physics 2112 unit 8: capacitors

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


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


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


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


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


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


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


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


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


CheckPoint: Capacitors and Dielectrics 1


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



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



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)


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


k kA1 =3/4 Ao A2 =1/4 Ao

physics 2112 unit 8: capacitors

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