NCEA Level 3 Physics Electricity AS91526 Capacitors

1. Capacitors
Storage of charge

2. 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

3. Electronic Components
• Capacitors are
electronic components
that store charge
efficiently
• They can be charged
and discharged very
quickly and hold their
charge indefinitely
• Symbol

4. 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

5. 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

6. 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)
Q
• 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
C 
Where;
C=Capacitance in Farads (F)
Q=Charge in Coulombs (C)
V=Voltage in Volts(V)

7. Exercises
1. Calculate the capacitance of a capacitor
that stores 1.584  10-9 C at 7.2V
220 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

8. Capacitance (C)
Three factors determine
capacitance;
1. The area of the plates
(CA)
2. The distance separating
the plates
1
(C  )
d
3. The properties of the
dielectric (εr)
so
C= constant x
A
d

9. Capacitor Construction Formula
• 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;
A
C 0 

d

10. Exercises
C 0 
Using the absolute permittivity of free space
(ε0 = 8.84  10-12 Fm-1)
A
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


11. Capacitor Construction Formula
• 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
dielectic r air C  C
C r o  

d
A
Note that εr has no units as
dielectric
air
C
 
r C
Insulator εr
Air 1
Polystyrene 2.5
Glass 6.0
Water 80

12. 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

13. 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
A
C r o  
 (ε0 = 8.84 x 10-12 Fm-
1)

14. Networks of Capacitors
Capacitors in Parallel
• For two or more
capacitors in parallel the
capacitance is
1 2... C C C parallel  
• Each capacitor has the
same voltage
charging it so;
The more capacitors in parallel circuit the greater
the capacitance of the circuit

15. Capacitors in Series
• Capacitors share the supply
voltage
• The inner plates are an
isolated circuit where the
existing charges are just
rearranged
so;
...
1 1 1
 
1 2 C C C series
The more capacitors in series the less the total
capacitance of the circuit

16. 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)

17. 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;
1

E QV P
2
Q
V
Energy Produced by a Cell
Energy Stored by a Capacitor
Q
V

18. Energy Stored in Capacitors
1

• Energy of a capacitor can also be given by;
(because Q=CV)
or
Q
(because )
E QV P
2
1

2 E CV P
2
Q
C
EP
2
1

2
C
V 
Energy is stored as electrical charge on the plates of a
capacitor

19. Exercises
1

E CV 2 P
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 18V
11 μF
3. Calculate the voltage require to store 0.1J
of energy on a 1000μF capacitor
200V
2

20. 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)
Current
Time
Voltage
Supply voltage
Time
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the charge

21. Charging and Discharging Capacitors
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
Current
Time
Voltage
Time
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the discharge

22. 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:
  RC
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

23. 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
RC t
63.5
%
V
t
RC
37.
5%
C
For Decay V 
V e
when t V V e
1
1
C
t
C
 

as e 
 0.37, V  0.37 
V


 ,
, ( )
C
For growth V  V 1 
e
when t V V 1 e
1
1
  
C
t
C
as e 
 0.37, V  0.63 
V


( )



24. Examples
1. Calculate the time constant for 330μF
capacitor in a 20 charging circuit
6.6  10-3s
2. Calculate the time constant for 330μF
capacitor in a 15 discharging circuit
5.0  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

25. Exercises
• Try ESA, Activity 14A,B,C, Pg 224
• ABA, Pg 139-153