physics 202, lecture 9 · physics 202, lecture 9 current and resistance (ch 25) dc currents ohm’s...
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Physics 202, Lecture 9
Current and Resistance (Ch 25) DC currents Ohm’s Law: Resistors and Resistance Conductivity and Resistivity
Next lecture: DC circuits
Reminder: HW #4 due tomorrow, 11 PM
Charge Motion in a Conductor
Electrons in a conductor have random motion (vave=0)
In an external electric field (e.g. as supplied by a source ofpotential difference such as a battery),electrons accelerate, produces current:
I =dQ
dt
I =!Q
!t
Average current:
Instantaneous current:
Text: 25.1direct current (DC): I constant
2
++++ +
+++
Q Q
Current: Macroscopic View
Current: rate at which chargeflows through surface:
Unit:1 Ampere = 1 C/s Current is directional: Follows positive charge (convention)+q moving in +x direction –q in moving –x direction
Charge conservation Current conservation
A
++
+ +
++
+
+
+
I
Iin IoutIin = Iout
v
Current: Microscopic ViewCurrent: motion of charged particles
Current density:(vector!)
IAnqvt
QI daverage ==
!
!=
vd: average drift velocity
n: number density
!J id!A! = I
I
J =I
A= nqvd
3
Drift velocity of conduction electrons
acceleration a=qE/mvelocity v = vo + qEt / m
Lots of particles: averageover all particle velocitiesvave = (vo)ave + qEtave / m = qEτ / m
vd= Drift velocity= qEτ / m
vo= velocity after last collisiont = time since last collision
x
x
x
x
xx
τ=ave. time since last collision
In external electric field:
Ohm’s Law: ResistanceI = current = nqvdAvd= Drift velocity= qEτ / m
�
I = nqqE!m
"
# $
%
& ' A =
nq2!m
A
L
"
# $
%
& ' V (V = IR
Voltage proportional to current! This is Ohm’s law.
�
R =nq
2!m
A
L
"
# $
%
& '
(1
!J = nq
!vd =
nq2!m
"#$
%&'!E = (
!E =
1
)
!E
conductivity
resistivity
Text: 25.6
4
Conductivity, Resistivity, Resistance Ohm’s Law (microscopic): J=σE
Ohm’s Law (macroscopic): ΔV=IR
Resistance R (unit: Ohm Ω = Volt/Ampere)Exercise: relate R to ρ
AR
!!=
Resistivity (intrinsic)
Length &Cross-section
(shape) Resistance
ResistorsResistorsResistivity For Various Materials
AR
!!=
Text: 25.11, 25.14
5
Ohmic and non-Ohmic Materials
non-Ohmic:
Nonlinear I-V relationship
Ohmic:
Linear I-V relationship
(constant resistance over wide range of voltages)
Resistance And TemperatureResistivity is usually temperature dependent.
Normal Metal
Semiconductor
ρ
T
Superconductor
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SuperconductivitySuperconductors: temperature T<TC, resistivity ρ=0
(a quantum phenomenon!)
Electrical Power
Electrical Power:
Ohmic:
P =dU
dt=d(Q!V )
dt= I!V
P = I2R =
(!V )2
R
ΔV
I IR
+ -ΔV
Text example: 25.35(power delivered to resistor)
Unit: watts (W)energy unit: kWh
1 KWH = 3.6 MJ
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Example: Battery Connected To A Resistor
Energy flow of this battery-resistor set-up
+
-
1.5V
-------
+++++
Res
isto
r
R
e-
I
Chemical Process ΔV =1.5VΔV on Resistor Current I= ΔV/R
Charge flow through the resistor in Δt:Q=IΔt = ΔV/RΔt
Electrical potential energy released:U=QΔV = ΔV/RΔt ΔV = (ΔV)2/RΔt
Power: P=U/dt = (ΔV)2/R
Energy Flow: Chemical Electrical U KE thermal/light
e-
motion due to chemical process
motion due to E. field collisions
-----
++++
e-
Quiz: Consumption of Electric Power On Resistors
A voltage is applied to a wire of length L . If L increases,does power consumed increase or decrease?
IncreasesDecreasesSame
Ni
ΔV
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Quiz: Consumption of Electric Power On Resistors
When a current passes through serially connected wiresegments made of copper and nichrome, whichmetal: copper or nichrome, consumes more energy?
(ρCu ~ 10-8 Ωm, ρNi ~ 10-6 Ωm, All segments have about the samelength and diameter.)
CopperNichromeSame
Cu Ni Cu NiI
Resistors in Circuits
• Resistors:
Purpose is to limit thecurrent in a circuit.
Next lecture: DC circuits with resistors, capacitors
ΔV
I IR
+ -ΔVBasic rule: voltage “drops”
as current flows through resistor
But first: a preview of resistors in series, parallel
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Resistors in Series: Preview
a
c
Reffective
a
b
c
R1
R2
I
Intuitively: voltage “drops”
Hence: Reffective = (R1 + R2 )
Va!V
b= IR
1
Vb!V
c= IR
2
Va!V
c= I(R
1+ R
2)
Current same in both!
Another (intuitive) way…
Consider two cylindrical resistors with lengths L1 and L2 :
V
R1
R2
L2
L1
Put them together, end to end to make a longer one...
R1= !
L1
A
R2= !
L2
A
Reffective = !L1+ L
2
A= R
1+ R
2R = R
1+ R
2
What about parallel?