10/8/2008

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REMEMBER, THE ELECTRONS

ARE ACTUALLY MOVING THE

OTHER WAY!-

-

Battery

A wire is a conductor We will assume that the conductor is

essentially an equi-potential◦ It really isn’t.

Electrons are moving in a conductor if a current is flowing. ◦ This means that there must be an electric field

in the conductor.◦ This implies a difference in potential since

E=V/d◦ We assume that the difference in potential is

small and that it can often be neglected.◦ In this chapter, we will consider this difference

and what causes it.

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

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

A charged belt, 30 cm wide, travels at 40 m/s between a source of charge and a sphere. The belt carries charge into the sphere at a rate corresponding to 100 µA. Compute the surface charge density on the belt.

[8.33e-06] C/m2

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?

Today we continue on Resistance and Resistors.

EXAM #2 is NEXT FRIDAY – the 17th of October

Covers Potential through Resistance Quiz Grades are being re-normalized. Next topic will be electric circuits

An electric current is given by the expression I(t) = 100 sin(120πt), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = (1/240) s?

A

I

area

currentJ

The figure 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?

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.

IRV

Resistance Varies with Applied Voltage (actually with current)

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 ……

-

+

l

VV ab E

We defined◦ Current (and Amperes)◦ Current Density

We defined Resistance and Ohm’s Law

IRV

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

They probably follow a path like …

Average “drift”speed - vd

OUTIN

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

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”.

m

eEvv

m

eE

m

Fa

atatvv

d

0

1

2

2

m

ne

so

Em

EneJ

orm

eEnenevnqvJ dd

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

We showed two slides ago:

resistivity

dv

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

How can a current go through a resistor and generate heat (Power) without decreasing the

current itself?

Loses Energy

Gets it back

Exit

EJ

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

is the conductivity of the material.

=(1/) is the resistivity of the material

)(1 00 TT

A conductor of uniform radius 1.20 cm carries a current of 3.00 A produced by an electric field of 120 V/m. What is the resistivity of the material?

IRVVA

lR

IA

lV

A

I

l

VEJ

ElV

(def) 1

IRVA

LR

)1(0 T T

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

that’s it, Doc