Transcript Document

Lectures 8,9 (Ch. 25)
Electric Current
1. Drift velocity
2. Ohm’s law
3. Volt-Amper characteristics
4. Thermal dependence of resistance
5. Resistors in series and parallel
6. Electric power
7. emf, battery
8. Simple circuits
Caution
So 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

 
F
v  v0  t
m

if F  0  v  v0  0
(though vrms 
( v 2 ) ~ 105 m / s )




qE
if F  qE  0  v  vd 

m
 is an average time between collisions

typically vd  vrms
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)
dQ
[Q] 1C
I
; SI unite : [ I ] 

 1A ( Amper)
dt
[t ] 1s


dQ  qnAvd dt  I  qnAvd

 q 2 nA 



qE
vd 

I 
E  I  E
I
m
m


I is in direction of vd of  ch arg es
2

qi ni A i 
E
If different types of carriers present: I  
mi
i
V
I
R
Ohm’s Law:
Georg Ohm
(1787 - 1854).


I  E
V
q 2 nA
E ;I
V
L
mL
V
mL
I  where R  2
Resistance
R
q nA
SI unite of R: [R]=[V]/[I]=1V/1A=1Ω (Ohm)

 I q 2 n 
J 
E;
A
m
m
  2 ;R  
q n

J
L
A
ῤ is called a resistivity, [ῤ]=Ωm
σ=1/ῤ is called a conductivity

E

Volt-Amper characteristics
V
Ohm’s Law: I 
R
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 with
positive (p) and negative (n) carriers
p
+
I→
n
-
+
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
 ~    ~T
T
(invalid at lowT  )

   0 [1   (T  T0 )]

L
R
A
Hence if L(T),A(T) are negligible then

R  R0 [1   (T  T0 )]

Measuring R allows to find T (termistors)
In semicoductors n~T→ῤ~1/T
Superconductors
1911, Hg, Tc~4.2K , H.Kamerlingh Onnes ,
Nobel Prize in Physics in 1913
Up to 1986 Tc<20K
1986 , Tc~40K Karl Müller and Johannes
H.Kamerlingh
Bednorz, Nobel Prize in Physics in 1987
cuprate-perovskite ceramic materials, such Onnes,1853-1926
as bismuth strontium calcium copper oxide
(BSCCO) and yttrium barium copper oxide
(YBCO); 1987, Tc~90K,….
1993 Tc~135K still a record
2008 Tc~55K, Fe-based superconductors
10 Nobel prizes were given for studies of SC ;The last one in 2003 to theorists:
Alexei Abrikosov, Vitaly Ginzburg, Anthony J. Legget
Levitation
Applications: electromagnets,
motors, generators, transformers, etc.
Open problems:
1.
2.
3.
Mechanism of HTS? Why it’s possible?
How to sustain large current (high
magnetic field)
Fragility of the materials
VitalyGinzburg,
1916-2009
Resistors in series
Vab Vax  Vxy  Vyb
Req  
 R1  R2  R3
I
I
Resistors in parallel
I1
I2
I3
I1  I 2  I 3 1 1 1
1
I


  
Req Vab
Vab
R1 R2 R3
NB:
Opposite to capacitors!
C=Q/V
R=V/I
Example1.
Example 2
Electric Power
dWab
Pin 
; dWab  Vab dq  Pin  Vab I
dt
If Vab  0 and I flows from a to b Pin  0
IfVab  0 but I flows from b to a Pin  0 
Vab  0
a
b
I
In resistor:
Pout   Pin  0
Pin  Vab I  0 always!
2
V
V  IR  Pin  I 2 R 
R
U  Pt , 1kWhr  3.6  10 6 J
Alternative current (ac current)
V (t )  V0 cos t
V0
I  cos t  I 0 cos t
R
2
2
I
2
2
0 R
P (t )  I 0 R cos t 
 I rms R
2
2
I0
2
I rms  I (t )  I 0 cos t 
2
How to get more light with two bulbs?
Thomas Edison
(1847-1931)
1882
?
or
Bulb B
How to get more light with two bulbs?
P  I  I R 
2
P

Req

less light!
R
Bulb B
Req  2 R
2

2

2
2R
Req  R / 2
2
2 2
P


Req R / 2
R
more light!
2
emf, battery
Closed loop
R0
loss of energy→
need a source of
emf (ε), a battery
ε
a
+
b
emf (ε) is a work
per unite charge
by external
(nonelectric force).
Ideal case
(neglecting losses
in the battery):   Vab
Pout  Vab I
I
Terminal voltage and power output of the battery
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:
a
r
ε
b
Vab    Ir
Pout  Vab I
Pout  I  I r
2
Terminal voltage and power input into the battery
a
b
If the current through the battery is
from + to - then the terminal voltage
is larger then emf:
Vab    Ir
Pout  Vab I
Pout  I  I r
2
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.
IV=0
I
I
Simple resistors circuits
1.Open circuit. What ideal ammeter and voltmeter measure?
ε
r
V
A
I=0 (infinite resistance )
V=ε, P=0
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