(C )
3. The properties of the
dielectric (εr)
so
C= constant x
d
1
d
A
• If there is air or a vacuum between the plates the
constant is;
the absolute permittivity of free space (symbol ε0)
(ε0 = 8.84 x 10-12 Fm-1)
so;
d
AC 0
Capacitor Construction Formula
Exercises
Using the absolute permittivity of free space (ε0 = 8.84 10-12 Fm-1)
1. Calculate the capacitance of a capacitor that has a plate separation of 15 microns (μm) and measures 45cm by 28cm.
74nF
2. A 1000 μF has an area of 2cm by 4.8m. What is the distance between the plates in mm?
8.48 10-7mm
3. A 0.3 μF capacitor with a plate separation of 2 microns. What is the area of the capacitor?
0.68m2
d
AC 0
• When an insulator (dielectric) is placed between
the plates the capacitance increases
• The dielectric constant (symbol εr) gives the
proportion by which the capacitance will increase so;
and therefore
Note that εr has no units as
d
AC or
airrdielecticCC
air
dielectric
r
C
C
Insulator εr
Air 1
Polystyrene 2.5
Glass 6.0
Water 80
Capacitor Construction Formula
The Role of the Dielectric
• Charge separation in a
parallel-plate capacitor
causes an internal
electric field. A
dielectric (orange)
increases the field
strength and increases
the capacitance
Examples
1. Calculate the capacitance of a capacitor with a polystyrene dielectric (εr =2.5), an area of 1.2cm by 3.2m and a plate separation of 8 microns
1.06 10-7 F
2. Calculate the plate area required for a 1000 μF, glass (εr=6.0) capacitor, with a plate separation of 2.8 micrometres.
53m2
3. Calculate the dielectic constant of a 10000 μF capacitor with a 1.2μm plate separation and an area of 16.97m2
80
d
AC or
(ε0 = 8.84 x 10-12 Fm-
1)
Networks of Capacitors
• For two or more capacitors in parallel the capacitance is
• Each capacitor has the same voltagecharging it so;
...21 CCC parallel
Capacitors in Parallel
The more capacitors in parallel circuit the greater the capacitance of the circuit
Capacitors in Series
• Capacitors share the supply
voltage
• The inner plates are an
isolated circuit where the
existing charges are just
rearranged
so;
...111
21 CCCseries
The more capacitors in series the less the total
capacitance of the circuit
Examples
1. A circuit has three 330 μF capacitors in series. Calculate the total capacitance of the circuit 110 μF
2. Another circuit has three 330 μF capacitors in parallel. Calculate the total capacitance of the circuit. 990 μF
3. Briefly explain why these two circuits have a different total capacitance. The parallel capacitors are each charged separately while the series capacitors charge through one another, effectively just rearranging the charges within each capacitor (the electric field is weakened by the addition of each capacitor in series)
Energy Stored in Capacitors• The graph of voltage
against charge for a cell is
a horizontal line
– The energy provided by
the cell is equal to the
area under the line
• The graph of voltage
against charge is a straight
line through (0, 0)
– The energy stored in a
capacitor is;
QVEP
2
1
Q
V
Energy Produced by a Cell
Energy Stored by a Capacitor
Q
V
Energy Stored in Capacitors
• Energy of a capacitor can also be given by;
(because Q=CV)
or
(because )
QVEP
2
1
2CVEP
2
1
C
QE
P
2
2
1
C
QV
Energy is stored as electrical charge on the plates of a
capacitor
Exercises
1. Calculate the energy stored in a 330μF
capacitor charged by a 24V supply.0.095J
2. Calculate the capacitance of a capacitor
that stores 1.8 10-3 J of energy at 18V11 μF
3. Calculate the voltage require to store 0.1J
of energy on a 1000μF capacitor200V
2CVEP
2
1
Charging and Discharging Capacitors
1. Charging a Capacitor
• As a capacitor charges
the voltage increases to
the supply voltage(exponential growth curve)
• and the current
decreases as the plates
become “full” of charge (exponential decay curve)
Curr
ent
TimeV
olt
age Supply voltage
Time
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the charge
2. Discharging a Capacitor
• The voltage across the plates of the capacitor drops as the charges flow away from the plate
• The current decreases as there are fewer charges on the plates repelling each other
Cu
rren
tTime
Volt
age
Time
Charging and Discharging Capacitors
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the discharge
Time Constant ( )
• The time constant ( )is a measure of how
quickly a capacitor charges or discharges– This will depend on:
• The resistance (R) of the circuit (how much current
flows)
• The capacitance (C) of the capacitor (how much
charge is stored)
so:
NB; one time constant is not the total time to charge or
discharge but the time to discharge to 37.5% or to charge to
63.5% of the total
RC
Time Constant ( )
• One time constant is not the total
time to charge or discharge but the
time to discharge to 37.5% or to
charge to 63.5% of the total
• Experts; this is because of the exponential nature of the charge/discharge curves
V
tRC
63.5
%
V
tRC
37.
5%
C
1
1
C
t
C
V0.37V0.37,eas
eVVtwhen
eVVDecayFor
,
C
1
1
C
t
C
V0.63V0.37,eas
e1VVtwhen
e1VVgrowthFor
)(
)(,
Examples
1. Calculate the time constant for 330μF
capacitor in a 20 charging circuit6.6 10-3s
2. Calculate the time constant for 330μF
capacitor in a 15 discharging circuit5.0 10-3s
3. Calculate the amount of charge on each
of the capacitors in 1 and 2 after 1 time
constant when charged from 12V supply.1 = 2.5 10-3C, 2=1.5 10-3C
Exercises
• Try ESA, Activity 14A,B,C, Pg 224
• ABA, Pg 139-153