Transcript current - The University of Alabama

The Plan
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dielectrics, quickly
current & resistance
HW3 hints after the break (& in lab)
time permitting, some of dc circuits
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Exam 1
Right here, 3pm Thursday
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electric forces & fields
electrical potential & energy
current & resistance
NO RELATIVITY
study quick quizzes, example probs
our HW and quizzes
problems in notes
relax.
it will be ok.
not so funny now.
battery = pump
voltage = pressure
current = flow
resistor = constriction
capacitor = diaphragm / flexible reservoir
diode = check valve
inductor = paddle wheel
with the time left ...
let’s get a jump on dc circuits
real battery = ideal battery + R
actual circuit has a parasitic r
real current sources
series resistors: conservation of
energy
a
R1
b
R2
c
a
Req
c
I
I
+ ∆V
THE UNIVERSITY OF ALABAMA
+ ∆V
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
voltage divider
Vin
R1
Vout
R2
signal
in
R1
volume
R2
signal
out
R2
Vout =
Vin
R1+R2
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
parallel resistors: conservation of
charge
∆V1=∆V2=∆V
I1 a
I
1 = 1 1
+
Req R1 R2
Req
R2
R1
b
I2
+ ∆V
+ ∆V
current divider
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
more complex arrangements
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
measuring voltage
real voltmeters
measuring current
a simple ammeter
Thévenin equivalents
Vth = V (open circuit)
Rth =
any weird combinations of R’s and V’s
is equivalent
to a
SINGLE R and V
THE UNIVERSITY OF ALABAMA
V (open circuit)
I (closed circuit)
(or a single I source
in parallel with R)
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
so what?
E
I
R
V
R
real sources =
ideal sources + R
THE UNIVERSITY OF ALABAMA
real meter =
ideal meter with R
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
V source loading
∆Vload = V - Ir
V
Rload
for r ≪ Rload,
∆Vload ≈ V
r
source
like a battery
I
V source wants R high
one easy solution:
large resistor in parallel with load
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
I source loading
r
Iload = I r+R
r
Ip
I
Rload
for Rload ≪ r,
Iload ≈ I
Iload
source
I source wants R low
sourcing currents at high Rload is hard
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
measuring the meter
I
Rload
I
r
V
real
meter
∆Vload =
R
IReq = 1+R/r I
THE UNIVERSITY OF ALABAMA
Req
V
ideal
meter
Rload ≪ r, ∆Vload ≈ IR
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
summary
voltmeter wants R low!
can use a buffer/follower
I source wants R low
transformer pre-amp
consider sourcing V
V source wants R high
large series + parallel resistors
present large R
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
Sourcing current
This is what a hand meter does.
Why is it no good?
Rwires
I
V
Rthing
Rwires
THE UNIVERSITY OF ALABAMA
Vmeter = I(Rthing + 2Rwires)
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
Sourcing current, properly
Rwire
I
s
Rthin
V
g
Rwires
Rthing ≪ Rinternal
or add buffer
No problem.
You just need four wires.
What is still wrong?
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
Sourcing voltage
Rwires
Rthing
Vs
V
Rwires
Still have to measure voltage on device
the wires still use up some of V
What about current?
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
Sourcing voltage II
Rwires
Vs
Rs
Rthing
Rpar
Ι
Rwires
R = ∆V / I
V
Ι
=
Rprecise
Note we need 4 wires again
current meter - not hard
still problems?
THE UNIVERSITY OF ALABAMA
V
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
source/meter resistances
voltmeter wants R low
but V source wants R high
need buffer/amp on V meter
resistor in parallel with source
if V source is problem, R is too low
consider sourcing I
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
what if I want to measure a *really* high
R?
Vs
Ι
Rwires
Rthing
V
Rp
Rwires
source voltage
Rp has same voltage as Rthing
Rs has same current
have done >1010 Ohm
THE UNIVERSITY OF ALABAMA
Ι
=
Rs ≪ Rthing
V
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
what if I want to measure a *really* low
R?
Rwire
I
s
Rthin
V
g
Rwires
this works just fine ...
so long as your V meter is good
v. good amp / part of a bridge
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
what if I want to measure a small change
in R?
R1
R3
V
Vs
R2
THE UNIVERSITY OF ALABAMA
balance bridge to V=0
detect small changes from
null
R2 =
Rx+dR
R3same
make R1-R3 about≈the
trimming resistor on R2 = dR
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center
THE UNIVERSITY OF ALABAMA
CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY
An NSF Science and Engineering Center