physics 2112 unit 8: capacitors
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Physics 2112 Unit 8: Capacitors. Today’s Concept: Capacitors in a circuits Dielectrics Energy in capacitors. Where we are……. Simple Capacitor Circuit. Q. Q. - PowerPoint PPT PresentationTRANSCRIPT
Physics 2112Unit 8: Capacitors
Today’s Concept: Capacitors in a circuits Dielectrics Energy in capacitors
Unit 8, Slide 1
Where we are…….
Unit 8, Slide 2
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 3
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 4
QV
Key point: Q is the same for both capacitors
Key point: Q = VCtotal = V1C1 = V2C2
1Ctotal
1C1
1C2
+=
Series Capacitor CircuitQ
Q
Q = VCtotal
C1
C2
V1
V2
V
Also: V = V1 + V2 Q/Ctotal = Q/C1 + Q/C2
Electricity & Magnetism Lecture 8, Slide 5
Voltage
Current
Capacitance
Series Parallel
Different for each capacitor.Vtotal = V1 + V2
IncreasesCeq = C1 + C2
Same for each capacitorItotal = I1 = I2
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 resistor on a different wire.
Different for each capacitorItotal = I1 + I2
C1 C2
C1
C2
Capacitor Summary
Electricity & Magnetism Lecture 9, Slide 6
Example 8.1 (Capacitors in Series)
Unit 8, Slide 7
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 8
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 =
Ctotal = C/2
1/Ctotal = 1/C + 1/C
= 2/CCtotal = C Ctotal = 2C
CheckPoint: Three Capacitor Configurations
CC
CC C
Electricity & Magnetism Lecture 8, Slide 9
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 10
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
CheckPoint: Capacitor Network
Unit 8, Slide 11
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
Example 8.3 (Capacitor Network)
Unit 8, Slide 12
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 13
C3
C4
C2C1
C5
C34
C2C1
C5 C3
C1234
C5
C12345
In Prelecture 7 we calculated the work done to move charge Q from one plate to another:
This is potential energy waiting to be used…
+Q
V
-Q
U = 1/2QV= 1/2CV2
Since Q = VC= 1/2Q2/C
C
Energy in a Capacitor
Electricity & Magnetism Lecture 8, Slide 14
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
VQ1 = C1V1
= k CV = k Q
V1 = Q1/C1
= Q/k C = V /kElectricity & Magnetism Lecture 8, Slide 15
By adding a dielectric you are just making a new capacitor with larger capacitance (factor of k)
C0
V Q0 = VC0
Dielectrics
C1 = k C0
V Q1 = VC1
Electricity & Magnetism Lecture 8, Slide 16
CheckPoint: Capacitors and Dielectrics 1
Electricity & Magnetism Lecture 8, Slide 17
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 18
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
CheckPoint: Capacitors and Dielectrics 3
Electricity & Magnetism Lecture 8, Slide 19
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.
Example 8.4 (Partial Dielectric)
Electricity & Magnetism Lecture 8, Slide 20
An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V.
Conceptual Analysis:
V C0
x0 kV
x0/4
VQC
Strategic Analysis: Think of new capacitor as two capacitors in parallel Calculate new capacitance C Apply definition of capacitance to determine Q
A dielectric (k ) of width x0/4 is inserted into the gap as shown.
What is Qf, the final charge on the capacitor?
Calculation
Electricity & Magnetism Lecture 8, Slide 21
k kA1 =3/4 Ao A2 =1/4 Ao