Lesson 5Lesson 5Current and ResistanceCurrent and Resistance

BatteriesBatteriesCurrent DensityCurrent DensityElectron Drift VelocityElectron Drift VelocityConductivity and ResistivityConductivity and ResistivityResistance and Ohms’ LawResistance and Ohms’ LawTemperature Variation of ResistanceTemperature Variation of ResistanceElectrical Power and Joules LawElectrical Power and Joules LawClassical Model of Conduction in Classical Model of Conduction in Metals Metals

Lesson 5

Electrical Resistance is “friction” to the flow of electric chargeObserved in Conductors and Non ConductorsNot found in Super Conductors

Electrical Resistance

Charge Pump I

I

+-

Load Resistance

Capacitor will send current through

load resistance and loose charge

Charge Pump I

I

+-

Load Resistance

Battery will send current through load resistance and not loose charge

Charge in battery is regenerated by Chemical reactions

Flow of Charge

I

Current Picture

Current is the rate of Flow of positive

charge through whole cross sectional

area of conductor

Current Picture Definition I

I dQ

dt

I Q T

C

sA (Ampere)

Current Picture Definition II

Current is Conserved

I1

I2

I1+I2

Conservation of Current

Flowing charge experiences friction

Work must be done to overcome friction

Need driving force, hence needElectric FieldPotential Difference

Driving force for Current

Electrical Resistance = Potential Difference

Current

R V

I

R V I

V

A (Ohm )

SI units

I-V plots

I

V

I

V

slope constant = 1/R slope not constant

Ohmic Material Non Ohmic Material

V-I plots

Ohmic MaterialsOhmic MaterialsResistance I

V RI Ohms Law

RV

I constant

Non Ohmic MaterialsNon Ohmic Materials

R is not Constant, but R is not Constant, but varies with current varies with current

and voltage and voltage

Resistance II

Power = rate of doing work Power = rate of doing work by applied forceby applied force

Power

Power = dUdt

dQdt

V IV

Power I V AV C

s

Nm

C Nm

sJs W ( Watts)

For Ohmic Materials

IV I 2R V 2

R

Ohmic Materials I

For Ohmic MaterialsFor Ohmic Materials

Resistance is proportional to length of conductor

Resistance is inversely proportional to the cross sectional area of the conductor

Ohmic Materials II

R l

R la

R l

a resistivity of conductor

m

Resistivity

Picture

I

V+ V-

l

E

a

|V| V V El

I V

R

El

l

a

Ea

Divide by Area

Current Density magnitude = Current per cross sectional area

J I

a E

E

= conductivity 1

Current Density

Current Density

J E

I J dA

surface E

surface dA

current through surface

Integral Formula

Classical Microscopic Theory of Electrical

Conduction

Electrical Conduction

Random Walk

Picture

Definition of Variables

Charge in Volume V

Q nA x q nAvd t q

n number of charge carriers

per unit volume

A cross sectional area

q amount of charge on

each carrier x average distance moved in

time t after collision

vd drift velocity

Q

t nA q

dQ

dt I nAv

dq

J nvd q

J

nq v

d

Equations Ix t

Equations II

acceleration of charge q in field E

a q

mE

•Let average time between collisions

•at each collision charge carrier forgetsforgets

drift velocity , so we can take initial drift

velocity = 0 and just before collisions

vd a q

mE q

m

E

v d J

nq q

m E

J nq2 m

E

nq2 m

Temperature EffectsTemperature Temperature

EffectsEffects

1

m

nq 2

As temperature increases decreases

thus increases

T 0

1 T T0

1

0

ddT

Temperature Coefficient of Resistivity

Temperature Effects

T 0

1 T T0

1

0

ddT

Temperature Coefficient of Resistivity

Thus

R T R0

1 T T0

Equation