Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 11

Physics 212Physics 212Lecture 8Lecture 8

Today's Concept:Today's Concept:

CapacitorsCapacitors

How does a capacitor behave in a circuit?How does a capacitor behave in a circuit?More circuit examplesMore circuit examples

Main Point 1

First, filling the region between the plates of a capacitor with a dielectric will increase its capacitance. In particular, the ratio of the capacitance when filled with dielectric to that when filled with air is equal to kappa , the dielectric constant of the material.

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 22

Main Point 2

Second, the equivalent capacitance of two capacitors connected in parallel is equal to the sum of the individual capacitances. The voltage across each capacitor is the same and is the equivalent voltage of the combination. The equivalent charge of the combination is equal to the sum of the charges on the individual capacitors.

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 33

Main Point 3

Third, the equivalent inverse capacitance of two capacitors connected in series is equal to the sum of the individual inverse capacitances. The charge across each capacitor is the same and is the equivalent charge of the combination. The equivalent voltage of the combination is equal to the sum of the voltages across the individual capacitors.

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 44

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 55

CCVV +Q+Q-Q-Q

QQ

QQ

This “Q” really means that the battery has This “Q” really means that the battery has moved charge Q from one plate to the other,moved charge Q from one plate to the other,so that one plate holds +Q and the other -Q.so that one plate holds +Q and the other -Q.

CCVV Q=VCQ=VC

Simple Capacitor CircuitSimple Capacitor Circuit

8

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 66

CC00VV

DielectricsDielectrics

CC11==CC00

VV

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 77

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 88

VVCC22CC11

Parallel Capacitor CircuitParallel Capacitor Circuit

VV CC1212

CC11 + C + C22 = = CC1212

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 99

Series Capacitor CircuitSeries Capacitor Circuit

CC11

CC22

VV11

VV22

QQVV

QQ

11CC1212

11CC11

11CC22

++==

CC1212VV

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1010

Checkpoint 1Checkpoint 1

CCCC

CCCC CC

Which has lowest total capacitanceWhich has lowest total capacitance::

18

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1111

Checkpoint 2Checkpoint 2Which has lowest total capacitance:Which has lowest total capacitance:

CCCC

CC

CC

CC

20

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1212

Checkpoint 3Checkpoint 3

25

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.

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

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1313

Checkpoint 4a/bCheckpoint 4a/b

33

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

Compare the potential energy stored by the two capacitors.A. U1 > U2 B. U1 = U2 C. U1 < U2

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1414

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1515

Checkpoint 4cCheckpoint 4cTwo 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.

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.

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1616

In pre-lecture 7 we calculated the work done to move charge Q from one In pre-lecture 7 we calculated the work done to move charge Q from one plate to another:plate to another:

Energy in a Capacitor (1/2 QV)Energy in a Capacitor (1/2 QV)

+Q+Q

VV

-Q-Q

U = U = 11//22QVQV

CC

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1717

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1818

CalculationCalculationAn air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V.

A dielectric () of width x0/4 is inserted into the gap as shown.

What is Qf, the final charge on the capacitor?

• Conceptual Analysis:

V

C0

x0

V

x0/4

Physics 212 Lecture 8, Slide Physics 212 Lecture 8, Slide 1919

Calculation