Download Physics 209, Lecture 9 Charge Motion in a Conductor Current

Motion Of Charged Particle
In The Electric Field
Physics 209, Lecture 9
„
Charge Motion in a Conductor
‰ Without electric field:
ƒ electrons move randomly (thermal motion) |vav|=0, |v|av >0
‰ With electric field applied:
ƒ electron motion = thermal + drift (directional): |vav|= vdrift>0, |v|av >0
ƒ i.e. a net charge ΔQ is moving directionally
Motion of - q:
Opposite dir.
dir as E
From low V to high V
+q
-q
E
+
Current: Macroscopic View
+
‰ Definition: I=dQ/dt
Q
A
+
‰ Unit:1 Ampere = 1 Coulomb/1 sec
+
‰ Current is directional: Follows positive charge
¾ Equivalence Principle:
+q moving in +x direction ÅÆ –q in moving –x direction
¾ The following pictures represent the same current
+
E
Motion of +q:
Same dir. as E
From high V to low V
lower V
Current And Resistance (Ch. 27)
„ Motion of Charged Particle In Electric Field (review)
„ Current: Macroscopic and Microscopic Views
„ Resistance: Macroscopic and Microscopic Views
„ Electrical Power
™ Expected from Preview:
Current, current density, drift velocity, Ohm, Ampere, power, …
If initially at rest
‰ Fundamental Formulas:
ƒ F=qE
ƒ a=F/m = qE/m
ƒ v= vi +at Æ if vi =0, then v= at
‰ A Picture to remember
higher potential V
Today’s Topics
+
+
+
v
+
+
+
+
Q
+
+
+
+
+
I
ΔQ, I
ΔQ
¾ Average current: I =
Δt
¾ Instantaneous current :
i=
‰ Charge conservation Æ Current conservation
dQ
dt
“direct current (DC)”
I = constant
Iin
Iout
Iin = Iout
1
Current: Microscopic View
Ohm’s Law: Resistance
‰ It can be shown experimentally and theoretically that for many
material, the electric current is proportional to ΔV
‰ Current Å motion of charged particles
I ∝V
vd: average
drift velocity
y
‰ For a fixed material and geometry
n: number density
‰ Show that:
I average =
‰ Current density J=I/A = nqvd
note: vd ∝ E (why?)
(vector)
Conductivity And Resistance
R=ρ
l
A
Î
V
or V = RI
R
R: resistance
Resistors
Resistivity For Various Materials
‰ Ohm’s Law (microscopic): J=σE
ƒ σ is called conductivity
ƒ also: ρ=1/σ is called resistivity
‰ Ohm’s Law (macroscopic): ΔV=RI
‰ R: Resistance. (unit: Ohm Ω = Volt/Amper)
‰ Exercise: relate R to ρ
Resistance
I=
ΔQ
= nqvd A = I
Δt
R=ρ
Resistors
l
A
Length &
Cross-section
(shape)
Resistivity
(intrinsic)
2
Resistance And Temperature
Ohmic and non-Ohmic Materials
‰ Resistivity is usually temperature dependent.
‰ Ohmic:
Linear I-V relationship
ρ
‰ non-Ohmic:
Non-linear I-V
T
Semiconductor
Superconductor
Normal Metal
(See demo)
For the rest of the course, we assume ohmic for all materials
Superconductivity
‰ Superconductors: temperature T<TC, resistivity ρ=0
ƒ Super conductivity is a quantum phenomenon.
ƒ Super conductors have special electric and magnetic features
Electrical Power
‰ Electric Power:
P=
dU d (QΔV )
=
= I ΔV
dt
dt
‰ For resistors (ohmic):
P = I ΔV = I 2 R =
(ΔV ) 2
R
Power unit: watts (W=J/s)
Energy unit: kWH
1 kWH = 3.6 MJ
3
Example: Battery Connected To A Resistor
‰ Show the energy flow of this battery-resistor set-up
e-
¾Chemical Process Æ ΔV =1.5V
¾ΔV on Resistor Æ Current I= ΔV/R
I
+
+++++
R
Res
sistor
1.5V
V
++++
Charge flow through the resistor in Δt:
Q=IΔt = ΔV/RΔt
Demo/ Quiz 1:
Consumption of Electric Power On Resistors
‰ A voltage is applied to a wire of length L . When L increases,
Does power consumed increase or decrease?
1. Increases
Î 2. Decreases
3. Same
-----
e-
e-
-------
motion due to
motion due to
E. field
chemical process
Electrical potential energy released:
U=QΔV = ΔV/RΔt ΔV = (ΔV)2/RΔt
Power: P=U/dt = (ΔV)2/R
ΔV
collisions
Ni
Energy Flow: Chemical Æ Electrical U Æ KE Æthermal/light
Demo/ Quiz 2:
Consumption of Electric Power On Resistors
Î
‰ When a current passes through serially connected wire
segments made of copper and nichrome, which metal: copper
or nichrome, consume more energy?
(ρCu ~ 10-8 Ωm, ρNi ~ 10-6 Ωm, All segments have about the same
length and diameter.)
1. Copper
2. Nichrome
3. Same
I
Cu
Ni
Cu
Ni
4