L8 Ch26 Capacitors - uml.edu

Department of Physics and Applied PhysicsPHYS.1440 Lecture 8 Danylov

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture 8

Chapter 26

Capacitors and more


Today we are going to discuss:

Chapter 26:

Section 26.2 The Geometry of Potential and Field Section 26.3 A Conductor in Electrostatic equilibrium Section 26.5 Capacitance and Capacitors


The Geometry of Potential and Field

Let s be along an equipotential line, dsdVEs

where V=const. So dV=0. dsdVEs

0

0So, it is impossible to have an electric field along equipotential lines,

linesialequipotentE

Which set of equipotential surfaces matches this electric field?

A)

B)

C)

D)

E)

F)

E

ConcepTest Geometry E and V


Potential of a Conductor

i

f

sdEVVVf

iif

0V if VV

A conductor in electrostatic equilibrium is at the same potential.

constV


The Electric Battery

A battery transforms chemical energy into electrical energy.

Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them.

Atom of Zn gets dissolved leaving two electrons behind

Two electrons get attracted by the ion of Zn leaving behind positively charged electrode


Capacitor


Capacitor stores energy

You can store potential energy by pulling a bow, stretching a spring, etc.

A capacitor is a system that stores potential energy in a form of an electric field.

Ugh!It’s just energy


Capacitance (definition)

The ratio of the charge Q to the potential difference VC is called the capacitance C:

The SI unit of capacitance is the farad:

≝

VC


Parallel-plate capacitor

In its simplest form, a capacitor consists of a pair of parallel metal plates separated by air/insulating material.


Parallel-plate capacitorLet’s find capacitance of a parallel-plate capacitor

Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing.

≝

E

d

Aarea

+Q–Q

The electric field between the plates is ‐ surface

charge density

(Eq.25.26)The potential difference between plates:

We need to find Q and ΔV:

≝ =

This gives the capacitance:


Parallel-plate capacitor

We can increase capacitance by increasing area A by making “a roll of metal and insulator”


Parallel-plate capacitor/keyboard

Capacitors are important elements in electric circuits. They come in a variety of sizes and shapes.

The keys on most computer keyboards are capacitor switches. Pressing the key pushes two capacitor plates closer together, increasing their capacitance.

What is the capacitance of these two electrodes?

A) 8 nF

B) 4 nF

C) 2 nF

D) 1 nF

E) Some other value

ConcepTest Capacitance

Since the battery stays connected, the potential difference must remain constant!

+Q –Q

dAC 0

A parallel-plate capacitor initially has a voltage of 400 Vand stays connected to the battery. If the plate spacing is now doubled, what happens?

A) the voltage decreases

B) the voltage increases

C) the charge decreases

D) the charge increases

E) both voltage and charge change

ConcepTest Varying Capacitance I

Follow-up: How do you increase the charge?

Since , when the spacing d is doubled, the capacitance C is halved.

And since , that means the charge must decrease.

Q = C∆V

400 V

Once the battery is disconnected, Q has to

remain constant, since no charge can flow

either to or from the battery.

A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled, what is the new value of the voltage?

A) 100 V

B) 200 V

C) 400 V

D) 800 V

E) 1600 V

+Q –Q

dAC 0

ConcepTest Varying Capacitance II

Since , when the spacing d is

doubled, the capacitance C is halved. And since , that means the voltage must double

400 VQ = CV


CapacitorsIn Series and Parallel


Combinations of Capacitors In practice, two or more capacitors are sometimes joined together. The circuit diagrams below illustrate two basic combinations:

parallel capacitors and series capacitors.

The equivalent capacitance is the capacitance of the single capacitor that can replace a set of connected capacitors without changing the operation of the circuit


Capacitors in ParallelConsider three capacitors connected in parallel.

QRea

l cir

cuit

Equ

ival

ent c

ircu

it

ΔV

, ΔV

, ΔV

, ΔV

Q ΔV

Ceq

Capacitors in parallel have the same potential difference, ΔV

Q is a total charge drawn from the battery + +

Since ≝;;;

We have replaced 3 capacitors with a “equivalent” capacitor.

+ +

+ +

Conservation of charge

Ceq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit

Equivalent capacitance of capacitors in parallel.

=


+ +

Capacitors in SeriesConsider three capacitors connected in series.

QRea

l cir

cuit

Equ

ival

ent c

ircu

it

+Q

Q ΔV

Ceq

Capacitors in series have the same charge, Q.

+ +

Since ≝

Ceq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit

Equivalent capacitance of capacitors in series.

C1 C2 C3

+ -

-Q +Q -Q +Q -Q

ΔV

ΔV1 ΔV2 ΔV3

The 2 equal capacitors in series add up as inverses, giving 1/2C. These are parallel to the first one, which add up directly. Thus, the total equivalent capacitance is 3/2C.

ConcepTest Equivalent Capacitor I

o

o

C CCCeq

A) Ceq = 3/2CB) Ceq = 2/3CC) Ceq = 3CD) Ceq = 1/3CE) Ceq = 1/2C

What is the equivalent capacitance,

Ceq , of the combination below?

in series

o

o In parallelC2

in series

In parallel2

32


Thank youSee you next time

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L8 Ch26 Capacitors - uml.edu

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