# Capacitance and Capacitors

Document Sample

```					                 Capaticance

2
• Capacitor

1
• Connecting capacitors
0011 0010 1010 1101 0001 0100 1011

4
• Dielectrics and capacitors
• Energy stored in a capacitor
I read ____ per cent of the text for class today.
0011 0010 1010 1101 0001 0100 1011
1.   Less than 20
2.   20 to 40
3.   40 to 60
4.   60 to 80

1
2
5.   More than 80

4
EMF or Battery
0011 0010 1010 1101 0001 0100 1011

1
2
4
EMF or Battery
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
You should do this one.
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Class Question
A wire connects the positive and
negative terminals of a battery.
0011 0010 1010 1101 0001 0100 1011
Two identical wires connect the
positive and negative terminals of
an identical battery. Rank in order,
from largest to smallest, the

1
2
currents Ia to Id at points a to d.
1.   Ia = Ib = Ic = Id

4
2.   Ia = Ib > Ic = Id
3.   Ic = Id > Ia = Ib
4.   Ic = Id > Ia > Ib
5.   Ia > Ib > Ic = Id
Class Question
A wire connects the positive and
negative terminals of a battery.
0011 0010 1010 1101 0001 0100 1011
Two identical wires connect the
positive and negative terminals of
an identical battery. Rank in order,
from largest to smallest, the

1
2
currents Ia to Id at points a to d.
1.   Ia = Ib = Ic = Id

4
2.   Ia = Ib > Ic = Id
3.   Ic = Id > Ia = Ib
4.   Ic = Id > Ia > Ib
5.   Ia > Ib > Ic = Id
Resistance
Resistivity
0011 0010 1010 1101 0001 0100 1011
 T  
1          m

       ne2 (T )

1
2
L          l
A                          R
A

4
J  E
Resistivity
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
R
l
A

4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
V  IR

4
Class Question
Resistance is
0011 0010 1010 1101 AL 0100 1011
1. R  0001
A
2.   R
L
L
3.   R

1
2
A
A
4.   R
L

4
5. None of the above
Class Question
Resistance is
0011 0010 1010 1101 AL 0100 1011
1. R  0001
A
2.   R
L
ρL
3.   R

1
2
Α
A
4.   R
L

4
5. None of the above
Capacitance and Capacitors
Capacitors are used everywhere!
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
Even in the life sciences!
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011
Q
C
V

1
2
4
Capacitance and Capacitors
Parallel Plate Capacitor
0011 0010 1010 1101 0001 0100 1011
• First we would like to
calculate the capacitance for a
parallel plate capacitor. You
will recall that a capacitor is

1
2
formed with two conducting
plates, each with area A and       +Q.A
separated by a distance d,

4
small compared to plate size.
The two plate have equal
charge but with opposite          -Q
signs.
Capacitance and Capacitors
• Write the capacitance for a parallel plate capacitor.
0011 0010 1010 1101 0001 0100 1011
0 A
C   
d
• Now let’s derive this from the definition for capacitance.

1
2
What is the definition?
Q
C

4
V
• The electric field is constant in magnitude and direction
between the plates and the magnitude is
     Q
E  
0 0 A
Capacitance and Capacitors
• Write 1101 0001 0100 1011
0011 0010 1010 the general relationship (an integral) that allows you to
calculate the potential difference from the electric field.
 
V  V                 E  dl
path AB

1
2
• The electric field between the plates is constant in magnitude
and direction. Write the relationship for potential again for a
constant electric field.

4
 
V             E  dl   E             dl
path AB                  path A B

  Ed  Ed
Capacitance and Capacitors
• Finally, use the definition for capacitance and substitute in
the potential difference you just found.
0011 0010 1010 1101 0001 0100 1011

Q A A  0 A
C      
V  Ed       d

1
2
d
0

4
Capacitance and Capacitors
• The flash on your camera uses a capacitor to store the
0011 0010 1010 1101 0001 0100 1011
energy for the flash. If the voltage across the capacitor is 9
volts (from a battery) and the capacitance is 5,000 mF,
what is the charge on the plates?
