Current and ResistanceCurrent and Resistance

October 9, 2006October 9, 2006

Notes Notes

New topic today – Current and New topic today – Current and ResistanceResistance

Quiz on FridayQuiz on FridayFriday 7:30 review sessiomn.Friday 7:30 review sessiomn.There is a new WebAssign.There is a new WebAssign.

Is it AM or PM … only the shadow knows Is it AM or PM … only the shadow knows for sure.for sure.

I know too.I know too.

New Topic:Current and Resistance

Physical Resistors

More …

What Happens?

“+”

“+”

“+”

“+”

REMEMBER, THE ELECTRONS

ARE ACTUALLY MOVING THE

OTHER WAY!-

-

DEFINITION

Current is the motion of POSITIVE CHARGE through a circuit. Physically, it is electrons that move but …

Conducting material

Q,t

Conducting material

Q,t

dt

dqi

ort

Qi

CURRENT

UNITS

A current of one coulomb per second is defined as ONE AMPERE.

A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is ω. What average current does this rotating charge represent?

Fraggen …..

ANOTHER DEFINITION

A

I

area

currentJ

Figure P27.8 represents a section of a circular conductor of non-uniform diameter carrying a current of 5.00 A. The radius of cross section A1 is 0.400 cm. (a) What is the magnitude of the current density across A1? (b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor at A2?

Ohm A particular object will resist the flow of current.

It is found that for any conducting object, the current is proportional to the applied voltage.

STATEMENT: V=IR R is called the resistance of

the object. An object that allows a

current flow of one ampere when one volt is applied to it has a resistance of one OHM.

Graph

A DIODE

Resistance Varies with Applied Voltage (actually with current)

Let’s look at the atomic level ..

Conduction is via electrons. They are weak and small and don’t exercise

much. Positive charge is big and strong and doesn’t

intimidate easily. It’s an ugly situation … something like ……

-

+

Consider a metal conductor

So far, we have said that a metal is an equipotential because no charges were moving. Hence, no electric field in the metal You can move a charge freely in the metal BECAUSE there

is no electric field.

NOW we have a current. This can only happen if we allow an electric field to push

the charges. Thus, the metal is NO LONGER A TRUE

EQUIPOTENTIAL. But almost …. as we shall see in the next chapter.

l

VV ab E

The Current

Electrons are going the opposite way from the current. (WHY?)

They probably follow a path like …

Average “drift”speed - vd

OUTIN

Notation

vd average drift velocity of the electron n number of electrons (mobile) per unit

volume. t interval of time x average distance the electron moves

in time t. Q total amount of CHARGE that goes

through a surface of the conductor in time t.

dvJ ne

nevA

IJ

enAvt

QI

etnAvQ

davg

davg

d

)(

Often a Vector

The Diagram

We return to the diagram ….. Consider an electron. Assume that whenever it

“bumps” into something it loses its momentum and comes to rest.

It’s velocity therefore starts at zero, the electric field accelerates it until it has another debilitating collision with something else.

During the time it accelerates, its velocity increases linearly .

The average distance that the electron travels between collisions is called the “mean free path”.

Starting when the electron is at rest:

m

eEvv

m

eE

m

Fa

atatvv

d

0

Let n= number of charge carriersper unit volume (mobile electrons)

We showed two slides ago::

1

2

2

m

ne

so

Em

EneJ

orm

eEnenevnqvJ dd

Finally

dv

Reference

The average drift velocity of an electron is about 10-4 m/s

Ponder

How can a current go through a resistor and generate heat

(Power) without decreasing the current itself?

Loses Energy

Gets it back

Exit

Conductivity

In metals, the bigger the electric field at a point, the bigger the current density.

EJ is the conductivity of the material.

=(1/) is the resistivity of the material

Going to the usual limit …

JdAI

anddA

dIJ

Example

A cylindrical conductor of radius R has a current density given by

(a) J0 (constant)

(b) r

Find the total current in each case.

)(1 00 TT

Range of and

Ye old RESISTANCE

IRVVA

lR

IA

lV

A

I

l

VE

El

VEJ

ElV

11

REMEMBER

IRVA

LR

A closed circuit

Power

R

EIVRIP

RIIRIIVPPower

VIt

QV

t

22

2

W

:Power

QVW

:isbattery by the done

workofamount The battery. by theresistor the

throughpushed is Q charge a t, In time

Ponder

How can a current go through a resistor and generate heat

(Power) without decreasing the current itself?

Loses Energy

Gets it back

Exit

A Circuit

)( rR

EI

E=emf