Two Identical Light Bulbs in Series
i = nAuE = nAu
Lecture 16
ΔV
L
Chapter 20. Capacitors, Resistors and Batteries
Two identical light bulbs in
series are the same as one
light bulb with twice as long
a filament.
Identical light bulbs
i2 L >
1
iL
2
Electron mobility in metals decreases as temperature increases!
Conversely, electron mobility in metals increases as temperature
decreases. Thus, the current in the 2-bulb circuit is slightly
more than that in the one-bulb circuit.
Capacitor: Construction and Symbols
The capacitor in
your set is similar to
a large
two-disk capacitor
Announcement:
There will be no lectures on Monday March 28 and
Wednesday March 30, 2011 to compensate for the two
evening exams:
Exam #1 that took place on Feb 15th, 2011
Exam #2 that will take place on March 30st, 2010.
Capacitor: Charging and Discharging
D
Experiment 1
Experiment 2
s
There is no connecting path through a
capacitor
1
Capacitor: Charging
Capacitor: Discharge
Electron current
Fringe field of a capacitor rises until E=0 in a wire – static
equilibrium. Fringe field opposes the flow of current!
The Effect of Different Light Bulbs
Thin filament
Thick filament
Which light bulb will glow longer?
Effect of the Capacitor Disk Size
Use two different
capacitors in the same
circuit
In the first moment, which capacitor will cause
the bulb to produce more light?
Which capacitor will make the light bulb glow
longer?
Fringe field: E1 ≈
Q/ A s
2ε 0 R
2
Effect of the Capacitor Disk Separation
Parallel Capacitors
Initial moment: brighter?
Will it glow longer?
In the first moment, which capacitor will cause
the bulb to produce more light?
Fringe field: E1 ≈
Which capacitor will make the light bulb glow longer?
Fringe field: E1 ≈
Q/ A s
2ε 0 R
An Isolated Light Bulb
Q/ A s
2ε 0 R
Capacitors in parallel effectively increase A
Circuits with Capacitors
Experiments:
Will it glow at all?
How do electrons flow through
the bulb?
Charging
Discharging
Why do we show charges near
bulb as - on the left and + on
the right?
Isolated light bulb
Two parallel capacitors
3
Capacitor in a Circuit
I
The Current Node Rule in a Capacitor Circuit
Charging
Charge conservation:
I > 0 for incoming
∑i I i = 0 Iii < 0 for outgoing
time
Bulb
Brightness
I1 = I2+ I3
time
Energy conservation
…in steady state
Capacitor transients:
not a steady state!
Cannot use Kirchhoff rule for a
part of a capacitor (area 1 or 2)
Do 19.X.7!
Ecap
But can use for capacitor as a
whole (area 3)
time
Capacitance
Exercise
-Q
Electric field in a capacitor:E =
+Q
Q/ A
ε0
 
ΔV = − ∫ E • dl
f
i
E
The capacitor in
your set is
equivalent to a large
two-disk capacitor
How large would it be?
Definition of capacitance:
D
s=1 mm
s
Capacitance of a
parallel-plate capacitor:
4
A Capacitor With an Insulator Between the
Plates
No insulator:
Q/ A
E=
ε0
ΔV = Es
With insulator:
E=
Q/ A
Kε 0
D
ΔV = Es
s
5