l9 ch29 su15
TRANSCRIPT
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html
Lecture 9
Chapter 29
Capacitors and more
07.17.2015Physics II
95.144
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
The Geometry of Potential and Field
Which set of equipotential surfaces matches this electric field?
A)
B)
C)
ConcepTest 1 El. Potential/Area
D)
E)
F)
E
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Potential of a Conductor
i
f
sdEVVVf
iif
0V if VV
A conductor in electrostatic equilibrium is at the same potential.
constV
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
The Electric Battery
A battery transforms chemical energy into electrical energy.
Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them.
Atom of Zn gets dissolved leaving two electrons behind
Two electrons get attracted by the ion of Zn leaving behind positively charged electrode
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Capacitor
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Capacitor stores energy
You can store potential energy by pulling a bow, stretching a spring, etc.
A capacitor is a system that stores potential energy in a form of an electric field.
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Capacitance (definition)
The ratio of the charge Q to the potential difference VC is called the capacitance C:
The SI unit of capacitance is the farad:
≝
VC
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Parallel-plate capacitor
In its simplest form, a capacitor consists of a pair of parallel metal plates separated by air/insulating material.
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Parallel-plate capacitorLet’s find capacitance of a parallel-plate capacitor
Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing.
≝
E
d
Aarea
+Q–Q
The electric field between the plates is ‐ surface
charge density
(Eq.28.26)The potential difference between plates:
We need to find Q and ΔV:
≝ =
This gives the capacitance:
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Parallel-plate capacitor
We can increase capacitance by increasing area A (by making “a roll of metal and insulator”
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Parallel-plate capacitor/keyboard
Capacitors are important elements in electric circuits. They come in a variety of sizes and shapes.
The keys on most computer keyboards are capacitor switches. Pressing the key pushes two capacitor plates closer together, increasing their capacitance.
What is the capacitance of these two electrodes?
A) 8 nF
B) 4 nF
C) 2 nF
D) 1 nF
E) Some other value
ConcepTest 2 Capacitance
Since the battery stays connected, the potential difference must remain constant!
+Q –Q
dAC 0
A parallel-plate capacitor initially has a voltage of 400 Vand stays connected to the battery. If the plate spacing is now doubled, what happens?
A) the voltage decreases
B) the voltage increases
C) the charge decreases
D) the charge increases
E) both voltage and charge change
ConcepTest 3 Varying Capacitance I
Follow-up: How do you increase the charge?
Since , when the spacing d is doubled, the capacitance C is halved.
And since , that means the charge must decrease.
Q = C∆V
400 V
Once the battery is disconnected, Q has to
remain constant, since no charge can flow
either to or from the battery.
A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage?
A) 100 V
B) 200 V
C) 400 V
D) 800 V
E) 1600 V
+Q –Q
dAC 0
ConcepTest 4 Varying Capacitance II
Since , when the spacing d is
doubled, the capacitance C is halved. And since , that means the voltage must double
400 VQ = CV
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
CapacitorsIn Series
and Parallel
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Combinations of Capacitors In practice, two or more capacitors are sometimes joined together. The circuit diagrams below illustrate two basic combinations:
parallel capacitors and series capacitors.
The equivalent capacitance is the capacitance of the single capacitor that can replace a set of connected capacitors without changing the operation of the circuit
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Capacitors in ParallelConsider three capacitors connected in parallel.
QRea
l cir
cuit
Equ
ival
ent c
ircu
it
ΔV
, ΔV
, ΔV
, ΔV
Q ΔV
Ceq
Capacitors in parallel have the same potential difference, ΔV
Q is a total charge drawn from the battery + +
Since ≝;;;
We have replaced 3 capacitors with a “equivalent” capacitor.
+ +
+ +
Conservation of charge
Ceq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit
Equivalent capacitance of capacitors in parallel.
=
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
+ +
Capacitors in SeriesConsider three capacitors connected in series.
QRea
l cir
cuit
Equ
ival
ent c
ircu
it
+Q
Q ΔV
Ceq
Capacitors in series have the same charge, Q.
+ +
Since ≝
Ceq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit
Equivalent capacitance of capacitors in series.
C1 C2 C3
+ -
-Q +Q -Q +Q -Q
ΔV
ΔV1 ΔV2 ΔV3
The 2 equal capacitors in series add up as inverses, giving 1/2C. These are parallel to the first one, which add up directly. Thus, the total equivalent capacitance is 3/2C.
ConcepTest 5 Equivalent Capacitor I
o
o
C CCCeq
A) Ceq = 3/2CB) Ceq = 2/3CC) Ceq = 3CD) Ceq = 1/3CE) Ceq = 1/2C
What is the equivalent capacitance,
Ceq , of the combination below?
in series
o
o In parallelC2
in series
In parallel2
32
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
What you should read
Chapter 29 (Knight)
Sections 29.4 29.5
Department of Physics and Applied Physics95.144, Summer 2015, Lecture 9
Thank youSee you tomorrow