Transcript Capacitors in Circuits - McMaster Physics & Astronomy Outreach

Capacitance (II)
•Capacitors in circuits
•Electrostatic potential energy
Capacitors in Circuits
Symbols:
Capacitor 
Battery 
Switch 
-
+
or
-
+
Capacitor Combinations
Parallel
Series
A
B
A
B
What is the “effective capacitance” between A & B?
A
+Q
-Q
charge held
Ceff 
voltage difference
B
Parallel
A
V
C1
Q1
-Q1
C2
B
Q2
-Q2
C3
Q3
-Q3
Voltages are the same: V1 = V2 = V3 = … = V
Charges add:
Q1  Q2  Q3  ...  Q
Q  Q  ......
C 
V
1
2
eff
But… Q1  C1V , Q2  C2V , ...
 Ceff  C1  C2  ...
Series
A
+Q -Q
+Q -Q
+Q -Q
C2
C1
B
C3
Voltages add: V1 V2  ... V
Charges are equal: Q1  Q2  Q3  Q
And …
1 V  V  ...

, but
C
Q
1
V 1
 , ....
Q C
2
1
eff

1
C eff

1
C1

1
C2

1
1
C3
 ...
Example
Find the equivalent capacitance between a and b.
1uF
4uF
a
6uF
b
3uF
8uF
2uF
Solution
Example
Find the equivalent capacitance between points a and b in
the combination of capacitors shown below
Example
Consider the circuit shown below, where C1 = 6.00 μF, C2 = 3.00 μF,
and ΔV = 20.0 V. Capacitor C1 is first charged by the closing of
switch S1. Switch S1 is then opened, and the charged capacitor is
connected to the uncharged capacitor by the closing of S2.
Calculate the initial charge acquired by C1 and the final charge on
each capacitor.
Solution
Quiz
How does the potential
difference Vab between
a and b compare to the
potential difference Vbc
between b and c?
A) Vab  Vbc
B) Vab > Vbc
C) Vab < Vbc
a
6 V
5 mF
b
10 mF
c
Energy Stored in a Capacitor
dq
+q
-q
Increase in P.E.,
Remove dq from lower plate
and add to upper plate:
dU  Vdq 
q
dq
C
Q
Start at q = 0, finish at q = Q:
q dq Q 2
U 

C
2C
0
1Q 2 1
1
 U 
 QV  CV
2 C
2
2
2
Example
What is the energy stored in a parallel-plate capacitor,
in terms of the plates’ area and separation?
Area A
s
+Q
-Q
Example
Calculate the energy stored in a 18μF capacitor when it
is charged to a potential of 100V.
Example
Three capacitors of 8μF,10μF and 14μF are connected
to the terminals of a 12-volt battery. How much energy
does the battery supply if the capacitors are connected
a) In series
b) In parallel
Quiz
Conducting spheres and a long wire:
r1  10cm
r2  30cm
A total charge +12 μC is placed on one sphere. The
charge will move to the other sphere until
A) the electric fields on the spheres are equal
B) the electric potentials on the spheres are equal
C) the electric charges on the spheres are equal