Post on 25-Apr-2022
today: dc circuits
2RRI
a c
b
∆V = Vb − Va = −IR
I
a b
I
a b
I
a b
Va = 0 Vb = −IR
Va = +IR Vb = 0
(a)
(b)
(c)
0 20 40 60 80 100 120
52
54
56
58
60
R (!
)
T (K)
resistance of a Cobalt slab versus temperature
why does R go down as we cool it?
(measured in my lab)
Power
• energy is dissipated in a resistor
• why? how?
• how much?
real battery = ideal battery + R
actual circuit has a parasitic r
R in series with output(“steals” V)
real current sources
R in parallel with output(“steals” I)
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
series resistors: conservation of energy
-+
R2
I I
∆V
R1a cbReq
∆V
a c
-+
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
voltage divider
R2
R1Vin Vout
Vout = R2
R1+R2Vin
signal in signal
out
R1
R2
volume
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
parallel resistors: conservation of charge
current divider
I
-+
R1
∆V
R2
a bI1
I2
∆V1=∆V2=∆V
-+
Req
∆V
Req R1 R2
1 11 = +
1 2
3 4
5 6
rank the currents
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
more complex arrangements
measuring voltage
real voltmeters
measuring current
a simple ammeter
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Thévenin equivalents
any weird combinations of R’s and V’sis equivalent
to aSINGLE R and V (or a single I source
in parallel with R)
Vth = V (open circuit)
Rth = V (open circuit)
I (closed circuit)
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
so what?
V
R
real sources = ideal sources + R
real meter = ideal meter with R
VI R
what about ammeter?
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
V source loading
V
r
source
like a battery
Rload
∆Vload = V - Ir
for r ≪ Rload,
∆Vload ≈ V
V source wants R high
one easy solution:large resistor in parallel with load
I
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Ip
I source loading
source
Rload
I source wants R lowsourcing currents at high Rload is hard
Ir
Iload
Iload = Ir
r+R
for Rload ≪ r,
Iload ≈ I
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
measuring the meter
Rload
I
Vr
realmeter
Req
I
V
idealmeter
∆Vload = IReq = R1+R/r I Rload ≪ r, ∆Vload ≈ IR
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
summary
voltmeter wants R low!can use a buffer/follower
I source wants R lowtransformer pre-ampconsider sourcing V
V source wants R highlarge series + parallel resistorspresent large R
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Sourcing current
Rwires
Rwires
RthingI V
This is what a hand meter does.
Why is it no good?
Vmeter = I(Rthing + 2Rwires)
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Sourcing current, properly
No problem.You just need four wires.
Rwires
Rwires
RthingI V
Rthing ≪ Rinternal
or add buffer
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Sourcing voltage
Rwires
Rwires
RthingVs
Still have to measure voltage on device the wires still use up some of VWhat about current?
V
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Sourcing voltage II
R = ∆V / I
Note we need 4 wires againcurrent meter - not hardstill problems?
Rwires
Rwires
Rthing
Vs
V
ΙΙ=
Rprecise
V
RparRs
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Sourcing voltage properly
R = ∆V / I
Note we need 4 wires againcurrent meter - not hardstill problems?
Rwires
Rwires
Rthing
Vs
V
ΙΙ=
Rprecise
V
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
source/meter resistances
voltmeter wants R lowbut V source wants R high
need buffer/amp on V meter resistor in parallel with source
if V source is problem, R is too lowconsider sourcing I
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
what if I want to measure a *really* high R?
Rwires
Rwires
Rthing
Vs V
Ι=
Rs ≪ Rthing
Rp
Ι
=
V
source voltageRp has same voltage as Rthing
Rs has same current
have done >1010 Ohm
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
what if I want to measure a *really* low R?
Rwires
Rwires
RthingI V
this works just fine ...so long as your V meter is goodv. good amp / part of a bridge
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
what if I want to measure a small change in R?
V
R1 R3
R2 Rx+dR
Vs
balance bridge to V=0detect small changes from null
make R1-R3 about the sametrimming resistor on R2 = dR
R2 =
≈ R3
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Rules for analyzingmore complicated
circuits
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
+
+
+
THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center