physics 2112 unit 8: capacitors - college of dupage · 2020. 4. 1. · unit 8, slide 15 a circuit...
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Physics 2112
Unit 8: Capacitors
Today’s Concept:▪ Capacitors in a circuits
▪ Dielectrics
▪ Energy in capacitors
Unit 8, Slide 1
Where we are…….
Unit 8, Slide 2
What we thought…..
➢ Would like more clarification on the relationships between capacitors in the representation of a circuit.
➢ i need to see dielectric's in class, i dont get the at all
➢ need more practice with how voltage and energy and capacitance and distance and e field is all related Also, the last checkpoint section was confusing
➢ A lot of formula substitutions were used in the past two sections, which can be hard to keep track of. Can we possibly write some of the formulas on the board and keep them there so that we can see them as they're being used in substitutions?
➢ Really easy to understand the material in this prelecture
➢ its 12:38am....I'm alert....i got this guy...lets crank some of these out in class. when a dielectric is inserted between a capacitor...are they touching the capacitor or is there a very small space between them?
Electricity & Magnetism Lecture 7, Slide 3
CV
Q
Q
This “Q” really means that the battery has moved charge Q from one plate to the other,so that one plate holds +Q and the other -Q.
Simple Capacitor Circuit
CV Q = VC
Electricity & Magnetism Lecture 8, Slide 4
Direction of arrows is opposite of the direction of electron motion
Sorry. It’s historical. There is nothing I can do.
V
Q1 = C1V Q2 = C2V
C2C1
Key point: V is the same for both capacitors
Key Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2)
Ctotal = C1 + C2
Qtotal
Qtotal
Parallel Capacitor Circuit
Electricity & Magnetism Lecture 8, Slide 5
QV
Key point: Q is the same for both capacitors
Key point: Q = VCtotal = V1C1 = V2C2
1
Ctotal
1
C1
1
C2
+=
Series Capacitor Circuit
Q
Q
C1
C2
V1
V2
V
Also: V = V1 + V2 Q/Ctotal = Q/C1 + Q/C2
Electricity & Magnetism Lecture 8, Slide 6
Voltage
Charge
Capacitance
Series Parallel
Different for each capacitor.Vtotal = V1 + V2
IncreasesCeq = C1 + C2
Same for each capacitorQtotal = Q1 = Q2
Same for each capacitor.Vtotal = V1 = V2
Decreases1/Ceq = 1/C1 + 1/C2
WiringEvery electron that goes through one must go through the other
Each capacitor on a different wire.
Different for each capacitorQtotal = Q1 + Q2
C1 C2
C1
C2
Capacitor Summary
Electricity & Magnetism Lecture 9, Slide 7
Example 8.1 (Capacitors in Series)
Unit 8, Slide 8
C1 =3uF
C2 =9uF
V =12V
Given the circuit to the left:
What is Q1?
What is V1?
➢ Conceptual Idea:
➢ Plan:• Find equivalent capacitance
• Use knowledge that in series Q1 = Q2 = Qtot
• Find V using Q = CV
QCV =
Example 8.2 (Capacitors in Parallel)
Unit 8, Slide 9
C1 =3uFC2 =9uFV =12V
Given the circuit to the left:
What is Q1?
What is Q2?
➢ Conceptual Idea:
➢ Plan:• Find equivalent capacitance
• Use knowledge that in parallel V1 = V2
• Find Q using Q = CV
QCV =
Question
Which circuit has the most stored energy?
Unit 8, Slide 10
(a) (b)
A) The series circuit has more stored energy.
B) The parallel circuit has more stored energy.
C) They both have the same amount of stored energy.
CheckPoint: Three Capacitor Configurations
C
C
C
C C
Electricity & Magnetism Lecture 8, Slide 11
The three configurations shown below are constructed using identical capacitors. Which of these configurations has lowest total capacitance?
A B C
Ctotal = CCtotal = Cleft + Cright
Ctotal = C
CheckPoint: Two Capacitor Configurations
CC
C
C
C
Cleft = C/2 Cright = C/2
Electricity & Magnetism Lecture 8, Slide 12
The two configurations shown below are constructed using identical capacitors. Which of these configurations has the lowest overall capacitance?
A B
A. AB. BC. Both configurations have the same
capacitance
Ctotal
Which of the following is NOT necessarily true:A) V0 = V1
B) Ctotal > C1
C) V2 = V3
D) Q2 = Q3
E) V1 = V2 + V3
Question
Unit 8, Slide 13
C1
C2
C3
V0
V1 Q1
V2
Q2
V3 Q3
CheckPoint: Capacitor Network
Unit 8, Slide 14
A circuit consists of three unequal capacitors C1, C2, and C3 which are connected to a battery of voltage V0. The capacitance of C2 is twice that of C1. The capacitance of C3 is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3.
