Transcript ch25webct.ppt

Chapter 25
Capacitance
In this chapter we will cover the following topics:
-Capacitance C of a system of two isolated conductors.
-Calculation of the capacitance for some simple geometries.
-Methods of connecting capacitors (in series, in parallel).
-Equivalent capacitance.
-Energy stored in a capacitor.
-Behavior of an insulator (a.k.a. dielectric) when placed in the
electric field created in the space between the plates of a capacitor.
-Gauss’ law in the presence of dielectrics.
(25-1)
Checkpoint 1:
Does the capacitance C of a capacitor increase, decrease, or remain
the same
a) When the charge q on it is doubled and
b) When the potential difference V across it is tripled?
q
C
V
The capacitance of the capacitor depends only on the geometry of
the plates and not on their charge or potential difference.
Checkpoint 2:
For capacitors charged by the same battery, does the charge stored by the
capacitor increase, decrease, or remain the same in each of the following
situations?
a) The plate separation of a parallel-plate capacitor is increased.
b) The radius of the inner cylinder of a cylindrical capacitor is increased
c) The radius of the outer spherical shell of a spherical capacitor is increased
Ceq  C1  C2  C3
Capacitors in Parallel
In fig. a we show three capacitors
connected in parallel. This means that
the plate of each capacitor is connected
to the terminals of a battery of voltage V .
We will substitute the parallel combination
of fig. a with a single equivalent capacitor
shown in fig. b, which is also connected
to an identical battery.
The three capacitors have the same potential difference V across their plates.
The charge on C1 is q1  C1V . The charge on C2 is q2  C2V .
The charge on C3 is q3  C3V . The net charge q  q1  q2  q3   C1  C2  C3  V .
q  C1  C2  C3 V

 C1  C2  C3 .
V
V
For a parallel combination of n capacitors it is given by the expression:
The equivalent capacitance Ceq 
n
Ceq  C1  C2  ...  Cn   C j
j 1
(25-10)
Capacitors in Series
In fig. a we show three capacitors connected in series.
This means that one capacitor is connected after the other.
The combination is connected to the terminals of a battery
of voltage V . We will substitute the series combination
of fig. a with a single equivalent capacitor shown in fig. b,
which is also connected to an identical battery.
The three capacitors have the same charge q on their plates.
The voltage across C1 is V1  q / C1.
The voltage across C2 is V2  q / C2 .
The voltage across C3 is V3  q / C3 .
The net voltage across the combination V  V1  V2  V3 .
(25-11)
 1
1
1 
Thus we have: V  q  
 .
 C1 C2 C3 
q
The equivalent capacitance Ceq  
V
1
1
1
1
 

Ceq C1 C2 C3
q

 1
1
1 
q 
 
 C1 C2 C3 
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Example 6:
Example 7:
Example 8:
Example 9: