PHY 2049Chapter 26

Current and Resistance

Chapter 26 Current and Resistance In this chapter we will introduce the following new concepts:

-Electric current ( symbol i ) -Electric current density vector (symbol ) -Drift speed (symbol vd ) -Resistance (symbol R ) and resistivity (symbol ρ ) of a conductor -Ohmic and non-Ohmic conductors

We will also cover the following topics:

-Ohm’s law -Power in electric circuits

J

(26 - 1)

Physical Resistors

What Happens?

“+”

“+”

“+”

“+”

REMEMBER, THE ELECTRONS

ARE ACTUALLY MOVING THE

OTHER WAY!

What’s Moving?

What is making the charged move??

Battery

KEEP IN MIND 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.

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

i

+ q

conductor

v

i

- q

conductor

v

An electric current is represented by an arrow which has

the same direction as the charge velocity. The sense of the

current arrow is defined as follows:

If the current is due to t

Current direction :

1. he motion of charges

the current arrow is to the charge velocity

If the current is due to the motion of charges

the current arrow is to the charge veloci

t

vparallel

2.

ant

nega

iparallel

posit

tive

ive

y v

(26 - 3)

dqi

dt

UNITS

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

ANOTHER DEFINITION

A

I

area

currentJ

When a current flows through a conductor

the electric field causes the charges to move

with a constant drift speed . This drift speed

is superimposed on the random motion of the

charges.

dv

Drift speed

Consider the conductor of cross sectional area shown in the figure. We assume

that the current in the conductor consists of positive charges. The total charge

within a length is given by:

A

q L q nA . This charge moves through area

in a time . The current /

The current density

In vector form:

dd d

dd

d

L e A

L q nALet i nAv e

v t L v

nAv eiJ nv e

A A

J nev

dJ nev

dJ nv e

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+ -

i

V

If we apply a voltage across a conductor (see figure)

a current will flow through the conductor.

We define the conductor resistance as the ratio

V the Ohm (symbol

A

V

Ri

V

i

SI

R

Unit for R :

esist ance

A conductor across which we apply a voltage = 1 Volt

and results in a current = 1 Ampere is defined as

having resistance of 1

Why not use the symbol "O" instead of " "

Suppose we ha d

)

V

i

Q :

A : a 1000 resistor.

We would then write: 1000 O which can easily

be mistaken read as 10000 .

A conductor whose function is to provide a

specified resistance is known as a "resistor"

The symbol is

given to the left.

V

Ri

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R

Ohm’s Law

IRV

Graph

IRV

l

VV ab E

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.

E

+ -

i

V

E

Unlike the electrostatic case, the electric field in the

conductor of the figure is not zero. We define as

resistivity of the conductor the ratio

In vector form: E

J

J

E

Resi

SI u

stivit

nit r

y

fo

2

The conductivity is defined as:

Using the previou

V/m V m m

A/m

s equation takes the for

1

m

A

: J E

ρ :

Consider the conductor shown in the figure above. The electric field inside the

conductor . The current density We substitute and into

/ equation and get:

/

V iE J E J

L AE V L V A A

RJ i A i L L

L

RA

LR

A

E J

J E

(26 -7)

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

)(1 00 TT

Range of and

REMEMBER

IRVA

LR

TemperatureEffect

T

)1(0 T

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

If the device connected to the battery is a resistor R then the energy transfered by the

battery is converted as that appears on R. If we combine the equation

with Ohm's law: , we

P iV

Vi

R

heat

22

get the following two equivalent expressions for

the rate at which heat is dissipated on R.

and

VP i R P

R

V2 P i R

2

V

PR

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