Q
C   Q  CV  5,000 mF9V
V
 45mC
1
2
4
1    1
U  QV  0.045C 9V  2.0mJ
2    2
Capacitance and Capacitors
• The capacitance for a coaxial cable       electric field lines
0011 0010 1010 1101 0001 0100 1011

Q                                             E
C
V
Q  L                                       +Q

1
2
                              -Q
V           E  dl 
path AB

4
               b dr    
lnb  a 
b
       r  rdr 
ˆ ˆ              
a 2 r           2 0 a r 2 0
0

Q                   L      2 0 L
C                        
V             
lnb a    lnb a 
2 0
Capacitance and Capacitors
Energy Stored in Capacitors
0011 0010 1010 1101 0001 0100 1011
• One definition of a capacitor is a device that will store
electrical energy. Write the expression for the energy that is
in a capacitor in terms of the charge Q and the capacitance C.
1     1 Q2

1
2
U  QV 
2     2C
• Use the definition of capacitance to change the expression for

4
the energy to one in terms of voltage V and capacitance C.
1    1
U  QV  CV 2
2    2
Capacitance and Capacitors
• A parallel plate capacitor made from two metal pie pans (10
inches in diameter) places 2 mm apart is charged to 100
0011 0010 1010 1101 0001 0100 1011

volts. What is the electrical energy stored in the two pie
pans? Discuss this problem in your group before you work
the problem.

1
2
First find C.
Use parallel plate

4
A  r  3.14(2.45cm10in)  0.19m2
2

0 A
 8.85 X 10         C 2 Nm 2 0.19m 2 
12
C                                                     8.7 X 1010 F
d                            2mm
1    1
U  CV  (45mC)(100V )2  2.8mJ
2

2    2
Capacitance and Capacitors
Capacitors in parallel
0011 0010 1010 1101 0001 0100 1011

1
2
4
C  C1  C2  C3  
Capacitance and Capacitors
Capacitors in series
0011 0010 1010 1101 0001 0100 1011

1
2
1 1 1 1
    
C C1 C2 C3    4
Capacitance and Capacitors
A problem
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
• Discuss the circuit in your group. Where should you start?
Which capacitors are in series or parallel?
0011 0010 1010 1101 0001 0100 1011

C1 = 3.0 mF, C2 = 2.0 mF, C3 = 1.0 mF, C4 = 6.0 mF, and
C5 = 4.0 mF,
C1

1
2
A
C4

4
C5
C2       C
3

B

Capacitance and Capacitors
0011 0010 1010 110140001 0100 1011            C1
• C4 and C5 are in series.           A
1/C45 = 1/C4 +1/C5                                       C4

= 1/6.0 + 1/4.0 = 2/12 + 3/12                      C5
C2       C

1
2
C45 = 12/5 mF
3

B
• Now look at C2, C3, C45.               C1

• C2, C3, and C45 are in parallel. A
– C’ = C2 + C3 + C45
– = 2.0 + 1.0 +12/5 = 5 2/5 mF
• FinallyC1 and C’ are in series. B
1/C = 1/C4,5 +1/C1
C2

4
C
3       C
4,5
Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011

1
2
4
Capacitance and Capacitors
Capacitors and Dielectrics
0011 0010 1010 1101 0001 0100 1011
• When a dielectric in placed between the plates of a
capacitor the capacitance increases. What is the
relationship between the capacitance with the dielectric, C,
to the capacitance without the dielectric, C0?

1
2

C  C0  C0
0

4
• What is the capacitance for a
parallel plate capacitor with a
dielectric?
A  0 A
C        
d       d
Capacitance and Capacitors
• Capacitors and Dielectrics
0011 0010 1010 1101 0001 0100 1011

C  C0  C0
0

1
2
4
Capacitance and Capacitors
0011 0010 1010 1101plate capacitor with
• A parallel 0001 0100 1011      a capacitance 3.0 mF (for air
in between) has Teflon placed between the plates. What is
the capacitance with the Teflon?

C = 0A/d = C0 = 2.1*3.0mF = 6.3mF

1
• The capacitor above is connected to a 10 volt supply
without the dielectric. What is the energy stored in the

2
4
capacitor?

U = 1/2CV2 = ½ (3.0mF)(10V)2 = 0.15mJ
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Student Workbook
0011 0010 1010 1101 0001 0100 1011

1
2
4
Class Question
0011 0010 1010 1101 0001 0100 1011

1
2
Rank in order, from largest to smallest, the equivalent
capacitance (Ceq)a to (Ceq)d of circuits a to d.

4
1. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
2. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
3. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
4. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
5. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
Class Question
0011 0010 1010 1101 0001 0100 1011

1
2
Rank in order, from largest to smallest, the equivalent
capacitance (Ceq)a to (Ceq)d of circuits a to d.

4
1. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
2. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
3. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
4. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
5. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 4 posted: 3/11/2012 language: pages: 43