C1
C2
C3
V0
V1 Q1
V2
Q2
V3 Q3
Compare Q1, Q2, and Q3.A. Q1 > Q3 > Q2
B. Q1 > Q2 > Q3
C. Q1 > Q2 = Q3
D. Q1 = Q2 = Q3
E. Q1 < Q2 = Q3
CheckPoint: Capacitor Network
Unit 8, Slide 15
A circuit consists of three unequal capacitors C1, C2, and C3 which are connected to a battery of voltage V0. The capacitance of C2 is twice that of C1. The capacitance of C3 is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3.
C1
C2
C3
V0
V1
Q1
V2
Q2
V3
Q3
Compare Q1, Q2, and Q3.A. Q1 > Q3 > Q2
B. Q1 > Q2 > Q3
C. Q1 > Q2 = Q3
D. Q1 = Q2 = Q3
E. Q1 < Q2 = Q3
C) Let C1 = 3uF. The series combination of C2 and C3 = 3.6uF. Let V0 = 10V. The same
voltage flows through both branches of the parallel circuit, so we can multiply 3uF by 10V to
get 30uC, the charge through C1. The charge through C2+C3 is just (3.6uF * 10V) = 36uC.
Since those capacitors are in series, Q2 = Q3 = 18uC < 30uC..
D) In a series total Q = Q1 = Q2 = Q3 Therefore, the charges must be the same for
each part.
E) Q2 and Q3 have the same charge, which is the same as the charge of the capacitor
formed by combining them (Let this be C23). The voltage through C1 and C23 is the same,
and C23 has 6/5 of the capacitance of C1, so the charge must be greater.
Example 8.3 (Capacitor Network)
Unit 8, Slide 16
C3 =12uF
C4 =6uF
C2 =11uFC1 =3uF
C5 =9uF
V =12C
Given the circuit to the left:
What is Q1?
What is Q3?
➢ Conceptual Idea:
➢ Plan:• Break circuit down into elements that are in parrallel or in series.
• Find equivalent capacitance
• Work backwards to find DV across each one
• Fine Q using Q = CV
Find V at each capacitor and then Q .QCV =
Example 8.1 (Capacitor Network)
Unit 8, Slide 17
C3
C4
C2C1
C5
C34C2C1
C5
C1234
C5
C12345
Example 8.3 (Capacitor Network)
C3 =12uF
C4 =6uF
C2 =11uFC1 =3uF
C5 =9uF
DV =12C
What is Q1?
What is Q3?
0V
12V
12V 12V12V
0V
DV=-8V
8V 8V
10.67V
Dielectrics
Unit 8, Slide 19
C1 = k C0
Eo
ED
Same Q, smaller E (E1 = E0/k) -> smaller V
Since this means C got largerQCV =
+ + + + + + + + + + + + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Example 7.1 (Capacitor)
Unit 7, Slide 20
A flat plate capacitor has an area of
A=1cm2 and a distance between of
0.1mm. The area between the plates
is filled with a dielectric material with a
k of 4.1 What is it’s capacitance?
If connected to a battery V stays constant
If isolated then total Q stays constant
Messing with Capacitors
C1 = k C
V1 = V
C1 = k C
Q1 = Q
V
Q1 = C1V1
= k CV = k Q
V1 = Q1/C1
= Q/k C = V /k
Electricity & Magnetism Lecture 8, Slide 21
CheckPoint: Capacitors and Dielectrics 1
Electricity & Magnetism Lecture 8, Slide 22
Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric.
Compare the voltages of the two capacitors.
A. V1 > V2
B. V1 = V2
C. V1 < V2
CheckPoint: Capacitors and Dielectrics 2
Electricity & Magnetism Lecture 8, Slide 23
Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric.
Compare the potential energy stored by the two capacitors.
A. U1 > U2
B. U1 = U2
C. U1 < U2
U=1/2 Q2/C
U2/U1 = k
C1
V
C2
V
U = 1/2CV2Compare using
A) U1 < U2 B) U1 = U2 C) U1 > U2
Two identical parallel plate capacitors are connected to identical batteries. Then a dielectric is inserted between the plates of capacitor C1. Compare the energy stored in the two capacitors.
Question
Electricity & Magnetism Lecture 8, Slide 24
Potential Energy goes UP
CheckPoint: Capacitors and Dielectrics 3
Electricity & Magnetism Lecture 8, Slide 25
The two capacitors are now connected to each other by wires as shown. How will the charge redistribute itself, if at all?
A. The charges will flow so that the charge on C1 will become equal to the charge on C2.
B. The charges will flow so that the energy stored in C1 will become equal to the energy stored in C2
C. The charges will flow so that the potential difference across C1 will become the same as the potential difference across C2.
D. No charges will flow. The charge on the capacitors will remain what it was before they were connected.