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Unformatted text preview: Physics 142 7/27/2011 Midterm 1
Raw
Raw scores out of 50
– Average (mean): ~30
– Median: ~30 Chance
Chance to correct
two problems
Additionally
Additionally some
curve (TBD)
– Avg in low B
range Physics 142 Summer 2011 Midterm Corrections and HW
HWs
HWs 5 & 6 will be due next Tuesday/Wednesday
(MP/written)
Midterm
Midterm corrections will be due Friday
– Correct 2 exam problems
» Print out fresh copy of the page from ELMS
» Answer to the best of your ability (you can ask Anton or me for
help but not others)
» Give short explanation of how your thinking changed between the
exam version and your new answer – turn in in lecture Friday
– For those problems get the average of your old
and new scores
Physics 142 Summer 2011 How to think about current?
Unless
Unless we are going to be materials science
physicists, we don’t really need to understand the
quantum view of conduction.
Instead,
Instead, we construct a bunch analogies
that have some of the correct features.
– water flow
– air flow These
These help us make sense of the fundamental laws
that govern current flow. Physics 142 Summer 2011 Dr. Nick Cummings 1 Physics 142 7/27/2011 The fluid flow model
Key
Key concept: Pressure
Recall:
Recall: 1 2
3 4
– Pressure is like a tension but in 3D.
– It pushes in all directions at once,
so it has no direction.
– Forces due to pressure occur when you
only let it push on one side of an area. Then r
r
F = PA
Physics 142 Summer 2011 Viscous Drag
A fluid flowing in a pipe doesn’t slip through the
fluid
pipe frictionlessly.
The
The fluid sticks to the walls moves faster at the
middle of the pipe than at the edges.
As a result, it has to “slide over itself” (shear).
There
There is friction between layers of fluid moving at
different speeds that creates a viscous drag force,
trying to reduce the sliding.
The
The drag is proportional to the speed and the
length of pipe. Fdrag = 8πµLv Physics 142 Summer 2011 Implication: Pressure drop
If
If we have a fluid moving at a constant rate
and there is drag, N2 tells us there must be
another force to balance the drag.
The
The internal pressure in the fluid must drop
in the direction of the flow to balance drag.
Drag force
Flow in Flow out
Pressure force Pressure force
upstreamPhysics 142 Summer 2011
downstream Dr. Nick Cummings 2 Physics 142 7/27/2011 Waterflow Equations
Matter
Matter is moving:
describe how much J= ∆Volume
∆t J= Av
What
What keeps the mass
moving, even though
there is resistance? ma = Fp − cv
a=0 ⇒ v= Fp
c Physics 142 Summer 2011 Quantifying current
Consider
Consider a wire containing movable current
carriers (electrons).
Define
Define the electric current as rate at which
charge moves past a surface. v
n I= ∆q
∆t A
v ∆t The
The unit of current is the Ampere (= 1C/s)
Physics 142 Summer 2011 How Much Current?
If
If there is a density of electrons n per unit
volume and they are moving with a velocity v,
then how many cross the surface in a time ∆t?
L = v ∆t
Volume LA
Volume = LA
N = n (LA) = nAv ∆t
(LA)
I = qnAv
qnAv v n
A ∆x = v ∆ t
Physics 142 Summer 2011 Dr. Nick Cummings 3 Physics 142 7/27/2011 Charge Flow Equations
∆q
∆t Charge
Charge is moving:
describe how much I= How
How does this relate to
the individual charges? I=qnAv What
What pushes the charges
through resistance? ma = Fe − bv
a=0 ⇒ v= Fe b Physics 142 Summer 2011 Current Density
Another
Another way to express the
flow of charge is
How
How does this relate to
the individual charges? J= I
A J= q n v The
The current density tells us the amount of
current flowing per cross sectional area
Physics 142 Summer 2011 A set of sodium ions (Na+)
are flowing across an area
A at a velocity v. If the
speed of the ions doubles,
the current across A
0% 1.
0% 2.
0% 3.
0% 4.
0% 5. v n
A v ⊗t Doubles
Halves
Stays the same
Changes in some other way
There is not enough information to decide.
Physics 142 Summer 2011 Dr. Nick Cummings 4 Physics 142 7/27/2011 A set of sodium ions (Na+)
are flowing across an area A
at a velocity v. If the area the ions
v
are crossing doubles
(spreading out the same ions),
the current across A
0% 1.
0% 2.
0% 3.
0% 4.
0% 5. n
A Doubles
v ⊗t
Halves
Stays the same
Changes in some other way
There is not enough information to decide.
Physics 142 Summer 2011 Overcoming the drag
Consider
Consider an electron moving in a conductor
with a uniform electric field
To
To push the electrons through the drag
we need a force.
∆V ma = F net
0 = qE − bv
qE = bv d
Physics 142 Summer 2011 Rearrange
Express
Express E in terms of ∆V (easier to measure)
(easier
Express
Express v in terms of I (ditto).
∆V
d
I
I = qnAv ⇒ v =
qnA ∆V = Ed So qE = bv ⇒ ⇒ E= q∆V
bI
=
d
qnA bd ∆V = I 2 ≡ IR q nA Physics 142 Summer 2011 Dr. Nick Cummings 5 Physics 142 7/27/2011 Ohm’s Law
Current
Current proportional to velocity
Due
Due to resistance,
drag force proportional to velocity.
