Physics 2112 Unit 8: Capacitors - College of DuPage · 2020. 4. 1. · Unit 8, Slide 15 A circuit consists of three unequal capacitors C 1, C 2, and C 3 which are connected to a battery

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


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

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


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


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


What is Q1?

What is Q2?


➢ 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


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

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


What is Q1?

What is Q3?


➢ 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 =


Unit 8, Slide 17

C3

C4

C2C1

C5

C34C2C1

C5

C1234

C5

C12345


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


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

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


Potential Energy goes UP



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.

Documents

Physics 2112 Unit 8: Capacitors - College of DuPage · 2020. 4. 1. · Unit 8, Slide 15 A circuit consists of three unequal capacitors C 1, C 2, and C 3 which are connected to a battery