Chapter 16CapacitorsDielectrics

Chapter 17Current

Resistance

Hint: Be able to do the homework (both theproblems to turn in AND the recommended ones)you’ll do fine on the exam!

Friday, February 26, 1999 in class

Ch. 15 - 16

You may bring one 3”X5” index card (hand-writtenon both sides), a pencil or pen, and a scientificcalculator with you.

U = INTERNAL ENERGY of the capacitor.

This is where the energy comes from to power many of our cordless, rechargeable devices…When it’s gone, we have to plug the devices into the wall socket to recharge the capacitors!

W QQ

U VC

CV1

2 2

1

2

22

Just so you know...

Insulating materials between capacitor plates are known as dielectrics. In the circuits we have dealt with, that material is air. It could be other insulators (glass, rubber, etc.).

Dielectric materials are characterized by a dielectric constant such that when placed between the plates of a capacitor, the capacitance becomes

C = Co Co is the vacuum (air) capacitance.

Dielectrics, therefore, increase the charge a capacitor can hold at a given voltage, since...

Q = C V = Co V

Co

It’s time to develop an understanding ofelectrical systems that are NOT in electrostaticequilibrium. In these systems, charges move,under the influence of an externally imposedelectric fields. Such systems provide us withthe useful electricity we get out of flashlightbatteries and rechargeable devices.

Current and Resistance

We’ve already used this concept, even though we haven’t formally introduced it.

What do you think of when you hear the word “current?”

Electrical Current is simply the flow of electrical charges.

A

The current is the number of charges flowing through a surface A per unit time.

charge carriersmoving charges.can be + or -

I Q

t

I Q

t

By convention, we say that the direction of the current is the direction in which the positive charge carriers move.

Note: for most materials we examine, it’s really the negative charge carriers that move. Nevertheless, we say that electrons move in a direction opposite to the electrical current.

Leftover from Ben Franklin!

Why do charges move?

Well, what happens when you put an electric field across a conductor?

E

electrical force on the charges in the conductor.

charges can move in conductors.

a current flows!

E

A

Vd t

The charge carriers, each with charge q, move with

an average speed vd in response to the electric field. If there are n charge carriers per volume in the conductor, then the number of charge carriers passing a surface A in a time interval t is given by

Q n Av tdq

I Q

tn Avdq

Electric fields exert an electrical force on charges given by

And I remember from last semester that Newton’s 2nd Law says

F ma

So shouldn’t the charges be accelerating

instead of moving with an average velocity vd?

F qE

E

A

Vd t

Let’s follow the path of one of the charge carriers to see what’s really going on...

The thermal motion of the charges in the conductor keep thecharges bouncing around all over the places, hitting thefixed atoms in the conductor.

The electric field exerts a force which “gently” guides thepositive charges toward the right so that over time, theyappear to drift along the electric field.

You might think of the collisions as a frictional forceopposing the flow generated by the electric field.

You are probably asking yourself, “So, just how long does it take the average electron to traverse a 1m length of 14 gauge copper wire if the current in the wire is 1 amp?

How long does it take the averageelectron to traverse a 1m length of14 gauge copper wire if the currentin the wire is 1 amp?

Let’s try to guess first:

a) yearsb) weeksc) daysd) hourse) minutesf) secondsg) microsecondsh) nanoseconds

14 gauge wire is a common size of wire having a radius of 0.0814 cm

Let’s assume that atom of copper is able tosupply one free charge to the current.

The mass density of copper is 8.92 g/cm3

1 mole of copper weighs 63.5 g.

So, the number density of charge carriers in the copper is...

n ( . )(8. )

( . )

6 02 10 92

635

23 atoms

mol

g

cm3

g

mol

n = 8.46 X 1022 atoms/cm3

q = 1.6 X 10-19 CA = r2 = 2.1 X 10-2 cm2

vn Ad

I

q

I Q

tn Avdq

t = 7.8 hours!

vd

1

46 10 16 10 21 1022 19 2

A

cmchgs

cm3C

chg2(8. )( . )( . )

vd 355 10 3. cm

s

td

vd

100

355 102 8 10

34 cm scm

s.

.

Describes the degree to which a current through a conductor is impeded.

In particular, if a voltage V is applied across a conductor, a current I will flow. The resistance R is defined to be:

R = V / I

R = V / I

[R] = [V] / [I]

[R] = Volt / Amp

= Ohm ()

Georg Ohm (early 19th century) systematically examined the electrical properties of a large number of materials. He found that the resistance of a large number of objects is NOT dependent upon the applied voltage. That is...

V = I R