Electric
Electric force proportional to
“electric pressure drop”
= “electric PE”
Therefore,
Therefore, current proportional
to “electric PE” ∆V = IR
Physics 142 Summer 2011 Ohm’s “Law”
This
This is called a “law” for historical reasons
This
This is came from assuming a particular sort
of “drag” on the electrons
– Describes “ohmic resistors’
“ohmic ∆V = IR You
You could have other sorts of drag
– nonOhmic resistors
non Still,
Still, Ohms law is approximately correct for
many situations, so it’s very useful Physics 142 Summer 2011 Fluid vs. Electricity
Fluid:
Fluid: 8πµL ∆P = J 2 A Electricity:
Electricity: Resistance to
flow bd ∆V = IR = I 2 q nA – R is the resistance to the flow of current
– Goes up with d and down with A, like for a
fluid
Physics 142 Summer 2011 Dr. Nick Cummings 6 Physics 142 7/27/2011 Electric circuit elements
Batteries
Batteries —devices that maintain a
constant electrical pressure difference
across their terminals (like a water pump
that raises water to a certain height).
Resistance
Resistance —devices that have
significant drag and oppose current.
Pressure will drop across them.
Wires — have very little resistance.
Wires
We can ignore the drag in them (mostly –
as long as there are other resistances
present). Physics 142 Summer 2011 Analogy: The rope model
Since
Since like charges repel each other so
strongly, there can’t be a buildup of charge
anywhere in the circuit (unless we make a
special arrangement  see capacitance).
So
So moving charges push other movable
charges in front of them. The electrons
move like links in a chain or rope. Physics 142 Summer 2011 Properties of rope analogy
In
In a simple loop, the rope keeps moving around.
A battery is like a person holding the rope and
battery
pulling it, causing a tension throughout the rope.
A resistor is like a person squeezing the rope,
resistor
having it pulled through her hands. The friction
generates heat.
The
The more people are squeezing, the slower the
rope goes, even if the battery pulls with the same
tension.
Physics 142 Summer 2011 Dr. Nick Cummings 7 Physics 142 7/27/2011 Analogy:
Water flow
The
The rope analogy fails because electrons
can go either way at a junction.
A current can split in a way a rope cannot.
Water
Water flow is a useful analogy because
water
– can divide
– is conserved and cannot be compressed (for
practical purposes).
Physics 142 Summer 2011 Water Model
pump and
storage bin
(battery) water wheel
(bulb) sluices
(wires) Physics 142 Summer 2011 The current rule
The
The most useful result that carries over from
the water flow analogy to the flow of electric
current is:
Kirchhoff’s
Kirchhoff’s current rule:
– The total amount of current flowing into any
point in a network equals the amount flowing out
(there is no significant buildup of charge
buildanywhere).
Physics 142 Summer 2011 Dr. Nick Cummings 8 Physics 142 7/27/2011 The Potential Rule
The
The water flow and nail board analogy uses
gravity instead of electric force. It has the
following property:
Gravity
Gravity potential rule:
– Whenever you walk around a loop, however far you
went up is equal to however far you went down.
(You wind up at the same place.) Electric
Electric potential for electric forces is analogous
to height (times g) for gravitational forces.
Kirchhoff’s
Kirchhoff’s potential rule:
– Around any loop the sum of the potential drops = the
sum of the potential rises.
Physics 142 Summer 2011 Kirchoff’s Rules
Flow
Flow Rule
– The total amount of current flowing into any point
in a network equals the amount flowing out
(no significant buildup of charge anywhere).
build Potential
Potential Rule
– Following around any loop in an electrical network
the potential has to come back to the same value
(sum of drops = sum of rises). Ohm’s
Ohm’s Rule
– When a current I passes through a resistance R, there is a
R, there
voltage drop across the resistor of an amount ∆V = IR
Physics 142 Summer 2011 Very useful heuristic
The
The Constant Potential Trick
– Along any part of a circuit with 0 resistance,
then ∆V = 0, i.e., the voltage is constant.
0, Usually
Usually our circuits will have resistors with
big R values and wires with small R that
can be neglected
– Two points attached by a wire can be
considered to have the same potential
Physics 142 Summer 2011 Dr. Nick Cummings 9 Physics 142 7/27/2011 Electric Power Dissipation
We
We can figure out the energy needed
to push the electrons through the material
against the resistance using the WE theorem.
P = rate of doing work (using energy) = ∆W
∆t = (number of charges moved) ×
(force) × (distance moved in a time ∆t ) P= ( nAL)(qE )(v∆t )
∆V
= (nAL)qv
= (nAqv)∆V = I∆V
L
∆t
Physics 142 Summer 2011 Units of power
Since
Since the units of work (energy) is the Joule,
the unit of power is the Joule/second.
– 1 Watt = 1 Joule/second (definition) Our
Our analysis shows that
current x voltage = power.
1 Watt = 1 Ampere x 1 Volt
Watt Physics 142 Summer 2011 US Terminology
Current
Current is sometimes referred to as
“amperage”
In
In the US electrical energy is often
measured in kilowatthours
kilowatt– Energy = (power) x (time) J
1 kw ⋅ hr = 1000 ⋅ 3600 s = 3.6 MJ
s
Physics 142 Summer 2011 Dr. Nick Cummings 10 ...
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This note was uploaded on 10/03/2011 for the course BSCI 410 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
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