Lectures 8,9 (Ch. 25)

Electric Current1. Drift velocity2. Ohm’s law3. Volt-Amper characteristics4. Thermal dependence of resistance5. Resistors in series and parallel6. Electric power7.emf, battery8.Simple circuits

CautionSo far we studied electrostatics (equilibrium) Now we start to study electric current

(nonequilibrium state)The following statements are not correct in the

presence of electric current:• 1. E inside conductors=0• Electric charges reside on the outer surface of

conductor• 2. Inside conductors V=const=Vsurface

Drift velocity

rmsd

d

rms

vvtypicallycollisionsbetweentimeaverageanis

mEqvvEqFif

smvvthough

vvFif

tmFvv

0

)/10~)((

0052

0

0

Drift velocity does depend on a sign of charges+ ions in plasmas or electrolytes, holes in semiconductors Electrons in metals, - ions in plasmas, etc.

Electric current is a flow of charges (charge transferred per unite time via a given cross section)

eschofvofdirectioninisI

EIEmnAqI

mEqv

vqnAIdtqnAvdQ

AmperAsC

tQIuniteSI

dtdQI

d

d

dd

arg

)(111

][][][:;

2

If different types of carriers present:

I

i i

iii EmAnqI

2

Ohm’s Law:RVI

Georg Ohm (1787 - 1854).

nAqmLRwhere

RVI

VmLnAqI

LVE

2

2

;

EI

Resistance

ALR

nqm

EJEmnq

AIJ

;

;

2

2

SI unite of R: [R]=[V]/[I]=1V/1A=1Ω (Ohm)

ῤ is called a resistivity, [ῤ]=Ωm

σ=1/ῤ is called a conductivity

Volt-Amper characteristics

Ohm’s Law:RVI

R is constant (characteristic of the conductor)It is valid for many conductors in a wide range of conditions, but not always!

Semiconductor diode is a junction of two semiconductors withpositive (p) and negative (n) carriers

→p+

n-I

+Change of a polarity of the battery results in zero current.It can be used for rectification of the current.

Thermal dependence of R

In metals

)](1[

)(

~1~

00

TT

lowTatinvalid

TT

ALR Hence if L(T),A(T) are negligible then )](1[ 00

TTRR Measuring R allows to find T (termistors) In semicoductors n~T→ῤ~1/T

Superconductors

10 Nobel prizes were given for studies of SC ;The last one in 2003 to theorists: Alexei Abrikosov, Vitaly Ginzburg, Anthony J. Legget

1911, Hg, Tc~4.2K , H.Kamerlingh Onnes , Nobel Prize in Physics in 1913 Up to 1986 Tc<20K1986 , Tc~40K Karl Müller and Johannes Bednorz, Nobel Prize in Physics in 1987 cuprate-perovskite ceramic materials, such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO); 1987, Tc~90K,….1993 Tc~135K still a record2008 Tc~55K, Fe-based superconductors

H.Kamerlingh Onnes,1853-1926

VitalyGinzburg,1916-2009

Applications: electromagnets, motors, generators, transformers, etc.Open problems: 1.Mechanism of HTS? Why it’s possible?2.How to sustain large current (high magnetic field)3.Fragility of the materials

Levitation

Resistors in series

321 RRRI

VVVIVR ybxyaxab

eq

Resistors in parallel

321

321 1111RRRV

IIIVI

R ababeq

I3

I1

I2

NB:Opposite to capacitors!

C=Q/VR=V/I

Example1.

Example 2

Electric Power

00000

;

inout

inab

inab

abinababab

in

PPPatobfromflowsIbutIfVPbtoafromflowsIandVIf

IVPdqVdWdt

dWP

a b

I

0abV

In resistor:

JkWhrPtURVRIPIRV

alwaysIVP

in

abin

6

22

106.31,

!0

Alternative current (ac current)

2cos)(

2cos)(

coscos

cos)(

00

2

2202

0

00

0

2

2

ItItII

RIRItRItP

tItRVI

tVtV

rms

rms

How to get more light with two bulbs?

Bulb B

or ?

Thomas Edison (1847-1931)1882

How to get more light with two bulbs?

Bulb B

RRIIP

22

RRP

RR

eq

eq

2

222

RRRP

RR

eq

eq

222 22/

2/

less light! more light!

emf, batteryClosed loop

0Rloss of energy→need a source of emf (ε), a battery

I+

emf (ε) is a work per unite chargeby external (nonelectric force).Ideal case (neglecting losses in the battery): abV

IVP about

a bε

a b

εr

Terminal voltage and power output of the battery

rIIP

IVPIrV

out

about

ab

2

Terminal voltage is the voltage between the electrods of the battery connected to an external circuit, i.e. it is a voltage supplied by the battery to an external circuit. Real battery includes internal resistance, r. If the current through the battery is from – to + then the terminal voltage is smaller then emf:

Terminal voltage and power input into the battery

If the current through the battery is from + to - then the terminal voltage is larger then emf:

rIIP

IVPIrV

out

about

ab

2

a b

The rate at which the battery is charged The rate at which the

battery is heated

Alternator (the battery with larger emf delivers the energy to the battery with smaller emf

Ammeter measures the current. It should be placed in series with the element of circuit where it measures the current. Ideal ammeter has resistance=0 in order do not disturb in the current it measures. Voltmeter measure V. It should be placed in parallel with the element across which it measures the voltage. Ideal voltmeter has resistance=∞ in order do not disturb the voltage it measures.

I

IV=0

I

Simple resistors circuits1.Open circuit. What ideal ammeter and voltmeter measure?

A

V

I=0 (infinite resistance )

V=ε, P=0rε

It’s dangerous to touch the ends!

V=120V, R(wet body)=1kΩ→I~0.1A→ fibrillations (chaotic beatings of the heart)Defibrillator: I~1A complete stop